m1une's library

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:heavy_check_mark: verify/string/string_algorithms.test.cpp

Depends on

Code

#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"

#include "../../string/all.hpp"

#include <algorithm>
#include <cassert>
#include <cstdint>
#include "../../utilities/fast_io.hpp"
#include <numeric>
#include <string>
#include <vector>

namespace {

void test_edge_cases() {
    std::string empty;
    assert(m1une::string::z_algorithm(empty).empty());
    assert(m1une::string::prefix_function(empty).empty());
    assert(m1une::string::suffix_array(empty).empty());
    assert(m1une::string::lcp_array(empty, std::vector<int>()).empty());
    assert(m1une::string::lyndon_factor_boundaries(empty) == std::vector<int>(1, 0));
    assert(m1une::string::lyndon_factorization(empty).empty());
    assert(m1une::string::minimum_cyclic_shift(empty) == 0);

    auto empty_palindromes = m1une::string::manacher(empty);
    assert(empty_palindromes.empty());
    assert(empty_palindromes.longest_length() == 0);
    assert(empty_palindromes.is_palindrome(0, 0));

    std::string text = "aaaa";
    assert(
        m1une::string::kmp_search(text, std::string("aa")) ==
        std::vector<int>({0, 1, 2})
    );
    assert(
        m1une::string::kmp_search(text, empty) ==
        std::vector<int>({0, 1, 2, 3, 4})
    );

    std::vector<int> values;
    values.push_back(2);
    values.push_back(-1);
    values.push_back(2);
    assert(
        m1une::string::suffix_array(values) ==
        std::vector<int>({1, 2, 0})
    );
    assert(
        m1une::string::z_algorithm(values) ==
        std::vector<int>({3, 0, 1})
    );
    assert(
        m1une::string::lyndon_factor_boundaries(values) ==
        std::vector<int>({0, 1, 3})
    );
    assert(m1une::string::minimum_cyclic_shift(values) == 1);

    std::string bytes;
    bytes.push_back(char(255));
    bytes.push_back(char(0));
    bytes.push_back(char(128));
    assert(
        m1une::string::suffix_array(bytes) ==
        std::vector<int>({1, 2, 0})
    );
}

void test_randomized() {
    std::uint64_t state = 31;
    auto random = [&state]() {
        state ^= state << 7;
        state ^= state >> 9;
        return state;
    };

    for (int trial = 0; trial < 1500; trial++) {
        int n = int(random() % 45);
        std::string text(n, 'a');
        for (char& character : text) character = char('a' + random() % 4);

        std::vector<int> z = m1une::string::z_algorithm(text);
        for (int i = 0; i < n; i++) {
            [[maybe_unused]] int expected = 0;
            while (
                i + expected < n &&
                text[expected] == text[i + expected]
            ) {
                expected++;
            }
            assert(z[i] == expected);
        }

        std::vector<int> prefix = m1une::string::prefix_function(text);
        for (int i = 0; i < n; i++) {
            [[maybe_unused]] int expected = 0;
            for (int length = 1; length <= i; length++) {
                if (
                    text.substr(0, length) ==
                    text.substr(i - length + 1, length)
                ) {
                    expected = length;
                }
            }
            assert(prefix[i] == expected);
        }

        int pattern_length = int(random() % 12);
        std::string pattern(pattern_length, 'a');
        for (char& character : pattern) character = char('a' + random() % 4);
        std::vector<int> expected_occurrences;
        for (int i = 0; i + pattern_length <= n; i++) {
            if (text.substr(i, pattern_length) == pattern) {
                expected_occurrences.push_back(i);
            }
        }
        assert(
            m1une::string::kmp_search(text, pattern) ==
            expected_occurrences
        );

        m1une::string::ManacherResult palindromes =
            m1une::string::manacher(text);
        int longest = 0;
        for (int left = 0; left <= n; left++) {
            for (int right = left; right <= n; right++) {
                bool expected = true;
                for (int offset = 0; offset < (right - left) / 2; offset++) {
                    if (text[left + offset] != text[right - 1 - offset]) {
                        expected = false;
                        break;
                    }
                }
                assert(palindromes.is_palindrome(left, right) == expected);
                if (expected) longest = std::max(longest, right - left);
            }
        }
        assert(palindromes.longest_length() == longest);

        std::vector<int> suffixes = m1une::string::suffix_array(text);
        std::vector<int> expected_suffixes(n);
        std::iota(expected_suffixes.begin(), expected_suffixes.end(), 0);
        std::sort(
            expected_suffixes.begin(),
            expected_suffixes.end(),
            [&text](int a, int b) {
                return text.substr(a) < text.substr(b);
            }
        );
        assert(suffixes == expected_suffixes);

        std::vector<int> lcp = m1une::string::lcp_array(text, suffixes);
        for (int i = 0; i + 1 < n; i++) {
            int expected = 0;
            while (
                suffixes[i] + expected < n &&
                suffixes[i + 1] + expected < n &&
                text[suffixes[i] + expected] ==
                    text[suffixes[i + 1] + expected]
            ) {
                expected++;
            }
            assert(lcp[i] == expected);
        }

        std::vector<std::pair<int, int>> lyndon_factors =
            m1une::string::lyndon_factorization(text);
        int minimum_shift = m1une::string::minimum_cyclic_shift(text);
        assert(
            (n == 0 && minimum_shift == 0) ||
            (0 <= minimum_shift && minimum_shift < n)
        );
        std::string restored;
        std::vector<std::string> factor_words;
        for (auto [left, right] : lyndon_factors) {
            assert(0 <= left && left < right && right <= n);
            std::string word = text.substr(left, right - left);
            restored += word;
            factor_words.push_back(word);
        }
        assert(restored == text);
        for (int i = 0; i + 1 < int(factor_words.size()); i++) {
            assert(!(factor_words[i] < factor_words[i + 1]));
        }
    }
}

}  // namespace

int main() {
    m1une::utilities::FastInput fast_input;
    m1une::utilities::FastOutput fast_output;

    test_edge_cases();
    test_randomized();

    long long a, b;
    fast_input >> a >> b;
    fast_output << a + b << '\n';
}
#line 1 "verify/string/string_algorithms.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"

#line 1 "string/all.hpp"



#line 1 "string/aho_corasick.hpp"



#include <array>
#include <cassert>
#include <cstddef>
#include <limits>
#include <queue>
#include <vector>

namespace m1une {
namespace string {

// Aho-Corasick automaton for a contiguous character alphabet.
template <int AlphabetSize = 26, int FirstCharacter = 'a'>
struct AhoCorasick {
    static_assert(0 < AlphabetSize);

    using node_id = int;
    static constexpr node_id null_node = -1;

    struct Node {
        // Completed automaton transitions. Valid after build().
        std::array<node_id, AlphabetSize> next;
        node_id failure;
        node_id output_link;
        node_id parent;
        int parent_symbol;
        int depth;
        std::vector<node_id> children;
        std::vector<node_id> failure_children;
        std::vector<int> pattern_ids;

        Node(
            node_id parent_value = null_node,
            int parent_symbol_value = -1,
            int depth_value = 0
        ) : failure(0),
            output_link(null_node),
            parent(parent_value),
            parent_symbol(parent_symbol_value),
            depth(depth_value) {
            next.fill(null_node);
        }
    };

   private:
    std::vector<Node> _nodes;
    std::vector<int> _pattern_length;
    std::vector<node_id> _pattern_node;
    std::vector<node_id> _bfs_order;
    bool _built;

    template <class Symbol>
    static int symbol_index(const Symbol& symbol) {
        int index = int(symbol) - FirstCharacter;
        assert(0 <= index && index < AlphabetSize);
        return index;
    }

    node_id new_node(node_id parent, int parent_symbol) {
        assert(_nodes.size() < std::size_t(std::numeric_limits<int>::max()));
        assert(_nodes[parent].depth < std::numeric_limits<int>::max());
        _nodes.emplace_back(parent, parent_symbol, _nodes[parent].depth + 1);
        return int(_nodes.size()) - 1;
    }

   public:
    AhoCorasick() : _nodes(1), _built(false) {}

    node_id root() const {
        return 0;
    }

    bool built() const {
        return _built;
    }

    int pattern_count() const {
        return int(_pattern_length.size());
    }

    int pattern_length(int pattern_id) const {
        assert(0 <= pattern_id && pattern_id < pattern_count());
        return _pattern_length[pattern_id];
    }

    node_id pattern_node(int pattern_id) const {
        assert(0 <= pattern_id && pattern_id < pattern_count());
        return _pattern_node[pattern_id];
    }

    std::size_t node_count() const {
        return _nodes.size();
    }

    const std::vector<Node>& nodes() const {
        return _nodes;
    }

    const Node& node(node_id id) const {
        assert(0 <= id && std::size_t(id) < _nodes.size());
        return _nodes[id];
    }

    // Returns nodes in failure-link BFS order, beginning with the root.
    const std::vector<node_id>& bfs_order() const {
        assert(_built);
        return _bfs_order;
    }

    void reserve(std::size_t node_capacity) {
        assert(!_built);
        _nodes.reserve(node_capacity);
    }

    void clear() {
        _nodes.clear();
        _nodes.emplace_back();
        _pattern_length.clear();
        _pattern_node.clear();
        _bfs_order.clear();
        _built = false;
    }

    // Inserts a pattern and returns its insertion-order ID.
    template <class Sequence>
    int insert(const Sequence& pattern) {
        assert(!_built);
        int pattern_id = pattern_count();
        int length = 0;
        node_id state = root();
        for (const auto& symbol : pattern) {
            assert(length < std::numeric_limits<int>::max());
            int index = symbol_index(symbol);
            if (_nodes[state].next[index] == null_node) {
                node_id child = new_node(state, index);
                _nodes[state].next[index] = child;
                _nodes[state].children.push_back(child);
            }
            state = _nodes[state].next[index];
            length++;
        }
        _nodes[state].pattern_ids.push_back(pattern_id);
        _pattern_length.push_back(length);
        _pattern_node.push_back(state);
        return pattern_id;
    }

    // Builds failure links and completes every automaton transition.
    void build() {
        assert(!_built);
        std::queue<node_id> queue;
        _bfs_order.clear();
        _bfs_order.reserve(_nodes.size());
        _bfs_order.push_back(root());

        for (int symbol = 0; symbol < AlphabetSize; ++symbol) {
            node_id child = _nodes[root()].next[symbol];
            if (child == null_node) {
                _nodes[root()].next[symbol] = root();
            } else {
                _nodes[root()].next[symbol] = child;
                _nodes[child].failure = root();
                _nodes[child].output_link =
                    _nodes[root()].pattern_ids.empty() ? null_node : root();
                _nodes[root()].failure_children.push_back(child);
                queue.push(child);
            }
        }

        while (!queue.empty()) {
            node_id state = queue.front();
            queue.pop();
            _bfs_order.push_back(state);

            for (int symbol = 0; symbol < AlphabetSize; ++symbol) {
                node_id child = _nodes[state].next[symbol];
                if (child == null_node) {
                    _nodes[state].next[symbol] =
                        _nodes[_nodes[state].failure].next[symbol];
                    continue;
                }

                _nodes[state].next[symbol] = child;
                node_id failure =
                    _nodes[_nodes[state].failure].next[symbol];
                _nodes[child].failure = failure;
                _nodes[child].output_link =
                    _nodes[failure].pattern_ids.empty()
                        ? _nodes[failure].output_link
                        : failure;
                _nodes[failure].failure_children.push_back(child);
                queue.push(child);
            }
        }
        _built = true;
    }

    template <class Symbol>
    node_id transition(node_id state, const Symbol& symbol) const {
        assert(_built);
        assert(0 <= state && std::size_t(state) < _nodes.size());
        return _nodes[state].next[symbol_index(symbol)];
    }

    // Calls callback(pattern_id) for every pattern ending at `state`.
    template <class Callback>
    void for_each_output(node_id state, Callback callback) const {
        assert(_built);
        assert(0 <= state && std::size_t(state) < _nodes.size());
        while (state != null_node) {
            for (int pattern_id : _nodes[state].pattern_ids) {
                callback(pattern_id);
            }
            state = _nodes[state].output_link;
        }
    }

    // Calls callback(end, pattern_id) for every occurrence. `end` is the
    // exclusive end position. Empty patterns occur at every text boundary.
    template <class Sequence, class Callback>
    void match(const Sequence& text, Callback callback) const {
        assert(_built);
        node_id state = root();
        for_each_output(state, [&callback](int pattern_id) {
            callback(0, pattern_id);
        });

        int end = 0;
        for (const auto& symbol : text) {
            state = transition(state, symbol);
            end++;
            for_each_output(state, [&callback, end](int pattern_id) {
                callback(end, pattern_id);
            });
        }
    }

    // Counts occurrences of every inserted pattern in linear time.
    template <class Sequence>
    std::vector<long long> count_occurrences(const Sequence& text) const {
        assert(_built);
        std::vector<long long> visits(_nodes.size(), 0);
        node_id state = root();
        visits[root()]++;
        for (const auto& symbol : text) {
            state = transition(state, symbol);
            visits[state]++;
        }

        for (std::size_t index = _bfs_order.size(); index-- > 1;) {
            node_id current = _bfs_order[index];
            visits[_nodes[current].failure] += visits[current];
        }

        std::vector<long long> result(pattern_count(), 0);
        for (node_id current : _bfs_order) {
            for (int pattern_id : _nodes[current].pattern_ids) {
                result[pattern_id] = visits[current];
            }
        }
        return result;
    }
};

}  // namespace string
}  // namespace m1une


#line 1 "string/deque_eertree.hpp"



#line 7 "string/deque_eertree.hpp"
#include <deque>
#line 10 "string/deque_eertree.hpp"

namespace m1une {
namespace string {

template <int AlphabetSize = 26, int FirstCharacter = 'a'>
struct DequeEertree {
    static_assert(0 < AlphabetSize);

    using node_id = int;
    static constexpr node_id odd_root = 0;
    static constexpr node_id even_root = 1;
    static constexpr node_id null_node = -1;

   private:
    struct Node {
        std::array<node_id, AlphabetSize> next;
        node_id parent;
        node_id suffix_link;
        node_id quick_link;
        int length;
        int surface_count;
        int suffix_link_children;
        bool active;

        Node(
            int length_value = 0,
            node_id parent_value = null_node,
            node_id suffix_link_value = null_node,
            node_id quick_link_value = null_node
        )
            : parent(parent_value),
              suffix_link(suffix_link_value),
              quick_link(quick_link_value),
              length(length_value),
              surface_count(0),
              suffix_link_children(0),
              active(true) {
            next.fill(null_node);
        }
    };

    struct Position {
        int symbol;
        node_id prefix_surface;
        node_id suffix_surface;
    };

    std::vector<Node> _nodes;
    std::deque<Position> _text;
    int _distinct_palindromes;

    template <class Symbol>
    static int symbol_index(const Symbol& value) {
        int symbol = int(value) - FirstCharacter;
        assert(0 <= symbol && symbol < AlphabetSize);
        return symbol;
    }

    node_id new_node(node_id parent, node_id suffix_link, int length, int symbol) {
        assert(_nodes.size() < std::size_t(std::numeric_limits<int>::max()));
        node_id id = int(_nodes.size());
        _nodes.emplace_back(length, parent, suffix_link, odd_root);
        _nodes[parent].next[symbol] = id;
        _nodes[suffix_link].suffix_link_children++;
        _distinct_palindromes++;
        return id;
    }

    void remove_node(node_id id, int symbol) {
        Node& removed = _nodes[id];
        assert(removed.active);
        assert(removed.surface_count == 0);
        assert(removed.suffix_link_children == 0);
        assert(_nodes[removed.parent].next[symbol] == id);
        _nodes[removed.parent].next[symbol] = null_node;
        _nodes[removed.suffix_link].suffix_link_children--;
        removed.active = false;
        _distinct_palindromes--;
    }

    node_id back_appendable(int symbol, node_id node) const {
        int n = int(_text.size());
        while (true) {
            int length = _nodes[node].length;
            if (length == -1 || (length < n && _text[n - length - 1].symbol == symbol)) {
                return node;
            }
            node_id suffix = _nodes[node].suffix_link;
            int suffix_length = _nodes[suffix].length;
            if (suffix_length == -1 || _text[n - suffix_length - 1].symbol == symbol) {
                return suffix;
            }
            node = _nodes[node].quick_link;
        }
    }

    node_id front_appendable(int symbol, node_id node) const {
        int n = int(_text.size());
        while (true) {
            int length = _nodes[node].length;
            if (length == -1 || (length < n && _text[length].symbol == symbol)) {
                return node;
            }
            node_id suffix = _nodes[node].suffix_link;
            int suffix_length = _nodes[suffix].length;
            if (suffix_length == -1 || _text[suffix_length].symbol == symbol) {
                return suffix;
            }
            node = _nodes[node].quick_link;
        }
    }

    node_id prefix_node() const {
        return _text.empty() ? even_root : _text.front().prefix_surface;
    }

    node_id suffix_node() const {
        return _text.empty() ? even_root : _text.back().suffix_surface;
    }

    void initialize_roots() {
        _nodes.clear();
        _nodes.emplace_back(-1, odd_root, odd_root, odd_root);
        _nodes.emplace_back(0, odd_root, odd_root, odd_root);
        _distinct_palindromes = 0;
    }

   public:
    DequeEertree() {
        initialize_roots();
    }

    template <class Sequence>
    explicit DequeEertree(const Sequence& sequence) {
        initialize_roots();
        build(sequence);
    }

    int size() const {
        return _distinct_palindromes;
    }

    int text_length() const {
        return int(_text.size());
    }

    bool empty() const {
        return _text.empty();
    }

    int distinct_palindrome_count() const {
        return _distinct_palindromes;
    }

    int longest_prefix_length() const {
        return _nodes[prefix_node()].length;
    }

    int longest_suffix_length() const {
        return _nodes[suffix_node()].length;
    }

    void reserve(std::size_t operation_capacity) {
        _nodes.reserve(operation_capacity + 2);
    }

    void clear() {
        _text.clear();
        initialize_roots();
    }

    template <class Symbol>
    void push_back(const Symbol& value) {
        int symbol = symbol_index(value);
        node_id parent = _text.empty() ? odd_root : back_appendable(symbol, suffix_node());
        node_id palindrome = _nodes[parent].next[symbol];
        node_id suffix = even_root;

        if (palindrome == null_node) {
            if (parent != odd_root) {
                node_id suffix_parent = back_appendable(symbol, _nodes[parent].suffix_link);
                suffix = _nodes[suffix_parent].next[symbol];
                assert(suffix != null_node);
            }
        } else {
            suffix = _nodes[palindrome].suffix_link;
        }

        _text.push_back(Position{symbol, even_root, even_root});
        int n = int(_text.size());
        if (palindrome == null_node) {
            palindrome = new_node(parent, suffix, _nodes[parent].length + 2, symbol);

            Node& created = _nodes[palindrome];
            if (
                _nodes[suffix].suffix_link != odd_root &&
                _text[n - _nodes[suffix].length - 1].symbol ==
                    _text[n - _nodes[_nodes[suffix].suffix_link].length - 1].symbol
            ) {
                created.quick_link = _nodes[suffix].quick_link;
            } else {
                created.quick_link = _nodes[suffix].suffix_link;
            }
        }

        int left = n - _nodes[palindrome].length;
        _text.back().suffix_surface = palindrome;
        _text[left].prefix_surface = palindrome;
        if (
            _nodes[suffix].length >= 1 &&
            _text[left + _nodes[suffix].length - 1].suffix_surface == suffix
        ) {
            _text[left + _nodes[suffix].length - 1].suffix_surface = even_root;
        }
        _nodes[palindrome].surface_count++;
    }

    template <class Symbol>
    void push_front(const Symbol& value) {
        int symbol = symbol_index(value);
        node_id parent = _text.empty() ? odd_root : front_appendable(symbol, prefix_node());
        node_id palindrome = _nodes[parent].next[symbol];
        node_id suffix = even_root;

        if (palindrome == null_node) {
            if (parent != odd_root) {
                node_id suffix_parent = front_appendable(symbol, _nodes[parent].suffix_link);
                suffix = _nodes[suffix_parent].next[symbol];
                assert(suffix != null_node);
            }
        } else {
            suffix = _nodes[palindrome].suffix_link;
        }

        _text.push_front(Position{symbol, even_root, even_root});
        if (palindrome == null_node) {
            palindrome = new_node(parent, suffix, _nodes[parent].length + 2, symbol);

            Node& created = _nodes[palindrome];
            if (
                _nodes[suffix].suffix_link != odd_root &&
                _text[_nodes[suffix].length].symbol ==
                    _text[_nodes[_nodes[suffix].suffix_link].length].symbol
            ) {
                created.quick_link = _nodes[suffix].quick_link;
            } else {
                created.quick_link = _nodes[suffix].suffix_link;
            }
        }

        _text.front().prefix_surface = palindrome;
        _text[_nodes[palindrome].length - 1].suffix_surface = palindrome;
        if (
            _nodes[suffix].length >= 1 &&
            _text[_nodes[palindrome].length - _nodes[suffix].length].prefix_surface == suffix
        ) {
            _text[_nodes[palindrome].length - _nodes[suffix].length].prefix_surface = even_root;
        }
        _nodes[palindrome].surface_count++;
    }

    void pop_back() {
        assert(!_text.empty());
        node_id palindrome = suffix_node();
        node_id suffix = _nodes[palindrome].suffix_link;
        int left = text_length() - _nodes[palindrome].length;
        int suffix_end = left + _nodes[suffix].length - 1;

        if (
            _nodes[palindrome].length >= 2 &&
            _nodes[_text[suffix_end].suffix_surface].length < _nodes[suffix].length
        ) {
            _text[suffix_end].suffix_surface = suffix;
            _text[left].prefix_surface = suffix;
        } else {
            _text[left].prefix_surface = even_root;
        }

        _nodes[palindrome].surface_count--;
        int symbol = _text.back().symbol;
        if (
            _nodes[palindrome].surface_count == 0 &&
            _nodes[palindrome].suffix_link_children == 0
        ) {
            remove_node(palindrome, symbol);
        }
        _text.pop_back();
    }

    void pop_front() {
        assert(!_text.empty());
        node_id palindrome = prefix_node();
        node_id suffix = _nodes[palindrome].suffix_link;
        int suffix_start = _nodes[palindrome].length - _nodes[suffix].length;

        if (
            _nodes[palindrome].length >= 2 &&
            _nodes[_text[suffix_start].prefix_surface].length < _nodes[suffix].length
        ) {
            _text[suffix_start].prefix_surface = suffix;
            _text[_nodes[palindrome].length - 1].suffix_surface = suffix;
        } else {
            _text[_nodes[palindrome].length - 1].suffix_surface = even_root;
        }

        _nodes[palindrome].surface_count--;
        int symbol = _text.front().symbol;
        if (
            _nodes[palindrome].surface_count == 0 &&
            _nodes[palindrome].suffix_link_children == 0
        ) {
            remove_node(palindrome, symbol);
        }
        _text.pop_front();
    }

    template <class Sequence>
    void build(const Sequence& sequence) {
        for (const auto& symbol : sequence) push_back(symbol);
    }
};

template <int AlphabetSize = 26, int FirstCharacter = 'a'>
using DoubleEndedEertree = DequeEertree<AlphabetSize, FirstCharacter>;

template <int AlphabetSize = 26, int FirstCharacter = 'a'>
using DequePalindromicTree = DequeEertree<AlphabetSize, FirstCharacter>;

}  // namespace string
}  // namespace m1une


#line 1 "string/eertree.hpp"



#line 8 "string/eertree.hpp"
#include <utility>
#line 10 "string/eertree.hpp"

namespace m1une {
namespace string {

template <int AlphabetSize = 26, int FirstCharacter = 'a'>
struct Eertree {
    static_assert(0 < AlphabetSize);

    using node_id = int;
    static constexpr node_id even_root = 0;
    static constexpr node_id odd_root = 1;
    static constexpr node_id null_node = -1;

    struct Node {
        std::array<node_id, AlphabetSize> next;
        node_id suffix_link;
        node_id series_link;
        int length;
        int diff;
        int suffix_count;
        int first_end;
        long long suffix_occurrences;

        Node(int length_value = 0, node_id suffix_link_value = even_root, node_id series_link_value = even_root)
            : suffix_link(suffix_link_value),
              series_link(series_link_value),
              length(length_value),
              diff(0),
              suffix_count(0),
              first_end(0),
              suffix_occurrences(0) {
            next.fill(null_node);
        }
    };

   private:
    std::vector<Node> _nodes;
    std::vector<int> _text;
    std::vector<node_id> _longest_suffix;
    node_id _last;

    template <class Symbol>
    static int symbol_index(const Symbol& symbol) {
        int index = int(symbol) - FirstCharacter;
        assert(0 <= index && index < AlphabetSize);
        return index;
    }

    node_id find_extendable(node_id node, int position, int symbol) const {
        while (true) {
            int length = _nodes[node].length;
            int left = position - length - 1;
            if (0 <= left && _text[left] == symbol) return node;
            node = _nodes[node].suffix_link;
        }
    }

    node_id new_node(int length) {
        assert(_nodes.size() < std::size_t(std::numeric_limits<int>::max()));
        _nodes.emplace_back(length);
        return int(_nodes.size()) - 1;
    }

   public:
    Eertree() {
        clear();
    }

    template <class Sequence>
    explicit Eertree(const Sequence& sequence) {
        clear();
        build(sequence);
    }

    int size() const {
        return int(_nodes.size()) - 2;
    }

    bool empty() const {
        return size() == 0;
    }

    int node_count() const {
        return int(_nodes.size());
    }

    int text_length() const {
        return int(_text.size());
    }

    node_id last() const {
        return _last;
    }

    int longest_suffix_length() const {
        return _nodes[_last].length;
    }

    const Node& node(node_id id) const {
        assert(0 <= id && id < node_count());
        return _nodes[id];
    }

    const std::vector<Node>& nodes() const {
        return _nodes;
    }

    node_id longest_suffix_node(int prefix_length) const {
        assert(1 <= prefix_length && prefix_length <= text_length());
        return _longest_suffix[prefix_length - 1];
    }

    const std::vector<node_id>& longest_suffix_nodes() const {
        return _longest_suffix;
    }

    template <class Callback>
    void for_each_suffix(node_id id, Callback callback) const {
        assert(0 <= id && id < node_count());
        while (id >= 2) {
            callback(id);
            id = _nodes[id].suffix_link;
        }
    }

    template <class Callback>
    void for_each_suffix(Callback callback) const {
        for_each_suffix(_last, callback);
    }

    void reserve(std::size_t text_capacity) {
        _text.reserve(text_capacity);
        _longest_suffix.reserve(text_capacity);
        _nodes.reserve(text_capacity + 2);
    }

    void clear() {
        _nodes.clear();
        _nodes.emplace_back(0, odd_root, even_root);
        _nodes.emplace_back(-1, odd_root, odd_root);
        _text.clear();
        _longest_suffix.clear();
        _last = even_root;
    }

    template <class Symbol>
    node_id add(const Symbol& value) {
        int symbol = symbol_index(value);
        int position = int(_text.size());
        _text.push_back(symbol);

        node_id current = find_extendable(_last, position, symbol);
        node_id next = _nodes[current].next[symbol];
        if (next == null_node) {
            int length = _nodes[current].length + 2;
            next = new_node(length);
            _nodes[current].next[symbol] = next;

            node_id suffix_link = even_root;
            if (length != 1) {
                node_id candidate = find_extendable(_nodes[current].suffix_link, position, symbol);
                suffix_link = _nodes[candidate].next[symbol];
                assert(suffix_link != null_node);
            }

            Node& created = _nodes[next];
            created.suffix_link = suffix_link;
            created.diff = created.length - _nodes[suffix_link].length;
            created.series_link =
                created.diff == _nodes[suffix_link].diff ? _nodes[suffix_link].series_link : suffix_link;
            created.suffix_count = _nodes[suffix_link].suffix_count + 1;
            created.first_end = position + 1;
        }

        _last = next;
        _nodes[_last].suffix_occurrences++;
        _longest_suffix.push_back(_last);
        return _last;
    }

    template <class Sequence>
    void build(const Sequence& sequence) {
        for (const auto& symbol : sequence) add(symbol);
    }

    std::vector<long long> occurrence_counts() const {
        std::vector<long long> result(_nodes.size(), 0);
        for (node_id id = 0; id < node_count(); id++) {
            result[id] = _nodes[id].suffix_occurrences;
        }
        for (node_id id = node_count() - 1; id >= 2; id--) {
            result[_nodes[id].suffix_link] += result[id];
        }
        return result;
    }

    std::pair<int, int> first_occurrence(node_id id) const {
        assert(2 <= id && id < node_count());
        int end = _nodes[id].first_end;
        return {end - _nodes[id].length, end};
    }
};

template <int AlphabetSize = 26, int FirstCharacter = 'a'>
using PalindromicTree = Eertree<AlphabetSize, FirstCharacter>;

}  // namespace string
}  // namespace m1une


#line 1 "string/kmp.hpp"



#line 5 "string/kmp.hpp"

namespace m1une {
namespace string {

// Returns the KMP prefix function.
template <class Sequence>
std::vector<int> prefix_function(const Sequence& sequence) {
    int n = int(sequence.size());
    std::vector<int> prefix(n);
    for (int i = 1; i < n; i++) {
        int j = prefix[i - 1];
        while (j > 0 && sequence[i] != sequence[j]) {
            j = prefix[j - 1];
        }
        if (sequence[i] == sequence[j]) j++;
        prefix[i] = j;
    }
    return prefix;
}

// Returns every starting position where pattern occurs in text.
// An empty pattern occurs at every position from 0 through text.size().
template <class Text, class Pattern>
std::vector<int> kmp_search(const Text& text, const Pattern& pattern) {
    int n = int(text.size());
    int m = int(pattern.size());
    if (m == 0) {
        std::vector<int> occurrences(n + 1);
        for (int i = 0; i <= n; i++) occurrences[i] = i;
        return occurrences;
    }

    std::vector<int> prefix = prefix_function(pattern);
    std::vector<int> occurrences;
    int matched = 0;
    for (int i = 0; i < n; i++) {
        while (matched > 0 && text[i] != pattern[matched]) {
            matched = prefix[matched - 1];
        }
        if (text[i] == pattern[matched]) matched++;
        if (matched == m) {
            occurrences.push_back(i - m + 1);
            matched = prefix[matched - 1];
        }
    }
    return occurrences;
}

}  // namespace string
}  // namespace m1une


#line 1 "string/levenshtein_distance.hpp"



#include <algorithm>
#line 7 "string/levenshtein_distance.hpp"

namespace m1une {
namespace string {

namespace levenshtein_distance_detail {

template <class RowSequence, class ColumnSequence>
int solve(const RowSequence& rows, const ColumnSequence& columns) {
    int row_count = int(rows.size());
    int column_count = int(columns.size());
    std::vector<int> distance(column_count + 1);
    for (int column = 0; column <= column_count; column++) distance[column] = column;

    for (int row = 1; row <= row_count; row++) {
        int diagonal = distance[0];
        distance[0] = row;
        for (int column = 1; column <= column_count; column++) {
            int above = distance[column];
            int substitution = diagonal + (rows[row - 1] == columns[column - 1] ? 0 : 1);
            distance[column] =
                std::min({above + 1, distance[column - 1] + 1, substitution});
            diagonal = above;
        }
    }
    return distance[column_count];
}

template <class RowSequence, class ColumnSequence>
int solve_bounded(const RowSequence& rows, const ColumnSequence& columns,
                  int max_distance) {
    int row_count = int(rows.size());
    int column_count = int(columns.size());
    assert(column_count <= row_count);
    if (row_count - column_count > max_distance) return max_distance + 1;
    if (max_distance >= row_count) return solve(rows, columns);

    int infinity = max_distance + 1;
    int previous_left = 0;
    int previous_right = std::min(column_count, max_distance);
    std::vector<int> previous(previous_right + 1);
    for (int column = 0; column <= previous_right; column++) previous[column] = column;
    std::vector<int> current;

    for (int row = 1; row <= row_count; row++) {
        int current_left = std::max(0, row - max_distance);
        int current_right = int(std::min<long long>(column_count,
                                                    static_cast<long long>(row) + max_distance));
        current.assign(current_right - current_left + 1, infinity);

        for (int column = current_left; column <= current_right; column++) {
            int best = infinity;
            if (previous_left <= column && column <= previous_right) {
                best = std::min(best, previous[column - previous_left] + 1);
            }
            if (current_left < column) {
                best = std::min(best, current[column - current_left - 1] + 1);
            }
            if (0 < column && previous_left <= column - 1 && column - 1 <= previous_right) {
                int substitution = previous[column - 1 - previous_left] +
                                   (rows[row - 1] == columns[column - 1] ? 0 : 1);
                best = std::min(best, substitution);
            }
            current[column - current_left] = std::min(best, infinity);
        }

        previous.swap(current);
        previous_left = current_left;
        previous_right = current_right;
    }
    return previous[column_count - previous_left];
}

}  // namespace levenshtein_distance_detail

// Returns the minimum number of insertions, deletions, and substitutions
// needed to transform first into second.
template <class Sequence1, class Sequence2>
int levenshtein_distance(const Sequence1& first, const Sequence2& second) {
    if (first.size() < second.size()) {
        return levenshtein_distance_detail::solve(second, first);
    }
    return levenshtein_distance_detail::solve(first, second);
}

// Returns the exact distance when it is at most max_distance, and
// max_distance + 1 otherwise.
template <class Sequence1, class Sequence2>
int levenshtein_distance(const Sequence1& first, const Sequence2& second,
                         int max_distance) {
    assert(0 <= max_distance);
    if (first.size() < second.size()) {
        return levenshtein_distance_detail::solve_bounded(second, first, max_distance);
    }
    return levenshtein_distance_detail::solve_bounded(first, second, max_distance);
}

}  // namespace string
}  // namespace m1une


#line 1 "string/longest_common_extension.hpp"



#line 6 "string/longest_common_extension.hpp"
#include <string>
#line 9 "string/longest_common_extension.hpp"

#line 1 "string/suffix_array.hpp"



#line 6 "string/suffix_array.hpp"
#include <numeric>
#line 8 "string/suffix_array.hpp"
#include <type_traits>
#line 10 "string/suffix_array.hpp"

namespace m1une {
namespace string {
namespace detail {

template <class Sequence>
std::vector<int> suffix_array_impl(const Sequence& sequence) {
    int n = int(sequence.size());
    if (n == 0) return {};

    using Value = std::remove_cv_t<std::remove_reference_t<decltype(sequence[0])>>;
    std::vector<Value> sorted(sequence.begin(), sequence.end());
    std::sort(sorted.begin(), sorted.end());
    sorted.erase(std::unique(sorted.begin(), sorted.end()), sorted.end());

    int length = n + 1;
    std::vector<int> order(length);
    std::vector<int> rank(length);
    std::vector<int> key(length);
    key[n] = 0;
    for (int i = 0; i < n; i++) {
        key[i] = int(std::lower_bound(sorted.begin(), sorted.end(), sequence[i]) - sorted.begin()) + 1;
    }

    int alphabet = int(sorted.size()) + 1;
    std::vector<int> count(std::max(length, alphabet), 0);
    for (int value : key) count[value]++;
    for (int i = 1; i < alphabet; i++) count[i] += count[i - 1];
    for (int i = length - 1; i >= 0; i--) order[--count[key[i]]] = i;

    int classes = 1;
    rank[order[0]] = 0;
    for (int i = 1; i < length; i++) {
        if (key[order[i - 1]] != key[order[i]]) classes++;
        rank[order[i]] = classes - 1;
    }

    std::vector<int> shifted(length);
    std::vector<int> next_rank(length);
    for (long long half = 1; half < length; half <<= 1) {
        for (int i = 0; i < length; i++) {
            long long position = order[i] - half;
            if (position < 0) position += length;
            shifted[i] = int(position);
        }

        count.assign(classes, 0);
        for (int position : shifted) count[rank[position]]++;
        for (int i = 1; i < classes; i++) count[i] += count[i - 1];
        for (int i = length - 1; i >= 0; i--) {
            int position = shifted[i];
            order[--count[rank[position]]] = position;
        }

        int next_classes = 1;
        next_rank[order[0]] = 0;
        for (int i = 1; i < length; i++) {
            int current = order[i];
            int previous = order[i - 1];
            int current_second = int((current + half) % length);
            int previous_second = int((previous + half) % length);
            if (
                rank[current] != rank[previous] ||
                rank[current_second] != rank[previous_second]
            ) {
                next_classes++;
            }
            next_rank[current] = next_classes - 1;
        }
        rank.swap(next_rank);
        classes = next_classes;
        if (classes == length) break;
    }

    std::vector<int> suffixes(n);
    for (int i = 0; i < n; i++) suffixes[i] = order[i + 1];
    return suffixes;
}

}  // namespace detail

template <class Sequence>
std::vector<int> suffix_array(const Sequence& sequence) {
    return detail::suffix_array_impl(sequence);
}

inline std::vector<int> suffix_array(const std::string& text) {
    std::vector<unsigned char> values;
    values.reserve(text.size());
    for (unsigned char character : text) values.push_back(character);
    return detail::suffix_array_impl(values);
}

template <class Sequence>
std::vector<int> lcp_array(const Sequence& sequence, const std::vector<int>& suffixes) {
    int n = int(sequence.size());
    assert(int(suffixes.size()) == n);
    if (n == 0) return {};

    std::vector<int> rank(n);
    for (int i = 0; i < n; i++) {
        assert(0 <= suffixes[i] && suffixes[i] < n);
        rank[suffixes[i]] = i;
    }

    std::vector<int> lcp(n - 1);
    int common = 0;
    for (int i = 0; i < n; i++) {
        int position = rank[i];
        if (position == n - 1) {
            common = 0;
            continue;
        }
        int j = suffixes[position + 1];
        while (
            i + common < n &&
            j + common < n &&
            sequence[i + common] == sequence[j + common]
        ) {
            common++;
        }
        lcp[position] = common;
        if (common > 0) common--;
    }
    return lcp;
}

}  // namespace string
}  // namespace m1une


#line 11 "string/longest_common_extension.hpp"

namespace m1une {
namespace string {

template <class Sequence = std::string>
struct LongestCommonExtension {
   private:
    Sequence _sequence;
    std::vector<int> _suffix_array;
    std::vector<int> _rank;
    std::vector<int> _lcp;
    std::vector<int> _log;
    std::vector<std::vector<int>> _table;

    int range_min(int left, int right) const {
        assert(0 <= left && left < right && right <= int(_lcp.size()));
        int k = _log[right - left];
        return std::min(_table[k][left], _table[k][right - (1 << k)]);
    }

    void build() {
        int n = int(_sequence.size());
        _suffix_array = m1une::string::suffix_array(_sequence);
        _rank.assign(n, 0);
        for (int i = 0; i < n; i++) {
            _rank[_suffix_array[i]] = i;
        }

        _lcp = m1une::string::lcp_array(_sequence, _suffix_array);
        int m = int(_lcp.size());
        _log.assign(m + 1, 0);
        for (int i = 2; i <= m; i++) {
            _log[i] = _log[i >> 1] + 1;
        }

        _table.clear();
        if (m == 0) return;
        _table.assign(_log[m] + 1, std::vector<int>());
        _table[0] = _lcp;
        for (int k = 1; k < int(_table.size()); k++) {
            int width = 1 << k;
            int half = width >> 1;
            _table[k].resize(m - width + 1);
            for (int i = 0; i + width <= m; i++) {
                _table[k][i] = std::min(_table[k - 1][i], _table[k - 1][i + half]);
            }
        }
    }

   public:
    LongestCommonExtension() = default;

    explicit LongestCommonExtension(const Sequence& sequence) : _sequence(sequence) {
        build();
    }

    explicit LongestCommonExtension(Sequence&& sequence) : _sequence(std::move(sequence)) {
        build();
    }

    int size() const {
        return int(_sequence.size());
    }

    bool empty() const {
        return _sequence.empty();
    }

    const Sequence& sequence() const {
        return _sequence;
    }

    const std::vector<int>& suffix_array() const {
        return _suffix_array;
    }

    const std::vector<int>& rank() const {
        return _rank;
    }

    const std::vector<int>& lcp_array() const {
        return _lcp;
    }

    int longest_common_extension(int i, int j) const {
        int n = size();
        assert(0 <= i && i <= n);
        assert(0 <= j && j <= n);
        if (i == j) return n - i;
        if (i == n || j == n) return 0;

        int left = _rank[i];
        int right = _rank[j];
        if (left > right) std::swap(left, right);
        return range_min(left, right);
    }

    int longest_common_extension(int i, int j, int limit) const {
        assert(0 <= limit);
        return std::min(longest_common_extension(i, j), limit);
    }

    int lcp(int i, int j) const {
        return longest_common_extension(i, j);
    }

    int operator()(int i, int j) const {
        return longest_common_extension(i, j);
    }

    int compare_suffix(int i, int j) const {
        int n = size();
        assert(0 <= i && i <= n);
        assert(0 <= j && j <= n);
        if (i == j) return 0;
        int common = longest_common_extension(i, j);
        if (i + common == n && j + common == n) return 0;
        if (i + common == n) return -1;
        if (j + common == n) return 1;
        return _sequence[i + common] < _sequence[j + common] ? -1 : 1;
    }

    int compare(int l1, int r1, int l2, int r2) const {
        int n = size();
        assert(0 <= l1 && l1 <= r1 && r1 <= n);
        assert(0 <= l2 && l2 <= r2 && r2 <= n);
        int len1 = r1 - l1;
        int len2 = r2 - l2;
        int common = longest_common_extension(l1, l2, std::min(len1, len2));
        if (common == len1 && common == len2) return 0;
        if (common == len1) return -1;
        if (common == len2) return 1;
        return _sequence[l1 + common] < _sequence[l2 + common] ? -1 : 1;
    }
};

}  // namespace string
}  // namespace m1une


#line 1 "string/longest_common_subsequence.hpp"



#line 9 "string/longest_common_subsequence.hpp"

namespace m1une {
namespace string {

struct LongestCommonSubsequence {
    std::vector<std::pair<int, int>> matches;

    int length() const {
        return int(matches.size());
    }

    bool empty() const {
        return matches.empty();
    }

    std::vector<int> first_indices() const {
        std::vector<int> result;
        result.reserve(matches.size());
        for (auto [i, j] : matches) {
            (void)j;
            result.push_back(i);
        }
        return result;
    }

    std::vector<int> second_indices() const {
        std::vector<int> result;
        result.reserve(matches.size());
        for (auto [i, j] : matches) {
            (void)i;
            result.push_back(j);
        }
        return result;
    }

    template <class Sequence>
    std::vector<std::remove_cv_t<std::remove_reference_t<decltype(std::declval<const Sequence&>()[0])>>>
    values_from_first(const Sequence& first) const {
        using Value = std::remove_cv_t<std::remove_reference_t<decltype(std::declval<const Sequence&>()[0])>>;
        std::vector<Value> result;
        result.reserve(matches.size());
        for (auto [i, j] : matches) {
            (void)j;
            result.push_back(first[i]);
        }
        return result;
    }

    template <class Sequence>
    std::vector<std::remove_cv_t<std::remove_reference_t<decltype(std::declval<const Sequence&>()[0])>>>
    values_from_second(const Sequence& second) const {
        using Value = std::remove_cv_t<std::remove_reference_t<decltype(std::declval<const Sequence&>()[0])>>;
        std::vector<Value> result;
        result.reserve(matches.size());
        for (auto [i, j] : matches) {
            (void)i;
            result.push_back(second[j]);
        }
        return result;
    }
};

template <class FirstSequence, class SecondSequence>
int longest_common_subsequence_length(const FirstSequence& first, const SecondSequence& second) {
    int n = int(first.size());
    int m = int(second.size());
    if (m <= n) {
        std::vector<int> dp(m + 1, 0);
        for (int i = 0; i < n; i++) {
            int diagonal = 0;
            for (int j = 0; j < m; j++) {
                int up = dp[j + 1];
                if (first[i] == second[j]) {
                    dp[j + 1] = diagonal + 1;
                } else {
                    dp[j + 1] = std::max(dp[j + 1], dp[j]);
                }
                diagonal = up;
            }
        }
        return dp[m];
    } else {
        std::vector<int> dp(n + 1, 0);
        for (int j = 0; j < m; j++) {
            int diagonal = 0;
            for (int i = 0; i < n; i++) {
                int up = dp[i + 1];
                if (first[i] == second[j]) {
                    dp[i + 1] = diagonal + 1;
                } else {
                    dp[i + 1] = std::max(dp[i + 1], dp[i]);
                }
                diagonal = up;
            }
        }
        return dp[n];
    }
}

template <class FirstSequence, class SecondSequence>
LongestCommonSubsequence longest_common_subsequence(
    const FirstSequence& first,
    const SecondSequence& second
) {
    int n = int(first.size());
    int m = int(second.size());
    std::vector<std::vector<int>> dp(n + 1, std::vector<int>(m + 1, 0));
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < m; j++) {
            if (first[i] == second[j]) {
                dp[i + 1][j + 1] = dp[i][j] + 1;
            } else {
                dp[i + 1][j + 1] = std::max(dp[i][j + 1], dp[i + 1][j]);
            }
        }
    }

    LongestCommonSubsequence result;
    result.matches.reserve(dp[n][m]);
    int i = n;
    int j = m;
    while (i > 0 && j > 0) {
        if (first[i - 1] == second[j - 1]) {
            result.matches.emplace_back(i - 1, j - 1);
            i--;
            j--;
        } else if (dp[i - 1][j] >= dp[i][j - 1]) {
            i--;
        } else {
            j--;
        }
    }
    std::reverse(result.matches.begin(), result.matches.end());
    return result;
}

}  // namespace string
}  // namespace m1une


#line 1 "string/longest_common_substring.hpp"



#line 9 "string/longest_common_substring.hpp"

#line 11 "string/longest_common_substring.hpp"

namespace m1une {
namespace string {

struct LongestCommonSubstring {
    int first_left = 0;
    int first_right = 0;
    int second_left = 0;
    int second_right = 0;

    int length() const {
        assert(first_right - first_left == second_right - second_left);
        return first_right - first_left;
    }

    bool empty() const {
        return length() == 0;
    }

    std::pair<int, int> first_interval() const {
        return {first_left, first_right};
    }

    std::pair<int, int> second_interval() const {
        return {second_left, second_right};
    }
};

namespace detail {

template <class Sequence>
std::vector<int> compressed_join_with_separator(const Sequence& first, const Sequence& second) {
    using Value = std::remove_cv_t<std::remove_reference_t<decltype(first[0])>>;

    std::vector<Value> values;
    values.reserve(first.size() + second.size());
    for (const auto& value : first) values.push_back(value);
    for (const auto& value : second) values.push_back(value);
    std::sort(values.begin(), values.end());
    values.erase(std::unique(values.begin(), values.end()), values.end());

    std::vector<int> joined;
    joined.reserve(first.size() + second.size() + 1);
    for (const auto& value : first) {
        joined.push_back(int(std::lower_bound(values.begin(), values.end(), value) - values.begin()) + 2);
    }
    joined.push_back(1);
    for (const auto& value : second) {
        joined.push_back(int(std::lower_bound(values.begin(), values.end(), value) - values.begin()) + 2);
    }
    return joined;
}

}  // namespace detail

template <class Sequence>
LongestCommonSubstring longest_common_substring(const Sequence& first, const Sequence& second) {
    int n = int(first.size());
    int m = int(second.size());
    std::vector<int> joined = detail::compressed_join_with_separator(first, second);
    std::vector<int> suffixes = suffix_array(joined);
    std::vector<int> lcp = lcp_array(joined, suffixes);

    LongestCommonSubstring result;
    for (int i = 0; i + 1 < int(suffixes.size()); i++) {
        int a = suffixes[i];
        int b = suffixes[i + 1];
        if (a == n || b == n) continue;

        bool a_first = a < n;
        bool b_first = b < n;
        if (a_first == b_first) continue;

        int first_left = a_first ? a : b;
        int second_left = a_first ? b - n - 1 : a - n - 1;
        int length = lcp[i];
        length = std::min(length, n - first_left);
        length = std::min(length, m - second_left);
        if (length > result.length()) {
            result.first_left = first_left;
            result.first_right = first_left + length;
            result.second_left = second_left;
            result.second_right = second_left + length;
        }
    }
    return result;
}

}  // namespace string
}  // namespace m1une


#line 1 "string/lyndon_factorization.hpp"



#line 6 "string/lyndon_factorization.hpp"

#line 1 "string/minimum_rotation.hpp"



namespace m1une {
namespace string {

// Returns the smallest starting index of a lexicographically minimum cyclic shift.
template <class Sequence>
int minimum_cyclic_shift(const Sequence& sequence) {
    const int size = int(sequence.size());
    if (size == 0) return 0;

    auto less = [&](int left, int right) {
        return sequence[left < size ? left : left - size] <
               sequence[right < size ? right : right - size];
    };

    int answer = 0;
    int start = 0;
    while (start < size) {
        answer = start;
        int scan = start + 1;
        int matched = start;
        while (scan < 2 * size && !less(scan, matched)) {
            if (less(matched, scan)) {
                matched = start;
            } else {
                matched++;
            }
            scan++;
        }

        const int period = scan - matched;
        while (start <= matched) start += period;
    }
    return answer;
}

}  // namespace string
}  // namespace m1une


#line 8 "string/lyndon_factorization.hpp"

namespace m1une {
namespace string {

// Returns boundaries 0 = a[0] < a[1] < ... < a[k] = sequence.size()
// of the Lyndon factorization.
template <class Sequence>
std::vector<int> lyndon_factor_boundaries(const Sequence& sequence) {
    int n = int(sequence.size());
    std::vector<int> boundaries;
    boundaries.push_back(0);

    int i = 0;
    while (i < n) {
        int j = i + 1;
        int k = i;
        while (j < n && !(sequence[j] < sequence[k])) {
            if (sequence[k] < sequence[j]) {
                k = i;
            } else {
                k++;
            }
            j++;
        }

        int length = j - k;
        while (i <= k) {
            i += length;
            boundaries.push_back(i);
        }
    }
    return boundaries;
}

// Returns half-open intervals [left, right) of the Lyndon factorization.
template <class Sequence>
std::vector<std::pair<int, int>> lyndon_factorization(const Sequence& sequence) {
    std::vector<int> boundaries = lyndon_factor_boundaries(sequence);
    std::vector<std::pair<int, int>> factors;
    factors.reserve(boundaries.size() - 1);
    for (int i = 0; i + 1 < int(boundaries.size()); i++) {
        factors.emplace_back(boundaries[i], boundaries[i + 1]);
    }
    return factors;
}

}  // namespace string
}  // namespace m1une


#line 1 "string/manacher.hpp"



#line 7 "string/manacher.hpp"

namespace m1une {
namespace string {

struct ManacherResult {
    // odd[i] is the radius including center i.
    // The palindrome is [i - odd[i] + 1, i + odd[i]).
    std::vector<int> odd;

    // even[i] is the radius centered between i - 1 and i.
    // The palindrome is [i - even[i], i + even[i]).
    std::vector<int> even;

    int size() const {
        return int(odd.size());
    }

    bool empty() const {
        return odd.empty();
    }

    bool is_palindrome(int left, int right) const {
        int n = size();
        assert(0 <= left && left <= right && right <= n);
        int length = right - left;
        if (length == 0) return true;
        if (length & 1) {
            int center = (left + right) / 2;
            return length / 2 + 1 <= odd[center];
        }
        int center = (left + right) / 2;
        return length / 2 <= even[center];
    }

    int longest_length() const {
        int result = 0;
        for (int radius : odd) result = std::max(result, 2 * radius - 1);
        for (int radius : even) result = std::max(result, 2 * radius);
        return result;
    }
};

template <class Sequence>
ManacherResult manacher(const Sequence& sequence) {
    int n = int(sequence.size());
    ManacherResult result;
    result.odd.assign(n, 0);
    result.even.assign(n, 0);

    int left = 0;
    int right = -1;
    for (int i = 0; i < n; i++) {
        int radius = i > right ? 1 : std::min(result.odd[left + right - i], right - i + 1);
        while (
            0 <= i - radius &&
            i + radius < n &&
            sequence[i - radius] == sequence[i + radius]
        ) {
            radius++;
        }
        result.odd[i] = radius;
        if (right < i + radius - 1) {
            left = i - radius + 1;
            right = i + radius - 1;
        }
    }

    left = 0;
    right = -1;
    for (int i = 0; i < n; i++) {
        int radius = i > right ? 0 : std::min(result.even[left + right - i + 1], right - i + 1);
        while (
            0 <= i - radius - 1 &&
            i + radius < n &&
            sequence[i - radius - 1] == sequence[i + radius]
        ) {
            radius++;
        }
        result.even[i] = radius;
        if (right < i + radius - 1) {
            left = i - radius;
            right = i + radius - 1;
        }
    }
    return result;
}

}  // namespace string
}  // namespace m1une


#line 1 "string/map_trie.hpp"



#line 6 "string/map_trie.hpp"
#include <functional>
#line 8 "string/map_trie.hpp"
#include <map>
#line 10 "string/map_trie.hpp"

namespace m1une {
namespace string {

// A multiset trie whose outgoing edges are stored in ordered maps.
template <class Symbol, class Compare = std::less<Symbol>>
struct MapTrie {
    using node_id = int;
    static constexpr node_id null_node = -1;

    struct Node {
        std::map<Symbol, node_id, Compare> child;
        int subtree_count = 0;
        int terminal_count = 0;
    };

   private:
    std::vector<Node> _nodes;
    int _distinct_size;

    node_id new_node() {
        assert(_nodes.size() < std::size_t(std::numeric_limits<int>::max()));
        _nodes.emplace_back();
        return int(_nodes.size()) - 1;
    }

    template <class Sequence>
    node_id find_node(const Sequence& sequence) const {
        node_id node = 0;
        for (const auto& symbol : sequence) {
            auto iterator = _nodes[node].child.find(symbol);
            if (iterator == _nodes[node].child.end()) return null_node;
            node = iterator->second;
            if (_nodes[node].subtree_count == 0) return null_node;
        }
        return node;
    }

   public:
    MapTrie() : _nodes(1), _distinct_size(0) {}

    int size() const {
        return _nodes[0].subtree_count;
    }

    int distinct_size() const {
        return _distinct_size;
    }

    bool empty() const {
        return size() == 0;
    }

    node_id root() const {
        return 0;
    }

    const Node& node(node_id id) const {
        assert(0 <= id && std::size_t(id) < _nodes.size());
        return _nodes[id];
    }

    template <class Sequence>
    node_id find(const Sequence& sequence) const {
        return find_node(sequence);
    }

    std::size_t node_count() const {
        return _nodes.size();
    }

    void reserve(std::size_t node_capacity) {
        _nodes.reserve(node_capacity);
    }

    void clear() {
        _nodes.clear();
        _nodes.emplace_back();
        _distinct_size = 0;
    }

    template <class Sequence>
    node_id insert(const Sequence& sequence, int multiplicity = 1) {
        assert(0 < multiplicity);
        node_id node = 0;
        _nodes[node].subtree_count += multiplicity;
        for (const auto& symbol : sequence) {
            auto iterator = _nodes[node].child.find(symbol);
            node_id child;
            if (iterator == _nodes[node].child.end()) {
                child = new_node();
                _nodes[node].child.emplace(symbol, child);
            } else {
                child = iterator->second;
            }
            node = child;
            _nodes[node].subtree_count += multiplicity;
        }
        if (_nodes[node].terminal_count == 0) _distinct_size++;
        _nodes[node].terminal_count += multiplicity;
        return node;
    }

    template <class Sequence>
    int count(const Sequence& sequence) const {
        node_id node = find_node(sequence);
        return node == null_node ? 0 : _nodes[node].terminal_count;
    }

    template <class Sequence>
    bool contains(const Sequence& sequence) const {
        return count(sequence) != 0;
    }

    // Returns the number of stored sequences beginning with prefix.
    template <class Sequence>
    int prefix_count(const Sequence& prefix) const {
        node_id node = find_node(prefix);
        return node == null_node ? 0 : _nodes[node].subtree_count;
    }

    template <class Sequence>
    bool starts_with(const Sequence& prefix) const {
        return prefix_count(prefix) != 0;
    }

    template <class Sequence>
    bool erase_one(const Sequence& sequence) {
        node_id terminal = find_node(sequence);
        if (terminal == null_node || _nodes[terminal].terminal_count == 0) {
            return false;
        }

        node_id node = 0;
        _nodes[node].subtree_count--;
        for (const auto& symbol : sequence) {
            node = _nodes[node].child.find(symbol)->second;
            _nodes[node].subtree_count--;
        }
        _nodes[node].terminal_count--;
        if (_nodes[node].terminal_count == 0) _distinct_size--;
        return true;
    }

    template <class Sequence>
    bool erase(const Sequence& sequence) {
        return erase_one(sequence);
    }

    template <class Sequence>
    int erase_all(const Sequence& sequence) {
        int multiplicity = count(sequence);
        if (multiplicity == 0) return 0;

        node_id node = 0;
        _nodes[node].subtree_count -= multiplicity;
        for (const auto& symbol : sequence) {
            node = _nodes[node].child.find(symbol)->second;
            _nodes[node].subtree_count -= multiplicity;
        }
        _nodes[node].terminal_count = 0;
        _distinct_size--;
        return multiplicity;
    }

    // Calls callback(length, multiplicity) for every stored prefix.
    // The empty prefix is reported with length 0 when it is stored.
    template <class Sequence, class Callback>
    void for_each_prefix(const Sequence& sequence, Callback callback) const {
        node_id node = 0;
        if (_nodes[node].terminal_count != 0) {
            callback(0, _nodes[node].terminal_count);
        }

        int length = 0;
        for (const auto& symbol : sequence) {
            auto iterator = _nodes[node].child.find(symbol);
            if (iterator == _nodes[node].child.end()) return;
            node = iterator->second;
            if (_nodes[node].subtree_count == 0) return;
            length++;
            if (_nodes[node].terminal_count != 0) {
                callback(length, _nodes[node].terminal_count);
            }
        }
    }

    // Returns the length of the longest stored sequence that is a prefix.
    // Returns -1 when no stored prefix exists.
    template <class Sequence>
    int longest_prefix(const Sequence& sequence) const {
        int result = _nodes[0].terminal_count == 0 ? -1 : 0;
        for_each_prefix(sequence, [&result](int length, int) {
            result = length;
        });
        return result;
    }
};

}  // namespace string
}  // namespace m1une


#line 1 "string/palindrome_lexicographical_order.hpp"



#line 9 "string/palindrome_lexicographical_order.hpp"

#line 12 "string/palindrome_lexicographical_order.hpp"

namespace m1une {
namespace string {

// Indexes the distinct nonempty palindromic substrings of one sequence.
template <
    class Sequence = std::string,
    int AlphabetSize = 26,
    int FirstCharacter = 'a'
>
struct PalindromeLexicographicalOrder {
    static_assert(0 < AlphabetSize);

    using eertree_type = Eertree<AlphabetSize, FirstCharacter>;
    using node_id = typename eertree_type::node_id;

   private:
    Sequence _sequence;
    eertree_type _eertree;
    std::vector<node_id> _nodes_in_order;
    std::vector<int> _order_of_node;

    template <class Symbol>
    static int symbol_index(const Symbol& symbol) {
        int index = int(symbol) - FirstCharacter;
        assert(0 <= index && index < AlphabetSize);
        return index;
    }

    void build_order() {
        const int node_count = _eertree.node_count();
        std::vector<std::vector<node_id>> suffix_children(node_count);
        for (node_id id = 0; id < node_count; id++) {
            if (id == eertree_type::odd_root) continue;
            suffix_children[_eertree.node(id).suffix_link].push_back(id);
        }

        std::vector<int> enter(node_count);
        std::vector<int> leave(node_count);
        std::vector<std::pair<node_id, bool>> stack;
        stack.reserve(2 * node_count);
        stack.emplace_back(eertree_type::odd_root, false);
        int timer = 0;
        while (!stack.empty()) {
            auto [id, exiting] = stack.back();
            stack.pop_back();
            if (exiting) {
                leave[id] = timer;
                continue;
            }

            enter[id] = timer++;
            stack.emplace_back(id, true);
            const auto& children = suffix_children[id];
            for (int i = int(children.size()) - 1; i >= 0; i--) {
                stack.emplace_back(children[i], false);
            }
        }

        std::vector<int> suffixes = suffix_array(_sequence);
        std::vector<int> suffix_rank(_sequence.size());
        for (int rank = 0; rank < int(suffixes.size()); rank++) {
            suffix_rank[suffixes[rank]] = rank;
        }

        _nodes_in_order.resize(_eertree.size());
        for (int i = 0; i < _eertree.size(); i++) {
            _nodes_in_order[i] = i + 2;
        }

        auto is_ancestor = [&](node_id ancestor, node_id descendant) {
            return
                enter[ancestor] <= enter[descendant] &&
                leave[descendant] <= leave[ancestor];
        };
        std::sort(
            _nodes_in_order.begin(),
            _nodes_in_order.end(),
            [&](node_id first, node_id second) {
                if (first == second) return false;

                // A palindromic prefix is also a palindromic suffix, so prefix
                // cases are exactly the ancestor cases in the suffix-link tree.
                if (is_ancestor(first, second)) return true;
                if (is_ancestor(second, first)) return false;

                // Otherwise the first mismatch occurs inside both substrings,
                // and the ranks of representative suffixes give their order.
                int first_start = _eertree.first_occurrence(first).first;
                int second_start = _eertree.first_occurrence(second).first;
                return suffix_rank[first_start] < suffix_rank[second_start];
            }
        );

        _order_of_node.assign(node_count, -1);
        for (int order = 0; order < size(); order++) {
            _order_of_node[_nodes_in_order[order]] = order;
        }
    }

   public:
    PalindromeLexicographicalOrder() : _order_of_node(2, -1) {}

    explicit PalindromeLexicographicalOrder(const Sequence& sequence)
        : _sequence(sequence), _eertree(_sequence) {
        build_order();
    }

    explicit PalindromeLexicographicalOrder(Sequence&& sequence)
        : _sequence(std::move(sequence)), _eertree(_sequence) {
        build_order();
    }

    int size() const {
        return int(_nodes_in_order.size());
    }

    bool empty() const {
        return _nodes_in_order.empty();
    }

    int text_length() const {
        return int(_sequence.size());
    }

    const Sequence& sequence() const {
        return _sequence;
    }

    const eertree_type& eertree() const {
        return _eertree;
    }

    const std::vector<node_id>& nodes_in_order() const {
        return _nodes_in_order;
    }

    int order_of_node(node_id id) const {
        assert(2 <= id && id < _eertree.node_count());
        return _order_of_node[id];
    }

    node_id node_by_order(int order) const {
        assert(0 <= order && order < size());
        return _nodes_in_order[order];
    }

    template <class Palindrome>
    node_id find(const Palindrome& palindrome) const {
        const int length = int(palindrome.size());
        if (length == 0) return eertree_type::null_node;
        for (int i = 0; i < length / 2; i++) {
            if (palindrome[i] != palindrome[length - 1 - i]) {
                return eertree_type::null_node;
            }
        }

        node_id id =
            length & 1 ? eertree_type::odd_root : eertree_type::even_root;
        for (int i = (length - 1) / 2; i >= 0; i--) {
            int symbol = symbol_index(palindrome[i]);
            id = _eertree.node(id).next[symbol];
            if (id == eertree_type::null_node) return id;
        }
        return id;
    }

    template <class Palindrome>
    bool contains(const Palindrome& palindrome) const {
        return find(palindrome) != eertree_type::null_node;
    }

    template <class Palindrome>
    int order_of_palindrome(const Palindrome& palindrome) const {
        node_id id = find(palindrome);
        return id == eertree_type::null_node ? -1 : order_of_node(id);
    }

    std::pair<int, int> representative_occurrence(int order) const {
        return _eertree.first_occurrence(node_by_order(order));
    }

    Sequence palindrome(int order) const {
        auto [left, right] = representative_occurrence(order);
        return Sequence(_sequence.begin() + left, _sequence.begin() + right);
    }

    Sequence kth(int order) const {
        return palindrome(order);
    }
};

}  // namespace string
}  // namespace m1une


#line 1 "string/prefix_substring_lcs.hpp"



#line 9 "string/prefix_substring_lcs.hpp"

namespace m1une {
namespace string {

// Answers LCS-length queries between a prefix of the first sequence and a
// substring of the second sequence. Queries are evaluated as one offline batch.
template <class FirstSequence, class SecondSequence>
class PrefixSubstringLcs {
   private:
    struct Query {
        int first_prefix;
        int second_left;
        int second_right;
    };

    FirstSequence _first;
    SecondSequence _second;
    std::vector<Query> _queries;

   public:
    PrefixSubstringLcs(FirstSequence first, SecondSequence second)
        : _first(std::move(first)), _second(std::move(second)) {}

    int first_size() const {
        return int(_first.size());
    }

    int second_size() const {
        return int(_second.size());
    }

    int query_count() const {
        return int(_queries.size());
    }

    bool empty() const {
        return _queries.empty();
    }

    void reserve(int query_capacity) {
        assert(0 <= query_capacity);
        _queries.reserve(query_capacity);
    }

    void clear() {
        _queries.clear();
    }

    // Adds LCS(first[0..first_prefix), second[second_left..second_right)) and
    // returns its insertion-order ID.
    int add_query(int first_prefix, int second_left, int second_right) {
        assert(0 <= first_prefix && first_prefix <= first_size());
        assert(0 <= second_left && second_left <= second_right);
        assert(second_right <= second_size());
        const int id = query_count();
        _queries.push_back(Query{first_prefix, second_left, second_right});
        return id;
    }

    std::vector<int> calculate() const {
        const int first_length = first_size();
        const int second_length = second_size();
        const int count = query_count();
        std::vector<int> answers(count, 0);
        if (count == 0 || first_length == 0 || second_length == 0) {
            return answers;
        }

        std::vector<std::vector<int>> queries_by_prefix(first_length + 1);
        for (int id = 0; id < count; id++) {
            const Query& query = _queries[id];
            if (query.first_prefix > 0 &&
                query.second_left < query.second_right) {
                queries_by_prefix[query.first_prefix].push_back(id);
            }
        }

        // seaweed[j] is the bottom endpoint of the seaweed entering at j for
        // the current prefix of the first sequence. -1 denotes the left edge.
        std::vector<int> seaweed(second_length);
        for (int j = 0; j < second_length; j++) seaweed[j] = j;

        std::vector<int> heads(second_length + 1, -1);
        std::vector<int> next(count, -1);
        std::vector<int> fenwick(second_length + 1, 0);

        for (int i = 0; i < first_length; i++) {
            int displaced = -1;
            for (int j = 0; j < second_length; j++) {
                if (_first[i] == _second[j] || seaweed[j] < displaced) {
                    std::swap(seaweed[j], displaced);
                }
            }

            const std::vector<int>& prefix_queries = queries_by_prefix[i + 1];
            if (prefix_queries.empty()) continue;

            std::fill(heads.begin(), heads.end(), -1);
            for (int id : prefix_queries) {
                const int right = _queries[id].second_right;
                next[id] = heads[right];
                heads[right] = id;
            }
            std::fill(fenwick.begin(), fenwick.end(), 0);

            int inserted = 0;
            for (int right = 1; right <= second_length; right++) {
                const int endpoint = seaweed[right - 1];
                if (endpoint >= 0) {
                    inserted++;
                    for (int position = endpoint + 1;
                         position <= second_length;
                         position += position & -position) {
                        fenwick[position]++;
                    }
                }

                for (int id = heads[right]; id != -1; id = next[id]) {
                    const int left = _queries[id].second_left;
                    int below_left = 0;
                    for (int position = left; position > 0;
                         position -= position & -position) {
                        below_left += fenwick[position];
                    }
                    const int crossing = inserted - below_left;
                    answers[id] = (right - left) - crossing;
                }
            }
        }
        return answers;
    }
};

template <class FirstSequence, class SecondSequence>
PrefixSubstringLcs(FirstSequence&&, SecondSequence&&)
    -> PrefixSubstringLcs<
        std::decay_t<FirstSequence>,
        std::decay_t<SecondSequence>
    >;

}  // namespace string
}  // namespace m1une


#line 1 "string/rolling_hash.hpp"



#line 8 "string/rolling_hash.hpp"

namespace m1une {
namespace string {

// Standard Rolling Hash for static strings.
// Precomputes hashes to answer substring queries in O(1).
// Provides advanced operations like LCP, lexicographical comparison, and string repetition in O(log N).
template <long long Base = 10007, long long Mod = (1LL << 61) - 1>
struct RollingHash {
    std::string s;
    std::vector<long long> hash;
    std::vector<long long> power;

    RollingHash() = default;

    // Constructs the rolling hash table for the given string.
    explicit RollingHash(const std::string& str) : s(str) {
        int n = s.size();
        hash.assign(n + 1, 0);
        power.assign(n + 1, 1);
        for (int i = 0; i < n; ++i) {
            // Use __int128_t to prevent overflow during multiplication
            hash[i + 1] = (static_cast<__int128_t>(hash[i]) * Base + s[i]) % Mod;
            power[i + 1] = (static_cast<__int128_t>(power[i]) * Base) % Mod;
        }
    }

    // Returns the hash of the substring S[l..r) in O(1).
    long long get(int l, int r) const {
        long long res = hash[r] - (static_cast<__int128_t>(hash[l]) * power[r - l]) % Mod;
        if (res < 0) res += Mod;
        return res;
    }

    // Returns the hash of the concatenated substrings S[l1..r1) and S[l2..r2).
    long long concat(int l1, int r1, int l2, int r2) const {
        long long h1 = get(l1, r1);
        long long h2 = get(l2, r2);
        return combine(h1, h2, power[r2 - l2]);
    }

    // Calculates the Longest Common Prefix (LCP) length of S[l1..r1) and S[l2..r2) in O(log N).
    int lcp(int l1, int r1, int l2, int r2) const {
        int len = std::min(r1 - l1, r2 - l2);
        int low = 0, high = len + 1;
        while (high - low > 1) {
            int mid = low + (high - low) / 2;
            if (get(l1, l1 + mid) == get(l2, l2 + mid)) {
                low = mid;
            } else {
                high = mid;
            }
        }
        return low;
    }

    // Lexicographically compares S[l1..r1) and S[l2..r2) in O(log N).
    // Returns -1 if S[l1..r1) < S[l2..r2), 0 if equal, and 1 if S[l1..r1) > S[l2..r2).
    int compare(int l1, int r1, int l2, int r2) const {
        int l = lcp(l1, r1, l2, r2);
        bool end1 = (l1 + l == r1);
        bool end2 = (l2 + l == r2);
        if (end1 && end2) return 0;
        if (end1) return -1;
        if (end2) return 1;
        return s[l1 + l] < s[l2 + l] ? -1 : 1;
    }

    // Returns the hash of the substring S[l..r) repeated 'k' times.
    long long repeat(int l, int r, long long k) const {
        long long h = get(l, r);
        long long p = power[r - l];
        return repeat_hash(h, p, k);
    }

    // --- Static Helpers for dynamic processing and Monoid integration ---

    // Computes the hash of a single string in O(N) time and O(1) space.
    static long long compute_hash(const std::string& str) {
        long long h = 0;
        for (char c : str) {
            h = (static_cast<__int128_t>(h) * Base + c) % Mod;
        }
        return h;
    }

    // Combines two hashes. Equivalent to concatenating string 'b' to the right of string 'a'.
    static constexpr long long combine(long long h1, long long h2, long long base_power2) {
        return (static_cast<__int128_t>(h1) * base_power2 + h2) % Mod;
    }

    // Returns the hash of a string (with hash 'h' and base_power 'p') repeated 'k' times.
    static constexpr long long repeat_hash(long long h, long long p, long long k) {
        long long res_h = 0;
        long long res_p = 1;
        long long cur_h = h;
        long long cur_p = p;
        while (k > 0) {
            if (k & 1) {
                res_h = combine(res_h, cur_h, cur_p);
                res_p = (static_cast<__int128_t>(res_p) * cur_p) % Mod;
            }
            cur_h = combine(cur_h, cur_h, cur_p);
            cur_p = (static_cast<__int128_t>(cur_p) * cur_p) % Mod;
            k >>= 1;
        }
        return res_h;
    }

    // Creates the state pair {hash_value, base_power} for a single character.
    static constexpr std::pair<long long, long long> make_single(long long c) {
        return {c % Mod, Base % Mod};
    }
};

}  // namespace string
}  // namespace m1une


#line 1 "string/runs.hpp"



#line 5 "string/runs.hpp"
#include <set>
#line 8 "string/runs.hpp"

namespace m1une {
namespace string {

struct Run {
    int period;
    int left;
    int right;

    bool operator==(const Run&) const = default;
};

namespace internal {

template <class Sequence>
class RunEnumerator {
   private:
    const Sequence& _sequence;
    int _size;
    std::vector<std::vector<std::pair<int, int>>> _candidates;

    template <class Access>
    static std::vector<int> z_algorithm(int length, Access access) {
        std::vector<int> z(length + 1, 0);
        if (length == 0) return z;
        z[0] = length;
        int left = 0;
        int right = 0;
        for (int i = 1; i < length; i++) {
            if (i < right) z[i] = std::min(right - i, z[i - left]);
            while (
                i + z[i] < length &&
                access(z[i]) == access(i + z[i])
            ) {
                z[i]++;
            }
            if (right < i + z[i]) {
                left = i;
                right = i + z[i];
            }
        }
        return z;
    }

    decltype(auto) element(int index, bool reversed) const {
        int original_index = reversed ? _size - 1 - index : index;
        return _sequence[original_index];
    }

    void add_candidate(int period, int left, int right, bool reversed) {
        if (reversed) {
            left = _size - left;
            right = _size - right;
            std::swap(left, right);
        }
        _candidates[period].emplace_back(left, right);
    }

    void collect(int range_left, int range_right, int phase, bool reversed) {
        if (range_right - range_left <= 1) return;
        int middle = (range_left + range_right + phase) / 2;
        collect(range_left, middle, phase, reversed);
        collect(middle, range_right, phase, reversed);

        int left_length = middle - range_left;
        int right_length = range_right - middle;
        std::vector<int> left_z = z_algorithm(left_length, [&](int index) -> decltype(auto) {
            return element(middle - 1 - index, reversed);
        });

        int combined_length = right_length + range_right - range_left;
        std::vector<int> right_z = z_algorithm(combined_length, [&](int index) -> decltype(auto) {
            if (index < right_length) return element(middle + index, reversed);
            return element(range_left + index - right_length, reversed);
        });

        for (int start = middle - 1; start >= range_left; start--) {
            int period = middle - start;
            int extend_left = std::min(start - range_left, left_z[period]);
            int extend_right = std::min(
                range_right - middle,
                right_z[range_right - range_left - period]
            );
            int left = start - extend_left;
            int right = middle + extend_right;
            if (right - left >= 2 * period) {
                add_candidate(period, left, right, reversed);
            }
        }
    }

   public:
    explicit RunEnumerator(const Sequence& sequence)
        : _sequence(sequence),
          _size(int(sequence.size())),
          _candidates(_size / 2 + 1) {}

    std::vector<Run> enumerate() {
        collect(0, _size, 0, true);
        collect(0, _size, 1, false);

        std::set<std::pair<int, int>> used_intervals;
        std::vector<Run> result;
        for (int period = 1; period <= _size / 2; period++) {
            std::vector<std::pair<int, int>>& candidates = _candidates[period];
            std::sort(
                candidates.begin(),
                candidates.end(),
                [](const auto& first, const auto& second) {
                    if (first.first != second.first) {
                        return first.first < second.first;
                    }
                    return first.second > second.second;
                }
            );

            int farthest_right = -1;
            for (const auto& interval : candidates) {
                if (interval.second <= farthest_right) continue;
                farthest_right = interval.second;
                if (!used_intervals.insert(interval).second) continue;
                result.push_back(Run{period, interval.first, interval.second});
            }
        }
        return result;
    }
};

}  // namespace internal

// Returns all runs as (minimum period, maximal half-open interval),
// sorted lexicographically by (period, left, right).
template <class Sequence>
std::vector<Run> enumerate_runs(const Sequence& sequence) {
    return internal::RunEnumerator<Sequence>(sequence).enumerate();
}

}  // namespace string
}  // namespace m1une


#line 1 "string/string_hash.hpp"



#line 5 "string/string_hash.hpp"
#include <cstdint>
#line 7 "string/string_hash.hpp"
#include <string_view>

namespace m1une {
namespace string {

struct StringHash {
    std::uint32_t first;
    std::uint32_t second;
    std::uint32_t first_power;
    std::uint32_t second_power;
    std::size_t length;

    friend constexpr bool operator==(const StringHash& left, const StringHash& right) {
        return left.length == right.length && left.first == right.first && left.second == right.second;
    }
};

namespace string_hash_detail {

inline constexpr std::uint64_t first_mod = 1'000'000'007;
inline constexpr std::uint64_t second_mod = 1'000'000'009;
inline constexpr std::uint64_t base = 911'382'323;

}  // namespace string_hash_detail

// Computes a double polynomial hash. Bytes are interpreted as unsigned.
constexpr StringHash hash_string(std::string_view value) {
    using namespace string_hash_detail;
    std::uint64_t first = 0;
    std::uint64_t second = 0;
    std::uint64_t first_power = 1;
    std::uint64_t second_power = 1;
    for (char character : value) {
        std::uint64_t symbol = static_cast<unsigned char>(character) + std::uint64_t(1);
        first = (first * base + symbol) % first_mod;
        second = (second * base + symbol) % second_mod;
        first_power = first_power * base % first_mod;
        second_power = second_power * base % second_mod;
    }
    return StringHash{
        static_cast<std::uint32_t>(first),
        static_cast<std::uint32_t>(second),
        static_cast<std::uint32_t>(first_power),
        static_cast<std::uint32_t>(second_power),
        value.size(),
    };
}

constexpr StringHash hash_string(const std::string& value) {
    return hash_string(std::string_view(value));
}

constexpr StringHash hash_string(const char* value) {
    return hash_string(std::string_view(value));
}

// Returns the hash of the concatenation represented by `left` and `right`.
constexpr StringHash concat_string_hash(const StringHash& left, const StringHash& right) {
    using namespace string_hash_detail;
    return StringHash{
        static_cast<std::uint32_t>((std::uint64_t(left.first) * right.first_power + right.first) % first_mod),
        static_cast<std::uint32_t>((std::uint64_t(left.second) * right.second_power + right.second) % second_mod),
        static_cast<std::uint32_t>(std::uint64_t(left.first_power) * right.first_power % first_mod),
        static_cast<std::uint32_t>(std::uint64_t(left.second_power) * right.second_power % second_mod),
        left.length + right.length,
    };
}

// Hash adapter for std::unordered_map and std::unordered_set.
struct StringHasher {
    using is_transparent = void;

    constexpr std::size_t operator()(std::string_view value) const {
        return operator()(hash_string(value));
    }

    constexpr std::size_t operator()(const std::string& value) const {
        return operator()(std::string_view(value));
    }

    constexpr std::size_t operator()(const char* value) const {
        return operator()(std::string_view(value));
    }

    constexpr std::size_t operator()(const StringHash& value) const {
        std::uint64_t combined = (std::uint64_t(value.first) << 32) | value.second;
        combined ^= std::uint64_t(value.length) + 0x9e3779b97f4a7c15ULL;
        combined ^= combined >> 30;
        combined *= 0xbf58476d1ce4e5b9ULL;
        combined ^= combined >> 27;
        combined *= 0x94d049bb133111ebULL;
        combined ^= combined >> 31;
        return static_cast<std::size_t>(combined);
    }
};

}  // namespace string
}  // namespace m1une


#line 1 "string/suffix_automaton.hpp"



#line 11 "string/suffix_automaton.hpp"

namespace m1une {
namespace string {

template <int AlphabetSize = 26, int FirstCharacter = 'a'>
struct SuffixAutomaton {
    static_assert(0 < AlphabetSize);

    using state_id = int;
    static constexpr state_id root_state = 0;
    static constexpr state_id null_state = -1;

    struct State {
        std::array<state_id, AlphabetSize> next;
        state_id suffix_link;
        int length;
        int first_end;
        int direct_occurrences;
        bool clone;

        State(int length_value = 0)
            : suffix_link(null_state),
              length(length_value),
              first_end(0),
              direct_occurrences(0),
              clone(false) {
            next.fill(null_state);
        }
    };

   private:
    std::vector<State> _states;
    state_id _last;
    int _text_length;

    template <class Symbol>
    static int symbol_index(const Symbol& symbol) {
        int index = int(symbol) - FirstCharacter;
        assert(0 <= index && index < AlphabetSize);
        return index;
    }

    state_id new_state(int length) {
        assert(_states.size() < std::size_t(std::numeric_limits<int>::max()));
        _states.emplace_back(length);
        return int(_states.size()) - 1;
    }

   public:
    SuffixAutomaton() {
        clear();
    }

    template <class Sequence>
    explicit SuffixAutomaton(const Sequence& sequence) {
        clear();
        build(sequence);
    }

    int state_count() const {
        return int(_states.size());
    }

    int size() const {
        return state_count();
    }

    bool empty() const {
        return _text_length == 0;
    }

    int text_length() const {
        return _text_length;
    }

    state_id root() const {
        return root_state;
    }

    state_id last() const {
        return _last;
    }

    const State& state(state_id id) const {
        assert(0 <= id && id < state_count());
        return _states[id];
    }

    const std::vector<State>& states() const {
        return _states;
    }

    int minimum_length(state_id id) const {
        assert(0 <= id && id < state_count());
        return id == root_state ? 0 : _states[_states[id].suffix_link].length + 1;
    }

    template <class Symbol>
    state_id transition(state_id id, const Symbol& symbol) const {
        assert(0 <= id && id < state_count());
        return _states[id].next[symbol_index(symbol)];
    }

    void reserve(std::size_t text_capacity) {
        _states.reserve(2 * text_capacity);
    }

    void clear() {
        _states.clear();
        _states.emplace_back();
        _last = root_state;
        _text_length = 0;
    }

    template <class Symbol>
    state_id add(const Symbol& value) {
        int symbol = symbol_index(value);
        assert(_text_length < std::numeric_limits<int>::max());
        _text_length++;

        state_id current = new_state(_states[_last].length + 1);
        _states[current].first_end = _text_length;
        _states[current].direct_occurrences = 1;

        state_id p = _last;
        while (p != null_state && _states[p].next[symbol] == null_state) {
            _states[p].next[symbol] = current;
            p = _states[p].suffix_link;
        }

        if (p == null_state) {
            _states[current].suffix_link = root_state;
        } else {
            state_id q = _states[p].next[symbol];
            if (_states[p].length + 1 == _states[q].length) {
                _states[current].suffix_link = q;
            } else {
                state_id clone = new_state(_states[p].length + 1);
                _states[clone] = _states[q];
                _states[clone].length = _states[p].length + 1;
                _states[clone].direct_occurrences = 0;
                _states[clone].clone = true;

                while (p != null_state && _states[p].next[symbol] == q) {
                    _states[p].next[symbol] = clone;
                    p = _states[p].suffix_link;
                }
                _states[q].suffix_link = clone;
                _states[current].suffix_link = clone;
            }
        }

        _last = current;
        return current;
    }

    template <class Sequence>
    void build(const Sequence& sequence) {
        for (const auto& symbol : sequence) add(symbol);
    }

    template <class Sequence>
    state_id find(const Sequence& sequence) const {
        state_id current = root_state;
        for (const auto& symbol : sequence) {
            current = transition(current, symbol);
            if (current == null_state) return null_state;
        }
        return current;
    }

    template <class Sequence>
    bool contains(const Sequence& sequence) const {
        return find(sequence) != null_state;
    }

    std::vector<state_id> length_order() const {
        std::vector<int> count(_text_length + 1, 0);
        for (const State& current : _states) count[current.length]++;
        for (int length = 1; length <= _text_length; length++) count[length] += count[length - 1];

        std::vector<state_id> order(state_count());
        for (state_id id = state_count() - 1; id >= 0; id--) {
            order[--count[_states[id].length]] = id;
        }
        return order;
    }

    std::vector<long long> occurrence_counts() const {
        std::vector<long long> result(state_count(), 0);
        for (state_id id = 0; id < state_count(); id++) {
            result[id] = _states[id].direct_occurrences;
        }
        std::vector<state_id> order = length_order();
        for (int i = int(order.size()) - 1; i > 0; i--) {
            state_id id = order[i];
            result[_states[id].suffix_link] += result[id];
        }
        return result;
    }

    std::vector<bool> terminal_states() const {
        std::vector<bool> result(state_count(), false);
        for (state_id id = _last; id != null_state; id = _states[id].suffix_link) {
            result[id] = true;
        }
        return result;
    }

    long long distinct_substring_count() const {
        long long result = 0;
        for (state_id id = 1; id < state_count(); id++) {
            result += _states[id].length - _states[_states[id].suffix_link].length;
        }
        return result;
    }

    std::pair<int, int> longest_representative(state_id id) const {
        assert(0 <= id && id < state_count());
        int end = _states[id].first_end;
        return {end - _states[id].length, end};
    }

    template <class Sequence>
    std::pair<int, int> representative_occurrence(const Sequence& sequence) const {
        state_id id = root_state;
        int length = 0;
        for (const auto& symbol : sequence) {
            id = transition(id, symbol);
            if (id == null_state) return {-1, -1};
            length++;
        }
        int end = _states[id].first_end;
        return {end - length, end};
    }

    template <class Sequence>
    std::pair<int, int> longest_common_substring(const Sequence& sequence) const {
        state_id current = root_state;
        int current_length = 0;
        int best_length = 0;
        int best_end = 0;
        int end = 0;

        for (const auto& value : sequence) {
            int symbol = symbol_index(value);
            while (current != root_state && _states[current].next[symbol] == null_state) {
                current = _states[current].suffix_link;
                current_length = std::min(current_length, _states[current].length);
            }
            state_id next = _states[current].next[symbol];
            if (next == null_state) {
                current = root_state;
                current_length = 0;
            } else {
                current = next;
                current_length++;
            }
            end++;
            if (best_length < current_length) {
                best_length = current_length;
                best_end = end;
            }
        }
        return {best_end - best_length, best_end};
    }
};

}  // namespace string
}  // namespace m1une


#line 1 "string/suffix_tree.hpp"



#line 11 "string/suffix_tree.hpp"

namespace m1une {
namespace string {

template <int AlphabetSize = 26, int FirstCharacter = 'a'>
struct SuffixTree {
    static_assert(0 < AlphabetSize);

    using node_id = int;
    static constexpr node_id root_node = 0;
    static constexpr node_id null_node = -1;
    static constexpr int terminal_symbol = AlphabetSize;

    struct Node {
        std::array<node_id, AlphabetSize + 1> next;
        node_id suffix_link;
        node_id parent;
        int left;
        int right;
        int suffix_start;
        int representative_suffix;
        int leaf_count;
        int incoming_symbol;
        node_id first_child;
        node_id next_sibling;
        int child_count;

        Node(int left_value = 0, int right_value = 0, node_id parent_value = null_node)
            : suffix_link(null_node),
              parent(parent_value),
              left(left_value),
              right(right_value),
              suffix_start(-1),
              representative_suffix(-1),
              leaf_count(0),
              incoming_symbol(-1),
              first_child(null_node),
              next_sibling(null_node),
              child_count(0) {
            next.fill(null_node);
        }
    };

    struct Locus {
        node_id node;
        int offset;

        explicit operator bool() const {
            return node != null_node;
        }

        friend bool operator==(const Locus&, const Locus&) = default;
    };

   private:
    struct ActivePoint {
        node_id node;
        int offset;
    };

    std::vector<Node> _nodes;
    std::vector<int> _text;
    ActivePoint _active;
    int _text_length;

    template <class Symbol>
    static int symbol_index(const Symbol& symbol) {
        int index = int(symbol) - FirstCharacter;
        assert(0 <= index && index < AlphabetSize);
        return index;
    }

    int edge_length_unchecked(node_id id) const {
        return _nodes[id].right - _nodes[id].left;
    }

    node_id new_node(int left, int right, node_id parent) {
        assert(_nodes.size() < std::size_t(std::numeric_limits<int>::max()));
        _nodes.emplace_back(left, right, parent);
        return int(_nodes.size()) - 1;
    }

    ActivePoint go(ActivePoint point, int left, int right) const {
        while (left < right) {
            if (point.offset == edge_length_unchecked(point.node)) {
                point = {_nodes[point.node].next[_text[left]], 0};
                if (point.node == null_node) return point;
            } else {
                if (_text[_nodes[point.node].left + point.offset] != _text[left]) {
                    return {null_node, 0};
                }
                int remaining = edge_length_unchecked(point.node) - point.offset;
                if (right - left < remaining) {
                    point.offset += right - left;
                    return point;
                }
                left += remaining;
                point.offset = edge_length_unchecked(point.node);
            }
        }
        return point;
    }

    node_id split(ActivePoint point) {
        if (point.offset == edge_length_unchecked(point.node)) return point.node;
        if (point.offset == 0) return _nodes[point.node].parent;

        node_id child = point.node;
        node_id parent = _nodes[child].parent;
        int left = _nodes[child].left;
        node_id middle = new_node(left, left + point.offset, parent);
        _nodes[parent].next[_text[left]] = middle;
        _nodes[middle].next[_text[left + point.offset]] = child;
        _nodes[child].parent = middle;
        _nodes[child].left += point.offset;
        return middle;
    }

    node_id get_suffix_link(node_id id) {
        if (_nodes[id].suffix_link != null_node) return _nodes[id].suffix_link;
        node_id parent = _nodes[id].parent;
        if (parent == null_node) return root_node;

        node_id parent_link = get_suffix_link(parent);
        ActivePoint point = {
            parent_link,
            edge_length_unchecked(parent_link)
        };
        int left = _nodes[id].left + (parent == root_node);
        point = go(point, left, _nodes[id].right);
        assert(point.node != null_node);
        return _nodes[id].suffix_link = split(point);
    }

    void extend(int position) {
        while (true) {
            ActivePoint next = go(_active, position, position + 1);
            if (next.node != null_node) {
                _active = next;
                return;
            }

            node_id middle = split(_active);
            node_id leaf = new_node(position, int(_text.size()), middle);
            _nodes[middle].next[_text[position]] = leaf;

            _active.node = get_suffix_link(middle);
            _active.offset = edge_length_unchecked(_active.node);
            if (middle == root_node) return;
        }
    }

    void finish_metadata() {
        std::vector<node_id> order;
        order.reserve(_nodes.size());
        order.push_back(root_node);
        std::vector<int> depth(_nodes.size(), 0);

        for (std::size_t i = 0; i < order.size(); i++) {
            node_id id = order[i];
            node_id previous_child = null_node;
            for (int symbol = 0; symbol <= terminal_symbol; symbol++) {
                node_id child = _nodes[id].next[symbol];
                if (child == null_node) continue;
                _nodes[child].incoming_symbol = symbol;
                if (previous_child == null_node) {
                    _nodes[id].first_child = child;
                } else {
                    _nodes[previous_child].next_sibling = child;
                }
                previous_child = child;
                _nodes[id].child_count++;
                depth[child] = depth[id] + edge_length_unchecked(child);
                order.push_back(child);
            }
        }

        for (int i = int(order.size()) - 1; i >= 0; i--) {
            node_id id = order[i];
            bool leaf = true;
            for (node_id child : _nodes[id].next) {
                if (child == null_node) continue;
                leaf = false;
                _nodes[id].leaf_count += _nodes[child].leaf_count;
                if (_nodes[id].representative_suffix == -1) {
                    _nodes[id].representative_suffix = _nodes[child].representative_suffix;
                }
            }
            if (leaf) {
                _nodes[id].suffix_start = int(_text.size()) - depth[id];
                _nodes[id].representative_suffix = _nodes[id].suffix_start;
                _nodes[id].leaf_count = 1;
            }
        }
    }

    void initialize() {
        _nodes.clear();
        _nodes.reserve(2 * _text.size() + 1);
        _nodes.emplace_back();
        _nodes[root_node].suffix_link = root_node;
        _active = {root_node, 0};
        for (int position = 0; position < int(_text.size()); position++) extend(position);
        finish_metadata();
    }

   public:
    SuffixTree() {
        clear();
    }

    template <class Sequence>
    explicit SuffixTree(const Sequence& sequence) {
        build(sequence);
    }

    int size() const {
        return node_count();
    }

    bool empty() const {
        return _text_length == 0;
    }

    int node_count() const {
        return int(_nodes.size());
    }

    int text_length() const {
        return _text_length;
    }

    node_id root() const {
        return root_node;
    }

    const Node& node(node_id id) const {
        assert(0 <= id && id < node_count());
        return _nodes[id];
    }

    const std::vector<Node>& nodes() const {
        return _nodes;
    }

    int edge_length(node_id id) const {
        assert(0 <= id && id < node_count());
        return edge_length_unchecked(id);
    }

    bool is_leaf(node_id id) const {
        assert(0 <= id && id < node_count());
        return _nodes[id].suffix_start != -1;
    }

    template <class Symbol>
    node_id child(node_id id, const Symbol& symbol) const {
        assert(0 <= id && id < node_count());
        return _nodes[id].next[symbol_index(symbol)];
    }

    node_id child_by_index(node_id id, int symbol) const {
        assert(0 <= id && id < node_count());
        assert(0 <= symbol && symbol <= terminal_symbol);
        return _nodes[id].next[symbol];
    }

    template <class Callback>
    void for_each_child(node_id id, Callback callback) const {
        assert(0 <= id && id < node_count());
        for (
            node_id child_id = _nodes[id].first_child;
            child_id != null_node;
            child_id = _nodes[child_id].next_sibling
        ) {
            callback(_nodes[child_id].incoming_symbol, child_id);
        }
    }

    void clear() {
        _text.clear();
        _text.push_back(terminal_symbol);
        _text_length = 0;
        initialize();
    }

    template <class Sequence>
    void build(const Sequence& sequence) {
        _text.clear();
        for (const auto& symbol : sequence) _text.push_back(symbol_index(symbol));
        assert(_text.size() < std::size_t(std::numeric_limits<int>::max()));
        _text_length = int(_text.size());
        _text.push_back(terminal_symbol);
        initialize();
    }

    template <class Sequence>
    Locus find(const Sequence& sequence) const {
        ActivePoint point = {root_node, 0};
        for (const auto& value : sequence) {
            int symbol = symbol_index(value);
            if (point.offset == edge_length_unchecked(point.node)) {
                point = {_nodes[point.node].next[symbol], 0};
                if (point.node == null_node) return {null_node, 0};
            }
            if (_text[_nodes[point.node].left + point.offset] != symbol) {
                return {null_node, 0};
            }
            point.offset++;
        }
        return {point.node, point.offset};
    }

    template <class Sequence>
    bool contains(const Sequence& sequence) const {
        return bool(find(sequence));
    }

    template <class Sequence>
    int count_occurrences(const Sequence& sequence) const {
        Locus locus = find(sequence);
        return locus ? _nodes[locus.node].leaf_count : 0;
    }

    template <class Sequence>
    std::pair<int, int> representative_occurrence(const Sequence& sequence) const {
        Locus locus = {root_node, 0};
        int length = 0;
        for (const auto& value : sequence) {
            int symbol = symbol_index(value);
            if (locus.offset == edge_length_unchecked(locus.node)) {
                locus = {_nodes[locus.node].next[symbol], 0};
                if (locus.node == null_node) return {-1, -1};
            }
            if (_text[_nodes[locus.node].left + locus.offset] != symbol) return {-1, -1};
            locus.offset++;
            length++;
        }
        int left = _nodes[locus.node].representative_suffix;
        return {left, left + length};
    }

    long long distinct_substring_count() const {
        long long result = 0;
        for (node_id id = 1; id < node_count(); id++) {
            result += std::max(0, std::min(_nodes[id].right, _text_length) - _nodes[id].left);
        }
        return result;
    }
};

}  // namespace string
}  // namespace m1une


#line 1 "string/trie.hpp"



#line 9 "string/trie.hpp"

namespace m1une {
namespace string {

// A multiset trie for a contiguous character alphabet.
template <int AlphabetSize = 26, int FirstCharacter = 'a'>
struct Trie {
    static_assert(0 < AlphabetSize);

    using node_id = int;
    static constexpr node_id null_node = -1;

    struct Node {
        std::array<node_id, AlphabetSize> child;
        int subtree_count;
        int terminal_count;

        Node() : subtree_count(0), terminal_count(0) {
            child.fill(null_node);
        }
    };

   private:
    std::vector<Node> _nodes;
    int _distinct_size;

    template <class Symbol>
    static int symbol_index(const Symbol& symbol) {
        int index = int(symbol) - FirstCharacter;
        assert(0 <= index && index < AlphabetSize);
        return index;
    }

    node_id new_node() {
        assert(_nodes.size() < std::size_t(std::numeric_limits<int>::max()));
        _nodes.emplace_back();
        return int(_nodes.size()) - 1;
    }

    template <class Sequence>
    node_id find_node(const Sequence& sequence) const {
        node_id node = 0;
        for (const auto& symbol : sequence) {
            node = _nodes[node].child[symbol_index(symbol)];
            if (node == null_node || _nodes[node].subtree_count == 0) {
                return null_node;
            }
        }
        return node;
    }

   public:
    Trie() : _nodes(1), _distinct_size(0) {}

    int size() const {
        return _nodes[0].subtree_count;
    }

    int distinct_size() const {
        return _distinct_size;
    }

    bool empty() const {
        return size() == 0;
    }

    node_id root() const {
        return 0;
    }

    const Node& node(node_id id) const {
        assert(0 <= id && std::size_t(id) < _nodes.size());
        return _nodes[id];
    }

    template <class Sequence>
    node_id find(const Sequence& sequence) const {
        return find_node(sequence);
    }

    std::size_t node_count() const {
        return _nodes.size();
    }

    void reserve(std::size_t node_capacity) {
        _nodes.reserve(node_capacity);
    }

    void clear() {
        _nodes.clear();
        _nodes.emplace_back();
        _distinct_size = 0;
    }

    template <class Sequence>
    node_id insert(const Sequence& sequence, int multiplicity = 1) {
        assert(0 < multiplicity);
        node_id node = 0;
        _nodes[node].subtree_count += multiplicity;
        for (const auto& symbol : sequence) {
            int index = symbol_index(symbol);
            node_id child = _nodes[node].child[index];
            if (child == null_node) {
                child = new_node();
                _nodes[node].child[index] = child;
            }
            node = child;
            _nodes[node].subtree_count += multiplicity;
        }
        if (_nodes[node].terminal_count == 0) _distinct_size++;
        _nodes[node].terminal_count += multiplicity;
        return node;
    }

    template <class Sequence>
    int count(const Sequence& sequence) const {
        node_id node = find_node(sequence);
        return node == null_node ? 0 : _nodes[node].terminal_count;
    }

    template <class Sequence>
    bool contains(const Sequence& sequence) const {
        return count(sequence) != 0;
    }

    // Returns the number of stored strings beginning with prefix.
    template <class Sequence>
    int prefix_count(const Sequence& prefix) const {
        node_id node = find_node(prefix);
        return node == null_node ? 0 : _nodes[node].subtree_count;
    }

    template <class Sequence>
    bool starts_with(const Sequence& prefix) const {
        return prefix_count(prefix) != 0;
    }

    template <class Sequence>
    bool erase_one(const Sequence& sequence) {
        node_id terminal = find_node(sequence);
        if (terminal == null_node || _nodes[terminal].terminal_count == 0) {
            return false;
        }

        int node = 0;
        _nodes[node].subtree_count--;
        for (const auto& symbol : sequence) {
            node = _nodes[node].child[symbol_index(symbol)];
            _nodes[node].subtree_count--;
        }
        _nodes[node].terminal_count--;
        if (_nodes[node].terminal_count == 0) _distinct_size--;
        return true;
    }

    template <class Sequence>
    bool erase(const Sequence& sequence) {
        return erase_one(sequence);
    }

    template <class Sequence>
    int erase_all(const Sequence& sequence) {
        int multiplicity = count(sequence);
        if (multiplicity == 0) return 0;

        int node = 0;
        _nodes[node].subtree_count -= multiplicity;
        for (const auto& symbol : sequence) {
            node = _nodes[node].child[symbol_index(symbol)];
            _nodes[node].subtree_count -= multiplicity;
        }
        _nodes[node].terminal_count = 0;
        _distinct_size--;
        return multiplicity;
    }

    // Calls callback(length, multiplicity) for every stored prefix.
    // The empty prefix is reported with length 0 when it is stored.
    template <class Sequence, class Callback>
    void for_each_prefix(const Sequence& sequence, Callback callback) const {
        int node = 0;
        if (_nodes[node].terminal_count != 0) {
            callback(0, _nodes[node].terminal_count);
        }

        int length = 0;
        for (const auto& symbol : sequence) {
            node = _nodes[node].child[symbol_index(symbol)];
            if (node == null_node || _nodes[node].subtree_count == 0) return;
            length++;
            if (_nodes[node].terminal_count != 0) {
                callback(length, _nodes[node].terminal_count);
            }
        }
    }

    // Returns the length of the longest stored string that is a prefix.
    // Returns -1 when no stored prefix exists.
    template <class Sequence>
    int longest_prefix(const Sequence& sequence) const {
        int result = _nodes[0].terminal_count == 0 ? -1 : 0;
        for_each_prefix(sequence, [&result](int length, int) {
            result = length;
        });
        return result;
    }
};

}  // namespace string
}  // namespace m1une


#line 1 "string/wildcard_pattern_matching.hpp"



#line 7 "string/wildcard_pattern_matching.hpp"

#line 1 "math/fps/convolution.hpp"



#line 8 "math/fps/convolution.hpp"
#include <cstring>
#include <new>
#line 13 "math/fps/convolution.hpp"

#if defined(__GNUC__) && !defined(__clang__) && \
    (defined(__x86_64__) || defined(__i386__)) && \
    !defined(M1UNE_FPS_DISABLE_X86_SIMD)
#include <immintrin.h>
#define M1UNE_FPS_HAS_X86_SIMD 1
#pragma GCC push_options
#pragma GCC target("avx2,bmi")
#endif

#line 1 "math/fps/internal/ntt998_faster.hpp"



#ifdef M1UNE_FPS_HAS_X86_SIMD

#line 9 "math/fps/internal/ntt998_faster.hpp"

#include <immintrin.h>

namespace m1une {
namespace fps {
namespace internal {
namespace fast998_v2 {

// Fixed-modulus AVX2 transform with an in-register degree-8 residue product.

using u32=unsigned;
using u64=unsigned long long;
using idt=std::size_t;
using I256=__m256i;
inline void store256(void*p,I256 x){
    _mm256_store_si256((I256*)p,x);
}
inline I256 load256(const void*p){
    return _mm256_load_si256((const I256*)p);
}
constexpr u32 shrk(u32 x,u32 M){
    return std::min(x,x-M);
}
constexpr u32 dilt(u32 x,u32 M){
    return std::min(x,x+M);
}
constexpr u32 reduce(u64 x,u32 niv,u32 M){
    return (x+u64(u32(x)*niv)*M)>>32;
}
constexpr u32 mul(u32 x,u32 y,u32 niv,u32 M){
    return reduce(u64(x)*y,niv,M);
}
constexpr u32 mul_s(u32 x,u32 y,u32 niv,u32 M){
    return shrk(reduce(u64(x)*y,niv,M),M);
}
constexpr u32 qpw(u32 a,u32 b,u32 niv,u32 M,u32 r){
    for(;b;b>>=1,a=mul(a,a,niv,M)){
        if(b&1){
            r=mul(r,a,niv,M);
        }
    }
    return r;
}
constexpr u32 qpw_s(u32 a,u32 b,u32 niv,u32 M,u32 r){
    return shrk(qpw(a,b,niv,M,r),M);
}
inline I256 shrk32(I256 x,I256 M){
    return _mm256_min_epu32(x,_mm256_sub_epi32(x,M));
}
inline I256 dilt32(I256 x,I256 M){
    return _mm256_min_epu32(x,_mm256_add_epi32(x,M));
}
inline I256 Ladd32(I256 x,I256 y,I256){
    return _mm256_add_epi32(x,y);
}
inline I256 Lsub32(I256 x,I256 y,I256 M){
    return _mm256_add_epi32(_mm256_sub_epi32(x,y),M);
}
inline I256 add32(I256 x,I256 y,I256 M){
    return shrk32(_mm256_add_epi32(x,y),M);
}
inline I256 sub32(I256 x,I256 y,I256 M){
    return dilt32(_mm256_sub_epi32(x,y),M);
}
template<int msk>inline I256 neg32_m(I256 x,I256 M){
    return _mm256_blend_epi32(x,_mm256_sub_epi32(M,x),msk);
}
inline I256 reduce(I256 a,I256 b,I256 niv,I256 M){
    I256 c=_mm256_mul_epu32(a,niv),d=_mm256_mul_epu32(b,niv);
    c=_mm256_mul_epu32(c,M),d=_mm256_mul_epu32(d,M);
    return _mm256_blend_epi32(_mm256_srli_epi64(_mm256_add_epi64(a,c),32),_mm256_add_epi64(b,d),0xaa);
}
inline I256 mul(I256 a,I256 b,I256 niv,I256 M){
    return reduce(_mm256_mul_epu32(a,b),_mm256_mul_epu32(_mm256_srli_epi64(a,32),_mm256_srli_epi64(b,32)),niv,M);
}
inline I256 mul_s(I256 a,I256 b,I256 niv,I256 M){
    return shrk32(mul(a,b,niv,M),M);
}
inline I256 mul_bsm(I256 a,I256 b,I256 niv,I256 M){
    return reduce(_mm256_mul_epu32(a,b),_mm256_mul_epu32(_mm256_srli_epi64(a,32),b),niv,M);
}
inline I256 mul_bsmfxd(I256 a,I256 b,I256 bniv,I256 M){
    I256 cc=_mm256_mul_epu32(a,bniv),dd=_mm256_mul_epu32(_mm256_srli_epi64(a,32),bniv);
    I256 c=_mm256_mul_epu32(a,b),d=_mm256_mul_epu32(_mm256_srli_epi64(a,32),b);
    cc=_mm256_mul_epu32(cc,M),dd=_mm256_mul_epu32(dd,M);
    return _mm256_blend_epi32(_mm256_srli_epi64(_mm256_add_epi64(c,cc),32),_mm256_add_epi64(d,dd),0xaa);
}
inline I256 mul_bfxd(I256 a,I256 b,I256 bniv,I256 M){
    I256 cc=_mm256_mul_epu32(a,bniv),dd=_mm256_mul_epu32(_mm256_srli_epi64(a,32),_mm256_srli_epi64(bniv,32));
    I256 c=_mm256_mul_epu32(a,b),d=_mm256_mul_epu32(_mm256_srli_epi64(a,32),_mm256_srli_epi64(b,32));
    cc=_mm256_mul_epu32(cc,M),dd=_mm256_mul_epu32(dd,M);
    return _mm256_blend_epi32(_mm256_srli_epi64(_mm256_add_epi64(c,cc),32),_mm256_add_epi64(d,dd),0xaa);
}
inline I256 mul_upd_rt(I256 a,I256 bu,I256 M){
    I256 cc=_mm256_mul_epu32(a,bu),c=_mm256_mul_epu32(a,_mm256_srli_epi64(bu,32));
    cc=_mm256_mul_epu32(cc,M);
    return shrk32(_mm256_srli_epi64(_mm256_add_epi64(c,cc),32),M);
}
constexpr auto _mxlg=26,_lg_itth=6;
constexpr auto _itth=idt(1)<<_lg_itth;
static_assert(_lg_itth%2==0);
struct FNTT32_info{
    u32 mod,mod2,niv,one,r2,r3,img,imgniv,RT1[_mxlg];
    alignas(32) std::array<u32,8> rt3[_mxlg-2],rt3i[_mxlg-2],bwbr,bwb,bwbi,rt4[_mxlg-3],rt4niv[_mxlg-3],rt4i[_mxlg-3],rt4iniv[_mxlg-3],pr2,pr4,pr2niv,pr4niv,pr2i,pr2iniv,pr4i,pr4iniv;
    constexpr FNTT32_info(const u32 m):mod(m),mod2(m*2),niv([&]{u32 n=2+m;for(int i=0;i<4;++i){n*=2+m*n;}return n;}()),one((-m)%m),r2((-u64(m))%m),r3(mul_s(r2,r2,niv,m)),img{},imgniv{},RT1{},rt3{},rt3i{},bwbr{},bwb{},bwbi{},rt4{},rt4niv{},rt4i{},rt4iniv{},pr2{},pr4{},pr2niv{},pr4niv{},pr2i{},pr2iniv{},pr4i{},pr4iniv{}{
        const int k=__builtin_ctz(m-1);
		u32 _g=mul(3,r2,niv,mod);
        for(;;++_g){
            if(qpw_s(_g,mod>>1,niv,mod,one)!=one){
                break;
            }
        }
		_g=qpw(_g,mod>>k,niv,mod,one);
        u32 rt1[_mxlg-1],rt1i[_mxlg-1];
        rt1[k-2]=_g,rt1i[k-2]=qpw(_g,mod-2,niv,mod,one);
        for(int i=k-2;i>0;--i){
            rt1[i-1]=mul(rt1[i],rt1[i],niv,mod);
            rt1i[i-1]=mul(rt1i[i],rt1i[i],niv,mod);
        }
        RT1[k-1]=qpw_s(_g,3,niv,mod,one);
        for(int i=k-1;i>0;--i){
			RT1[i-1]=mul_s(RT1[i],RT1[i],niv,mod);
        }
        img=rt1[0],imgniv=img*niv;
        bwbr={one,0,one,0,one};
        bwb={rt1[1],0,rt1[0],0,mod-mul_s(rt1[0],rt1[1],niv,mod)};
        bwbi={rt1i[1],0,rt1i[0],0,mul_s(rt1i[0],rt1i[1],niv,mod)};
        u32 pr=one,pri=one;
        for(int i=0;i<k-2;++i){
            const u32 r=mul_s(pr,rt1[i+1],niv,mod),ri=mul_s(pri,rt1i[i+1],niv,mod);
            const u32 r2=mul_s(r,r,niv,mod),r2i=mul_s(ri,ri,niv,mod);
            const u32 r3=mul_s(r,r2,niv,mod),r3i=mul_s(ri,r2i,niv,mod);
            rt3[i]={r*niv,r,r2*niv,r2,r3*niv,r3};
            rt3i[i]={ri*niv,ri,r2i*niv,r2i,r3i*niv,r3i};
            pr=mul(pr,rt1i[i+1],niv,mod),pri=mul(pri,rt1[i+1],niv,mod);
        }
        pr=one,pri=one;
        for(int i=0;i<k-3;++i){
            const u32 r=mul_s(pr,rt1[i+2],niv,mod),ri=mul_s(pri,rt1i[i+2],niv,mod);
            rt4[i][0]=rt4i[i][0]=one;
            for(int j=1;j<8;++j){
                rt4[i][j]=mul_s(rt4[i][j-1],r,niv,mod);
                rt4i[i][j]=mul_s(rt4i[i][j-1],ri,niv,mod);
            }
            for(int j=0;j<8;++j){
                rt4niv[i][j]=rt4[i][j]*niv;
                rt4iniv[i][j]=rt4i[i][j]*niv;
            }
            pr=mul(pr,rt1i[i+2],niv,mod),pri=mul(pri,rt1[i+2],niv,mod);
        }
        pr2={one,one,one,img,one,one,one,img};
        pr4={one,one,one,one,one,rt1[1],img,mul_s(img,rt1[1],niv,mod)};
        const u32 nr2=mod-r2,imgr2=mul_s(img,r2,niv,mod);
        pr2i={nr2,nr2,nr2,imgr2,nr2,nr2,nr2,imgr2};
        pr4i={one,one,one,one,one,rt1i[1],rt1i[0],mul_s(rt1i[0],rt1i[1],niv,mod)};
        for(int j=0;j<8;++j){
            pr2niv[j]=pr2[j]*niv,pr4niv[j]=pr4[j]*niv;
            pr2iniv[j]=pr2i[j]*niv,pr4iniv[j]=pr4i[j]*niv;
        }
    }
};
inline void vector_dif(I256*const f,const idt n,const FNTT32_info*info){
    alignas(32) std::array<u32,8> st_1[_mxlg>>1];
    const I256 Mod=_mm256_set1_epi32(info->mod),Mod2=_mm256_set1_epi32(info->mod2),Niv=_mm256_set1_epi32(info->niv);
    const I256 Img=_mm256_set1_epi32(info->img),ImgNiv=_mm256_set1_epi32(info->imgniv),id=_mm256_setr_epi32(0,2,0,4,0,2,0,4);
    const int lgn=__builtin_ctzll(n);
    std::fill(st_1,st_1+(lgn>>1),info->bwb);
    const idt nn=n>>(lgn&1),m=std::min(n,_itth),mm=std::min(nn,_itth);
    // I256 rr=_mm256_set1_epi32(info->one);
    if(nn!=n){
        for(idt i=0;i<nn;++i){
            auto const p0=f+i,p1=f+nn+i;
            const auto f0=load256(p0),f1=load256(p1);
            const auto g0=add32(f0,f1,Mod2),g1=Lsub32(f0,f1,Mod2);
            store256(p0,g0),store256(p1,g1);
        }
    }
    for(idt L=nn>>2;L>0;L>>=2){
        for(idt i=0;i<L;++i){
            auto const p0=f+i,p1=p0+L,p2=p1+L,p3=p2+L;
            const auto f1=load256(p1),f3=load256(p3),f2=load256(p2),f0=load256(p0);
            const auto g3=mul_bsmfxd(Lsub32(f1,f3,Mod2),Img,ImgNiv,Mod),g1=add32(f1,f3,Mod2);
            const auto g0=add32(f0,f2,Mod2),g2=sub32(f0,f2,Mod2);
            const auto h0=add32(g0,g1,Mod2),h1=Lsub32(g0,g1,Mod2);
            const auto h2=Ladd32(g2,g3,Mod2),h3=Lsub32(g2,g3,Mod2);
            store256(p0,h0),store256(p1,h1),store256(p2,h2),store256(p3,h3);
        }
    }
    for(idt j=0;j<n;j+=m){
        int t=((j==0)?std::min(_lg_itth,lgn):__builtin_ctzll(j))&-2,p=(t-2)>>1;
        for(idt L=(idt(1)<<t)>>2;L>=_itth;L>>=2,t-=2,--p){
            auto rt=load256(st_1+p);
            const auto r1=_mm256_permutevar8x32_epi32(rt,id);
            const auto r1Niv=_mm256_permutevar8x32_epi32(_mm256_mul_epu32(rt,Niv),id);
            rt=mul_upd_rt(rt,load256(info->rt3+__builtin_ctzll(~j>>t)),Mod);
            const auto r2=_mm256_shuffle_epi32(r1,_MM_PERM_BBBB),nr3=_mm256_shuffle_epi32(r1,_MM_PERM_DDDD);
            const auto r2Niv=_mm256_shuffle_epi32(r1Niv,_MM_PERM_BBBB),nr3Niv=_mm256_shuffle_epi32(r1Niv,_MM_PERM_DDDD);
            store256(st_1+p,rt);
            for(idt i=0;i<L;++i){
                auto const p0=f+i+j,p1=p0+L,p2=p1+L,p3=p2+L;
                const auto f1=load256(p1),f3=load256(p3),f2=load256(p2),f0=load256(p0);
                const auto g1=mul_bsmfxd(f1,r1,r1Niv,Mod),ng3=mul_bsmfxd(f3,nr3,nr3Niv,Mod);
                const auto g2=mul_bsmfxd(f2,r2,r2Niv,Mod),g0=shrk32(f0,Mod2);
                const auto h3=mul_bsmfxd(Ladd32(g1,ng3,Mod2),Img,ImgNiv,Mod),h1=sub32(g1,ng3,Mod2);
                const auto h0=add32(g0,g2,Mod2),h2=sub32(g0,g2,Mod2);
                const auto u0=Ladd32(h0,h1,Mod2),u1=Lsub32(h0,h1,Mod2);
                const auto u2=Ladd32(h2,h3,Mod2),u3=Lsub32(h2,h3,Mod2);
                store256(p0,u0),store256(p1,u1),store256(p2,u2),store256(p3,u3);
            }
        }
        I256*const g=f+j;
        for(idt l=mm,L=mm>>2;L;l=L,L>>=2,t-=2,--p){
            auto rt=load256(st_1+p);
            for(idt i=(j==0?l:0),k=(j+i)>>t;i<m;i+=l,++k){
                const auto r1=_mm256_permutevar8x32_epi32(rt,id);
                const auto r2=_mm256_shuffle_epi32(r1,_MM_PERM_BBBB);
                const auto nr3=_mm256_shuffle_epi32(r1,_MM_PERM_DDDD);
                for(idt j=0;j<L;++j){
                    auto const p0=g+i+j,p1=p0+L,p2=p1+L,p3=p2+L;
                    const auto f1=load256(p1),f3=load256(p3),f2=load256(p2),f0=load256(p0);
                    const auto g1=mul_bsm(f1,r1,Niv,Mod),ng3=mul_bsm(f3,nr3,Niv,Mod);
                    const auto g2=mul_bsm(f2,r2,Niv,Mod),g0=shrk32(f0,Mod2);
                    const auto h3=mul_bsmfxd(Ladd32(g1,ng3,Mod2),Img,ImgNiv,Mod),h1=sub32(g1,ng3,Mod2);
                    const auto h0=add32(g0,g2,Mod2),h2=sub32(g0,g2,Mod2);
                    const auto u0=Ladd32(h0,h1,Mod2),u1=Lsub32(h0,h1,Mod2);
                    const auto u2=Ladd32(h2,h3,Mod2),u3=Lsub32(h2,h3,Mod2);
                    store256(p0,u0),store256(p1,u1),store256(p2,u2),store256(p3,u3);
                }
                rt=mul_upd_rt(rt,load256(info->rt3+__builtin_ctzll(~k)),Mod);
            }
            store256(st_1+p,rt);
        }
        // const auto pr2=load256(&info->pr2),pr4=load256(&info->pr4);
        // const auto pr2Niv=load256(&info->pr2niv),pr4Niv=load256(&info->pr4niv);
        // for(idt i=j;i<j+m;++i){
        //     auto fi=load256(f+i);
        //     fi=mul(fi,rr,Niv,Mod);
        //     rr=shrk32(mul_bfxd(rr,load256(info->rt4+__builtin_ctzll(~i)),load256(info->rt4niv+__builtin_ctzll(~i)),Mod),Mod);
        //     fi=mul_bfxd(Ladd32(neg32_m<0xf0>(fi,Mod2),_mm256_permute2x128_si256(fi,fi,1),Mod2),pr4,pr4Niv,Mod);
        //     fi=mul_bfxd(Ladd32(neg32_m<0xcc>(fi,Mod2),_mm256_shuffle_epi32(fi,0x4e),Mod2),pr2,pr2Niv,Mod);
        //     fi=sub32(_mm256_shuffle_epi32(fi,0xb1),neg32_m<0x55>(fi,Mod2),Mod2);
        //     store256(f+i,fi);
        // }
    }
}
template<bool shrk=false>inline void vector_dit(I256*const f,idt n,const FNTT32_info*const info){
    alignas(32) std::array<u32,8> st_1[_mxlg>>1];
    const I256 Mod=_mm256_set1_epi32(info->mod),Mod2=_mm256_set1_epi32(info->mod2),Niv=_mm256_set1_epi32(info->niv);
    const I256 Img=_mm256_set1_epi32(info->img),ImgNiv=_mm256_set1_epi32(info->imgniv),id=_mm256_setr_epi32(0,2,0,4,0,2,0,4);
    const int lgn=__builtin_ctzll(n);
    std::fill(st_1,st_1+(_lg_itth>>1),info->bwbr);
    std::fill(st_1+(_lg_itth>>1),st_1+(_mxlg>>1),info->bwbi);
    const idt nn=n>>(lgn&1),mm=std::min(nn,_itth);
    // I256 rr=_mm256_set1_epi32((info->mod-1)>>(lgn+3));
    for(idt j=0;j<n;j+=mm){
        // const auto pr2=load256(&info->pr2i),pr4=load256(&info->pr4i);
        // const auto pr2Niv=load256(&info->pr2iniv),pr4Niv=load256(&info->pr4iniv);
        // for(idt i=j;i<j+mm;++i){
        //     auto fi=load256(f+i);
        //     const auto rt=rr;
        //     rr=shrk32(mul_bfxd(rr,load256(info->rt4i+__builtin_ctzll(~i)),load256(info->rt4iniv+__builtin_ctzll(~i)),Mod),Mod);
        //     fi=mul_bfxd(Ladd32(neg32_m<0xaa>(fi,Mod2),_mm256_shuffle_epi32(fi,0xb1),Mod2),pr2,pr2Niv,Mod);
        //     fi=mul_bfxd(Ladd32(neg32_m<0xcc>(fi,Mod2),_mm256_shuffle_epi32(fi,0x4e),Mod2),pr4,pr4Niv,Mod);
        //     fi=mul(Ladd32(neg32_m<0xf0>(fi,Mod2),_mm256_permute2x128_si256(fi,fi,1),Mod2),rt,Niv,Mod);
        //     store256(f+i,fi);
        // }
        I256*const g=f+j;
        int t=2,p=0;
        for(idt l=4,L=1;l<=mm;L=l,l<<=2,t+=2,++p){
            auto rt=load256(st_1+p);
            for(idt i=0,k=j>>t;i<mm;i+=l,++k){
                const auto r1=_mm256_permutevar8x32_epi32(rt,id);
                const auto r2=_mm256_shuffle_epi32(r1,_MM_PERM_BBBB);
                const auto r3=_mm256_shuffle_epi32(r1,_MM_PERM_DDDD);
                for(idt j=0;j<L;++j){
                    auto const p0=g+i+j,p1=p0+L,p2=p1+L,p3=p2+L;
                    const auto f0=load256(p0),f1=load256(p1),f2=load256(p2),f3=load256(p3);
                    const auto g0=add32(f0,f1,Mod2),g1=sub32(f0,f1,Mod2);
                    const auto g2=add32(f2,f3,Mod2),g3=mul_bsmfxd(Lsub32(f3,f2,Mod2),Img,ImgNiv,Mod);
                    const auto h0=Ladd32(g0,g2,Mod2),h1=Ladd32(g1,g3,Mod2);
                    const auto h2=Lsub32(g0,g2,Mod2),h3=Lsub32(g1,g3,Mod2);
                    const auto u0=shrk32(h0,Mod2),u1=mul_bsm(h1,r1,Niv,Mod);
                    const auto u2=mul_bsm(h2,r2,Niv,Mod),u3=mul_bsm(h3,r3,Niv,Mod);
                    store256(p0,u0),store256(p1,u1),store256(p2,u2),store256(p3,u3);
                }
                rt=mul_upd_rt(rt,load256(info->rt3i+__builtin_ctzll(~k)),Mod);
            }
            store256(st_1+p,rt);
        }
        int tt=std::min(__builtin_ctzll(~(j>>_lg_itth))+_lg_itth,lgn);
        for(idt L=_itth,l=L<<2;t<=tt;L=l,l<<=2,t+=2,++p){
            if((j+_itth)==l){
                if(shrk && l==n){
                    for(idt i=0;i<L;++i){
                        auto const p0=f+i,p1=p0+L,p2=p1+L,p3=p2+L;
                        const auto f2=load256(p2),f3=load256(p3),f0=load256(p0),f1=load256(p1);
                        const auto g3=mul_bsmfxd(Lsub32(f3,f2,Mod2),Img,ImgNiv,Mod),g2=add32(f2,f3,Mod2);
                        const auto g0=add32(f0,f1,Mod2),g1=sub32(f0,f1,Mod2);
                        const auto h0=add32(g0,g2,Mod2),h1=add32(g1,g3,Mod2);
                        const auto h2=sub32(g0,g2,Mod2),h3=sub32(g1,g3,Mod2);
                        const auto u0=shrk32(h0,Mod),u1=shrk32(h1,Mod);
                        const auto u2=shrk32(h2,Mod),u3=shrk32(h3,Mod);
                        store256(p0,u0),store256(p1,u1),store256(p2,u2),store256(p3,u3);
                    }
                }
                else{
                    for(idt i=0;i<L;++i){
                        auto const p0=f+i,p1=p0+L,p2=p1+L,p3=p2+L;
                        const auto f2=load256(p2),f3=load256(p3),f0=load256(p0),f1=load256(p1);
                        const auto g3=mul_bsmfxd(Lsub32(f3,f2,Mod2),Img,ImgNiv,Mod),g2=add32(f2,f3,Mod2);
                        const auto g0=add32(f0,f1,Mod2),g1=sub32(f0,f1,Mod2);
                        const auto h0=add32(g0,g2,Mod2),h1=add32(g1,g3,Mod2);
                        const auto h2=sub32(g0,g2,Mod2),h3=sub32(g1,g3,Mod2);
                        store256(p0,h0),store256(p1,h1),store256(p2,h2),store256(p3,h3);
                    }
                }
            }
            else{
                auto rt=load256(st_1+p);
                const auto r1=_mm256_permutevar8x32_epi32(rt,id);
                const auto r1Niv=_mm256_permutevar8x32_epi32(_mm256_mul_epu32(rt,Niv),id);
                rt=mul_upd_rt(rt,load256(info->rt3i+__builtin_ctzll(~j>>t)),Mod);
                const auto r2=_mm256_shuffle_epi32(r1,_MM_PERM_BBBB),r3=_mm256_shuffle_epi32(r1,_MM_PERM_DDDD);
                const auto r2Niv=_mm256_shuffle_epi32(r1Niv,_MM_PERM_BBBB),r3Niv=_mm256_shuffle_epi32(r1Niv,_MM_PERM_DDDD);
                store256(st_1+p,rt);
                for(idt i=0;i<L;++i){
                    auto const p0=f+j+_itth-l+i,p1=p0+L,p2=p1+L,p3=p2+L;
                    const auto f0=load256(p0),f1=load256(p1),f2=load256(p2),f3=load256(p3);
                    const auto g0=add32(f0,f1,Mod2),g1=sub32(f0,f1,Mod2);
                    const auto g2=add32(f2,f3,Mod2),g3=mul_bsmfxd(Lsub32(f3,f2,Mod2),Img,ImgNiv,Mod);
                    const auto h0=Ladd32(g0,g2,Mod2),h1=Ladd32(g1,g3,Mod2);
                    const auto h2=Lsub32(g0,g2,Mod2),h3=Lsub32(g1,g3,Mod2);
                    const auto u0=shrk32(h0,Mod2),u1=mul_bsmfxd(h1,r1,r1Niv,Mod);
                    const auto u2=mul_bsmfxd(h2,r2,r2Niv,Mod),u3=mul_bsmfxd(h3,r3,r3Niv,Mod);
                    store256(p0,u0),store256(p1,u1),store256(p2,u2),store256(p3,u3);
                }
            }
        }
    }
    if(shrk && nn==n && n<=_itth){
        for(idt i=0;i<n;++i){
            const auto f0=load256(f+i);
            store256(f+i,shrk32(f0,Mod));
        }
    }
    if(nn!=n){
        for(idt i=0;i<nn;++i){
            auto const p0=f+i,p1=f+nn+i;
            const auto f0=load256(p0),f1=load256(p1);
            const auto g0=add32(f0,f1,Mod2),g1=sub32(f0,f1,Mod2);
            if constexpr(shrk){
                const auto h0=shrk32(g0,Mod),h1=shrk32(g1,Mod);
                store256(p0,h0),store256(p1,h1);
            }
            else{
                store256(p0,g0),store256(p1,g1);
            }
        }
    }
}
// Returns fx * f[0,8) * g[0,8) (mod x^8 - ww).
[[gnu::always_inline]] inline I256 convolve8(const I256*f,const I256*g,I256 ww,I256 fx,I256 Niv,I256 Mod,I256 Mod2){
    const auto raa=load256(f),rbb=load256(g);
    const auto taa=shrk32(raa,Mod2),bb=shrk32(mul_bsm(rbb,fx,Niv,Mod),Mod);
    const auto aw=shrk32(mul_bsm(taa,ww,Niv,Mod),Mod);
    const auto aa=shrk32(taa,Mod);
    const auto awa=_mm256_permute2x128_si256(aa,aw,3);
    
    const auto b0=_mm256_permute4x64_epi64(bb,0x00),b1=_mm256_shuffle_epi32(b0,_MM_PERM_CDAB);
    const auto a0=aa,a1=_mm256_srli_epi64(a0,32);
    const auto aw7=_mm256_alignr_epi8(aa,awa,12);
    auto res00=_mm256_mul_epu32(a0,b0);
    auto res01=_mm256_mul_epu32(a1,b0);
    auto res10=_mm256_mul_epu32(aw7,b1);
    auto res11=_mm256_mul_epu32(a0,b1);

    const auto b2=_mm256_permute4x64_epi64(bb,0x55),b3=_mm256_shuffle_epi32(b2,_MM_PERM_CDAB);
    const auto aw6=_mm256_alignr_epi8(aa,awa,8);
    const auto aw5=_mm256_alignr_epi8(aa,awa,4);
    res00=_mm256_add_epi64(res00,_mm256_mul_epu32(aw6,b2));
    res01=_mm256_add_epi64(res01,_mm256_mul_epu32(aw7,b2));
    res10=_mm256_add_epi64(res10,_mm256_mul_epu32(aw5,b3));
    res11=_mm256_add_epi64(res11,_mm256_mul_epu32(aw6,b3));

    const auto b4=_mm256_permute4x64_epi64(bb,0xaa),b5=_mm256_shuffle_epi32(b4,_MM_PERM_CDAB);
    const auto aw3=_mm256_alignr_epi8(awa,aw,12);
    res00=_mm256_add_epi64(res00,_mm256_mul_epu32(awa,b4));
    res01=_mm256_add_epi64(res01,_mm256_mul_epu32(aw5,b4));
    res10=_mm256_add_epi64(res10,_mm256_mul_epu32(aw3,b5));
    res11=_mm256_add_epi64(res11,_mm256_mul_epu32(awa,b5));

    const auto b6=_mm256_permute4x64_epi64(bb,0xff),b7=_mm256_shuffle_epi32(b6,_MM_PERM_CDAB);
    const auto aw2=_mm256_alignr_epi8(awa,aw,8);
    const auto aw1=_mm256_alignr_epi8(awa,aw,4);
    res00=_mm256_add_epi64(res00,_mm256_mul_epu32(aw2,b6));
    res01=_mm256_add_epi64(res01,_mm256_mul_epu32(aw3,b6));
    res10=_mm256_add_epi64(res10,_mm256_mul_epu32(aw1,b7));
    res11=_mm256_add_epi64(res11,_mm256_mul_epu32(aw2,b7));

    res00=_mm256_add_epi64(res00,res10);
    res01=_mm256_add_epi64(res01,res11);

    return shrk32(reduce(res00,res01,Niv,Mod),Mod2);
}
inline void vector_convolution_direct(I256*f,const I256*g,idt lm,const FNTT32_info*const info){
    u32 RR=info->one;
    const auto mod=info->mod,niv=info->niv;
    const auto Fx=_mm256_set1_epi32(mul_s((mod-((mod-1)>>(__builtin_ctzll(lm)))),info->r3,niv,mod));
    const auto Niv=_mm256_set1_epi32(niv),Mod=_mm256_set1_epi32(mod),Mod2=_mm256_set1_epi32(info->mod2);
    for(idt i=0;i<lm;++i){
        store256(f+i,convolve8(f+i,g+i,_mm256_set1_epi32(RR),Fx,Niv,Mod,Mod2));
        RR=mul(RR,info->RT1[__builtin_ctzll(~i)],niv,mod);
    }
}
inline void vector_convolution_accumulate(I256*const result,const I256*const f,
                                          const I256*const g,idt lm,
                                          const FNTT32_info*const info){
    u32 RR=info->one;
    const auto mod=info->mod,niv=info->niv;
    const auto Fx=_mm256_set1_epi32(mul_s((mod-((mod-1)>>(__builtin_ctzll(lm)))),info->r3,niv,mod));
    const auto Niv=_mm256_set1_epi32(niv),Mod=_mm256_set1_epi32(mod),Mod2=_mm256_set1_epi32(info->mod2);
    for(idt i=0;i<lm;++i){
        const auto product=convolve8(f+i,g+i,_mm256_set1_epi32(RR),Fx,Niv,Mod,Mod2);
        store256(result+i,add32(load256(result+i),product,Mod2));
        RR=mul(RR,info->RT1[__builtin_ctzll(~i)],niv,mod);
    }
}

}  // namespace fast998_v2
}  // namespace internal
}  // namespace fps
}  // namespace m1une

#endif  // M1UNE_FPS_HAS_X86_SIMD


#line 24 "math/fps/convolution.hpp"
#ifdef M1UNE_FPS_HAS_X86_SIMD
#pragma GCC pop_options
#endif

#line 1 "math/modint.hpp"



#line 6 "math/modint.hpp"
#include <iostream>
#line 9 "math/modint.hpp"

namespace m1une {
namespace math {

template <uint32_t Modulus>
struct ModInt {
    static_assert(0 < Modulus, "Modulus must be positive");

   private:
    uint32_t _v;

   public:
    static constexpr uint32_t mod() {
        return Modulus;
    }

    static constexpr ModInt raw(uint32_t v) noexcept {
        ModInt x;
        x._v = v;
        return x;
    }

    constexpr ModInt() noexcept : _v(0) {}

    template <class Integer, std::enable_if_t<std::is_integral_v<Integer>, int> = 0>
    constexpr ModInt(Integer v) noexcept {
        if constexpr (std::is_signed_v<Integer>) {
            int64_t x = static_cast<int64_t>(v) % static_cast<int64_t>(Modulus);
            if (x < 0) x += Modulus;
            _v = static_cast<uint32_t>(x);
        } else {
            _v = static_cast<uint32_t>(static_cast<uint64_t>(v) % Modulus);
        }
    }

    constexpr uint32_t val() const noexcept {
        return _v;
    }

    constexpr ModInt& operator++() noexcept {
        _v++;
        if (_v == Modulus) _v = 0;
        return *this;
    }

    constexpr ModInt& operator--() noexcept {
        if (_v == 0) _v = Modulus;
        _v--;
        return *this;
    }

    constexpr ModInt operator++(int) noexcept {
        ModInt res = *this;
        ++*this;
        return res;
    }

    constexpr ModInt operator--(int) noexcept {
        ModInt res = *this;
        --*this;
        return res;
    }

    constexpr ModInt& operator+=(const ModInt& rhs) noexcept {
        _v += rhs._v;
        if (_v >= Modulus) _v -= Modulus;
        return *this;
    }

    constexpr ModInt& operator-=(const ModInt& rhs) noexcept {
        _v -= rhs._v;
        if (_v >= Modulus) _v += Modulus;
        return *this;
    }

    constexpr ModInt& operator*=(const ModInt& rhs) noexcept {
        uint64_t z = _v;
        z *= rhs._v;
        _v = static_cast<uint32_t>(z % Modulus);
        return *this;
    }

    constexpr ModInt& operator/=(const ModInt& rhs) noexcept {
        return *this *= rhs.inv();
    }

    constexpr ModInt operator+(const ModInt& rhs) const noexcept {
        return ModInt(*this) += rhs;
    }
    constexpr ModInt operator-(const ModInt& rhs) const noexcept {
        return ModInt(*this) -= rhs;
    }
    constexpr ModInt operator*(const ModInt& rhs) const noexcept {
        return ModInt(*this) *= rhs;
    }
    constexpr ModInt operator/(const ModInt& rhs) const noexcept {
        return ModInt(*this) /= rhs;
    }

    constexpr bool operator==(const ModInt& rhs) const noexcept {
        return _v == rhs._v;
    }
    constexpr bool operator!=(const ModInt& rhs) const noexcept {
        return _v != rhs._v;
    }

    constexpr ModInt pow(long long n) const noexcept {
        ModInt res = raw(1 % Modulus);
        ModInt x = n < 0 ? inv() : *this;
        uint64_t exponent = n < 0 ? uint64_t(-(n + 1)) + 1 : uint64_t(n);
        while (exponent > 0) {
            if (exponent & 1) res *= x;
            x *= x;
            exponent >>= 1;
        }
        return res;
    }

    constexpr ModInt inv() const noexcept {
        int64_t a = _v, b = Modulus, u = 1, v = 0;
        while (b) {
            int64_t t = a / b;
            a -= t * b;
            std::swap(a, b);
            u -= t * v;
            std::swap(u, v);
        }
        assert(a == 1);
        u %= Modulus;
        if (u < 0) u += Modulus;
        return raw(static_cast<uint32_t>(u));
    }

    friend std::ostream& operator<<(std::ostream& os, const ModInt& rhs) {
        return os << rhs._v;
    }

    friend std::istream& operator>>(std::istream& is, ModInt& rhs) {
        long long v;
        is >> v;
        rhs = ModInt(v);
        return is;
    }
};

using modint998244353 = ModInt<998244353>;
using modint1000000007 = ModInt<1000000007>;

template <int Id = 0>
struct DynamicModInt {
   private:
    uint32_t _v;
    inline static uint32_t _mod = 1;

   public:
    static uint32_t mod() noexcept {
        return _mod;
    }

    static void set_mod(uint32_t modulus) noexcept {
        assert(modulus > 0);
        assert(modulus <= uint32_t(1) << 31);
        _mod = modulus;
    }

    static DynamicModInt raw(uint32_t v) noexcept {
        assert(v < _mod);
        DynamicModInt x;
        x._v = v;
        return x;
    }

    DynamicModInt() noexcept : _v(0) {}

    template <class Integer, std::enable_if_t<std::is_integral_v<Integer>, int> = 0>
    DynamicModInt(Integer v) noexcept {
        if constexpr (std::is_signed_v<Integer>) {
            int64_t x = static_cast<int64_t>(v) % static_cast<int64_t>(_mod);
            if (x < 0) x += _mod;
            _v = static_cast<uint32_t>(x);
        } else {
            _v = static_cast<uint32_t>(static_cast<uint64_t>(v) % _mod);
        }
    }

    uint32_t val() const noexcept {
        return _v;
    }

    DynamicModInt& operator++() noexcept {
        _v++;
        if (_v == _mod) _v = 0;
        return *this;
    }

    DynamicModInt& operator--() noexcept {
        if (_v == 0) _v = _mod;
        _v--;
        return *this;
    }

    DynamicModInt operator++(int) noexcept {
        DynamicModInt result = *this;
        ++*this;
        return result;
    }

    DynamicModInt operator--(int) noexcept {
        DynamicModInt result = *this;
        --*this;
        return result;
    }

    DynamicModInt& operator+=(const DynamicModInt& rhs) noexcept {
        _v += rhs._v;
        if (_v >= _mod) _v -= _mod;
        return *this;
    }

    DynamicModInt& operator-=(const DynamicModInt& rhs) noexcept {
        _v -= rhs._v;
        if (_v >= _mod) _v += _mod;
        return *this;
    }

    DynamicModInt& operator*=(const DynamicModInt& rhs) noexcept {
        _v = static_cast<uint32_t>(uint64_t(_v) * rhs._v % _mod);
        return *this;
    }

    DynamicModInt& operator/=(const DynamicModInt& rhs) noexcept {
        return *this *= rhs.inv();
    }

    DynamicModInt operator+(const DynamicModInt& rhs) const noexcept {
        return DynamicModInt(*this) += rhs;
    }

    DynamicModInt operator-(const DynamicModInt& rhs) const noexcept {
        return DynamicModInt(*this) -= rhs;
    }

    DynamicModInt operator*(const DynamicModInt& rhs) const noexcept {
        return DynamicModInt(*this) *= rhs;
    }

    DynamicModInt operator/(const DynamicModInt& rhs) const noexcept {
        return DynamicModInt(*this) /= rhs;
    }

    bool operator==(const DynamicModInt& rhs) const noexcept {
        return _v == rhs._v;
    }

    bool operator!=(const DynamicModInt& rhs) const noexcept {
        return _v != rhs._v;
    }

    DynamicModInt pow(long long exponent) const noexcept {
        DynamicModInt result = raw(1 % _mod);
        DynamicModInt base = exponent < 0 ? inv() : *this;
        uint64_t magnitude =
            exponent < 0 ? uint64_t(-(exponent + 1)) + 1 : uint64_t(exponent);
        while (magnitude > 0) {
            if (magnitude & 1) result *= base;
            base *= base;
            magnitude >>= 1;
        }
        return result;
    }

    DynamicModInt inv() const noexcept {
        int64_t a = _v, b = _mod, u = 1, v = 0;
        while (b) {
            int64_t quotient = a / b;
            a -= quotient * b;
            std::swap(a, b);
            u -= quotient * v;
            std::swap(u, v);
        }
        assert(a == 1);
        u %= _mod;
        if (u < 0) u += _mod;
        return raw(static_cast<uint32_t>(u));
    }

    friend std::ostream& operator<<(std::ostream& os, const DynamicModInt& rhs) {
        return os << rhs._v;
    }

    friend std::istream& operator>>(std::istream& is, DynamicModInt& rhs) {
        long long value;
        is >> value;
        rhs = DynamicModInt(value);
        return is;
    }
};

}  // namespace math
}  // namespace m1une


#line 29 "math/fps/convolution.hpp"

namespace m1une {
namespace fps {

namespace internal {

template <class Mint, class = void>
struct has_static_modulus : std::false_type {};

template <class Mint>
struct has_static_modulus<
    Mint, std::void_t<decltype(std::integral_constant<uint32_t, Mint::mod()>{})>>
    : std::true_type {};

constexpr uint32_t primitive_root_constexpr(uint32_t mod) {
    if (mod == 2) return 1;
    if (mod == 167772161) return 3;
    if (mod == 469762049) return 3;
    if (mod == 754974721) return 11;
    if (mod == 998244353) return 3;
    if (mod == 1224736769) return 3;

    uint32_t divisors[32] = {};
    int count = 0;
    uint32_t x = mod - 1;
    for (uint32_t p = 2; uint64_t(p) * p <= x; p++) {
        if (x % p != 0) continue;
        divisors[count++] = p;
        while (x % p == 0) x /= p;
    }
    if (x > 1) divisors[count++] = x;

    for (uint32_t g = 2;; g++) {
        bool ok = true;
        for (int i = 0; i < count; i++) {
            uint64_t value = 1;
            uint64_t base = g;
            uint32_t exponent = (mod - 1) / divisors[i];
            while (exponent > 0) {
                if (exponent & 1) value = value * base % mod;
                base = base * base % mod;
                exponent >>= 1;
            }
            if (value == 1) {
                ok = false;
                break;
            }
        }
        if (ok) return g;
    }
}

constexpr int two_adic_order(uint32_t x) {
    int result = 0;
    while ((x & 1) == 0) {
        x >>= 1;
        result++;
    }
    return result;
}

template <class Mint>
struct NttRoots {
    static constexpr int max_base = two_adic_order(Mint::mod() - 1);
    std::array<Mint, max_base + 1> root;
    std::array<Mint, max_base + 1> inverse_root;
    std::array<Mint, max_base> rate;
    std::array<Mint, max_base> inverse_rate;
    std::array<Mint, max_base> rate_radix4;
    std::array<Mint, max_base> inverse_rate_radix4;

    NttRoots() {
        constexpr uint32_t primitive_root = primitive_root_constexpr(Mint::mod());
        for (int level = 1; level <= max_base; level++) {
            root[level] = Mint(primitive_root).pow((Mint::mod() - 1) >> level);
            inverse_root[level] = root[level].inv();
        }
        Mint product = 1;
        Mint inverse_product = 1;
        for (int i = 0; i + 1 < max_base; i++) {
            rate[i] = root[i + 2] * product;
            inverse_rate[i] = inverse_root[i + 2] * inverse_product;
            product *= inverse_root[i + 2];
            inverse_product *= root[i + 2];
        }
        product = 1;
        inverse_product = 1;
        for (int i = 0; i + 2 < max_base; i++) {
            rate_radix4[i] = root[i + 3] * product;
            inverse_rate_radix4[i] = inverse_root[i + 3] * inverse_product;
            product *= inverse_root[i + 3];
            inverse_product *= root[i + 3];
        }
    }
};

template <class Mint>
const NttRoots<Mint>& ntt_roots() {
    static const NttRoots<Mint> roots;
    return roots;
}

template <class Mint>
void ntt(std::vector<Mint>& a, bool inverse, bool normalize = true) {
    const int n = int(a.size());
    assert(n > 0 && (n & (n - 1)) == 0);
    assert((Mint::mod() - 1) % uint32_t(n) == 0);

    const auto& roots = ntt_roots<Mint>();
    const int height = two_adic_order(uint32_t(n));
    if (!inverse) {
        int phase = 0;
        while (phase < height) {
            if (height - phase == 1) {
                const int width = 1 << (height - phase - 1);
                Mint twiddle = 1;
                for (int block = 0; block < (1 << phase); block++) {
                    const int offset = block << (height - phase);
                    for (int i = 0; i < width; i++) {
                        const Mint left = a[offset + i];
                        const Mint right = a[offset + i + width] * twiddle;
                        a[offset + i] = left + right;
                        a[offset + i + width] = left - right;
                    }
                    if (block + 1 != (1 << phase))
                        twiddle *= roots.rate[__builtin_ctz(~uint32_t(block))];
                }
                phase++;
                continue;
            }

            const int width = 1 << (height - phase - 2);
            Mint twiddle = 1;
            const Mint imaginary = roots.root[2];
            for (int block = 0; block < (1 << phase); block++) {
                const Mint twiddle2 = twiddle * twiddle;
                const Mint twiddle3 = twiddle2 * twiddle;
                const int offset = block << (height - phase);
                for (int i = 0; i < width; i++) {
                    const uint64_t mod2 = uint64_t(Mint::mod()) * Mint::mod();
                    const uint64_t a0 = a[offset + i].val();
                    const uint64_t a1 = uint64_t(a[offset + i + width].val()) * twiddle.val();
                    const uint64_t a2 =
                        uint64_t(a[offset + i + 2 * width].val()) * twiddle2.val();
                    const uint64_t a3 =
                        uint64_t(a[offset + i + 3 * width].val()) * twiddle3.val();
                    const uint64_t a1na3i =
                        uint64_t(Mint(a1 + mod2 - a3).val()) * imaginary.val();
                    const uint64_t negative_a2 = mod2 - a2;
                    a[offset + i] = Mint(a0 + a2 + a1 + a3);
                    a[offset + i + width] = Mint(a0 + a2 + 2 * mod2 - a1 - a3);
                    a[offset + i + 2 * width] = Mint(a0 + negative_a2 + a1na3i);
                    a[offset + i + 3 * width] = Mint(a0 + negative_a2 + mod2 - a1na3i);
                }
                if (block + 1 != (1 << phase))
                    twiddle *= roots.rate_radix4[__builtin_ctz(~uint32_t(block))];
            }
            phase += 2;
        }
    } else {
        int phase = height;
        while (phase > 0) {
            if (phase == 1) {
                const int width = 1 << (height - phase);
                Mint twiddle = 1;
                for (int block = 0; block < (1 << (phase - 1)); block++) {
                    const int offset = block << (height - phase + 1);
                    for (int i = 0; i < width; i++) {
                        const Mint left = a[offset + i];
                        const Mint right = a[offset + i + width];
                        a[offset + i] = left + right;
                        a[offset + i + width] = (left - right) * twiddle;
                    }
                    if (block + 1 != (1 << (phase - 1)))
                        twiddle *= roots.inverse_rate[__builtin_ctz(~uint32_t(block))];
                }
                phase--;
                continue;
            }

            const int width = 1 << (height - phase);
            Mint twiddle = 1;
            const Mint inverse_imaginary = roots.inverse_root[2];
            for (int block = 0; block < (1 << (phase - 2)); block++) {
                const Mint twiddle2 = twiddle * twiddle;
                const Mint twiddle3 = twiddle2 * twiddle;
                const int offset = block << (height - phase + 2);
                for (int i = 0; i < width; i++) {
                    const uint64_t a0 = a[offset + i].val();
                    const uint64_t a1 = a[offset + i + width].val();
                    const uint64_t a2 = a[offset + i + 2 * width].val();
                    const uint64_t a3 = a[offset + i + 3 * width].val();
                    const uint64_t a2na3i =
                        uint64_t(Mint((Mint::mod() + a2 - a3) * inverse_imaginary.val()).val());
                    a[offset + i] = Mint(a0 + a1 + a2 + a3);
                    a[offset + i + width] =
                        Mint((a0 + Mint::mod() - a1 + a2na3i) * twiddle.val());
                    a[offset + i + 2 * width] = Mint(
                        (a0 + a1 + 2ULL * Mint::mod() - a2 - a3) * twiddle2.val());
                    a[offset + i + 3 * width] = Mint(
                        (a0 + Mint::mod() - a1 + Mint::mod() - a2na3i) * twiddle3.val());
                }
                if (block + 1 != (1 << (phase - 2)))
                    twiddle *= roots.inverse_rate_radix4[__builtin_ctz(~uint32_t(block))];
            }
            phase -= 2;
        }
        if (normalize) {
            const Mint inverse_n = Mint(n).inv();
            for (Mint& value : a) value *= inverse_n;
        }
    }
}

#ifdef M1UNE_FPS_HAS_X86_SIMD

#pragma GCC push_options
#pragma GCC target("avx2,bmi")

template <class Mint>
__attribute__((target("avx2,bmi"), hot))
std::vector<Mint> convolution_998244353_simd(const std::vector<Mint>& a,
                                             const std::vector<Mint>& b) {
    const int result_size = int(a.size() + b.size() - 1);
    int n = 1;
    while (n < result_size) n <<= 1;
    const bool squaring = &a == &b;
    auto* transformed_a = static_cast<uint32_t*>(
        ::operator new[](sizeof(uint32_t) * n, std::align_val_t(32)));
    auto* transformed_b = squaring
                              ? transformed_a
                              : static_cast<uint32_t*>(::operator new[](
                                    sizeof(uint32_t) * n, std::align_val_t(32)));
    if constexpr (std::is_same_v<Mint, math::ModInt<998244353>>) {
        static_assert(sizeof(Mint) == sizeof(uint32_t) && std::is_trivially_copyable_v<Mint>);
        std::memcpy(transformed_a, a.data(), sizeof(uint32_t) * a.size());
        if (!squaring)
            std::memcpy(transformed_b, b.data(), sizeof(uint32_t) * b.size());
    } else {
        for (int i = 0; i < int(a.size()); i++) transformed_a[i] = a[i].val();
        if (!squaring)
            for (int i = 0; i < int(b.size()); i++) transformed_b[i] = b[i].val();
    }
    std::memset(transformed_a + a.size(), 0, sizeof(uint32_t) * (n - a.size()));
    if (!squaring)
        std::memset(transformed_b + b.size(), 0, sizeof(uint32_t) * (n - b.size()));

    static constexpr fast998_v2::FNTT32_info transform(998244353);
    const std::size_t vector_size = std::size_t(n) >> 3;
    fast998_v2::vector_dif(reinterpret_cast<__m256i*>(transformed_a), vector_size, &transform);
    if (!squaring)
        fast998_v2::vector_dif(reinterpret_cast<__m256i*>(transformed_b), vector_size,
                              &transform);
    fast998_v2::vector_convolution_direct(
        reinterpret_cast<__m256i*>(transformed_a),
        reinterpret_cast<const __m256i*>(transformed_b), vector_size, &transform);
    fast998_v2::vector_dit<true>(reinterpret_cast<__m256i*>(transformed_a), vector_size,
                                 &transform);

    std::vector<Mint> result(result_size);
    for (int j = 0; j < result_size; j++) result[j] = Mint::raw(transformed_a[j]);
    ::operator delete[](transformed_a, std::align_val_t(32));
    if (!squaring) ::operator delete[](transformed_b, std::align_val_t(32));
    return result;
}

#pragma GCC pop_options

#endif

}  // namespace internal

template <class Mint>
std::vector<Mint> convolution_naive(const std::vector<Mint>& a, const std::vector<Mint>& b) {
    if (a.empty() || b.empty()) return {};
    std::vector<Mint> result(a.size() + b.size() - 1);
    if (a.size() < b.size()) {
        for (int i = 0; i < int(a.size()); i++) {
            for (int j = 0; j < int(b.size()); j++) result[i + j] += a[i] * b[j];
        }
    } else {
        for (int j = 0; j < int(b.size()); j++) {
            for (int i = 0; i < int(a.size()); i++) result[i + j] += a[i] * b[j];
        }
    }
    return result;
}

template <class Mint>
std::vector<Mint> convolution_ntt(const std::vector<Mint>& a, const std::vector<Mint>& b) {
    const int result_size = int(a.size() + b.size() - 1);
    int n = 1;
    while (n < result_size) n <<= 1;
    assert((Mint::mod() - 1) % uint32_t(n) == 0);

#ifdef M1UNE_FPS_HAS_X86_SIMD
    if constexpr (Mint::mod() == 998244353) {
        if (n >= 64 && __builtin_cpu_supports("avx2"))
            return internal::convolution_998244353_simd(a, b);
    }
#endif

    // Allocate the padded buffers directly.  Constructing from the inputs and
    // then resizing used to allocate and copy both large operands twice.
    const bool squaring = &a == &b;
    std::vector<Mint> fa(n);
    std::copy(a.begin(), a.end(), fa.begin());
    internal::ntt(fa, false);
    const Mint inverse_n = Mint(n).inv();
    if (squaring) {
        for (int i = 0; i < n; i++) fa[i] *= fa[i] * inverse_n;
    } else {
        std::vector<Mint> fb(n);
        std::copy(b.begin(), b.end(), fb.begin());
        internal::ntt(fb, false);
        for (int i = 0; i < n; i++) fa[i] *= fb[i] * inverse_n;
    }
    internal::ntt(fa, true, false);
    fa.resize(result_size);
    return fa;
}

namespace internal {

template <class Mint>
std::vector<Mint> convolution_998244353_blocked_scalar(const std::vector<Mint>& a,
                                                       const std::vector<Mint>& b,
                                                       int transform_size) {
    assert(Mint::mod() == 998244353);
    assert(transform_size >= 2 && (transform_size & (transform_size - 1)) == 0);
    assert((Mint::mod() - 1) % uint32_t(transform_size) == 0);

    const int block_size = transform_size / 2;
    const int a_blocks = int((a.size() + block_size - 1) / block_size);
    const int b_blocks = int((b.size() + block_size - 1) / block_size);

    auto transform_blocks = [&](const std::vector<Mint>& values, int block_count) {
        std::vector<std::vector<Mint>> blocks;
        blocks.reserve(block_count);
        for (int block = 0; block < block_count; block++) {
            const int begin = block * block_size;
            const int count = std::min(block_size, int(values.size()) - begin);
            std::vector<Mint> transformed(transform_size);
            std::copy_n(values.begin() + begin, count, transformed.begin());
            ntt(transformed, false);
            blocks.emplace_back(std::move(transformed));
        }
        return blocks;
    };

    std::vector<std::vector<Mint>> transformed_a = transform_blocks(a, a_blocks);
    std::vector<std::vector<Mint>> transformed_b = transform_blocks(b, b_blocks);
    const int result_size = int(a.size() + b.size() - 1);
    std::vector<Mint> result(result_size);
    std::vector<Mint> transformed_result(transform_size);
    for (int diagonal = 0; diagonal < a_blocks + b_blocks - 1; diagonal++) {
        std::fill(transformed_result.begin(), transformed_result.end(), Mint(0));
        const int first_a = std::max(0, diagonal - (b_blocks - 1));
        const int last_a = std::min(a_blocks - 1, diagonal);
        for (int a_block = first_a; a_block <= last_a; a_block++) {
            const int b_block = diagonal - a_block;
            for (int i = 0; i < transform_size; i++)
                transformed_result[i] +=
                    transformed_a[a_block][i] * transformed_b[b_block][i];
        }
        ntt(transformed_result, true);

        const int output_offset = diagonal * block_size;
        const int output_count = std::min(transform_size, result_size - output_offset);
        for (int i = 0; i < output_count; i++)
            result[output_offset + i] += transformed_result[i];
    }
    return result;
}

#ifdef M1UNE_FPS_HAS_X86_SIMD

class AlignedUint32Buffer {
   private:
    uint32_t* data_;

   public:
    explicit AlignedUint32Buffer(std::size_t size)
        : data_(static_cast<uint32_t*>(
              ::operator new[](sizeof(uint32_t) * size, std::align_val_t(32)))) {}

    AlignedUint32Buffer(const AlignedUint32Buffer&) = delete;
    AlignedUint32Buffer& operator=(const AlignedUint32Buffer&) = delete;

    AlignedUint32Buffer(AlignedUint32Buffer&& other) noexcept : data_(other.data_) {
        other.data_ = nullptr;
    }

    AlignedUint32Buffer& operator=(AlignedUint32Buffer&& other) noexcept {
        if (this == &other) return *this;
        ::operator delete[](data_, std::align_val_t(32));
        data_ = other.data_;
        other.data_ = nullptr;
        return *this;
    }

    ~AlignedUint32Buffer() {
        ::operator delete[](data_, std::align_val_t(32));
    }

    uint32_t* data() {
        return data_;
    }

    const uint32_t* data() const {
        return data_;
    }
};

template <class Mint>
__attribute__((target("avx2,bmi"), hot))
std::vector<Mint> convolution_998244353_blocked_simd(const std::vector<Mint>& a,
                                                     const std::vector<Mint>& b,
                                                     int transform_size) {
    assert(Mint::mod() == 998244353);
    assert(transform_size >= 64 && (transform_size & (transform_size - 1)) == 0);
    assert((Mint::mod() - 1) % uint32_t(transform_size) == 0);

    const int block_size = transform_size / 2;
    const int a_blocks = int((a.size() + block_size - 1) / block_size);
    const int b_blocks = int((b.size() + block_size - 1) / block_size);
    static constexpr fast998_v2::FNTT32_info transform(998244353);
    const std::size_t vector_size = std::size_t(transform_size) / 8;

    auto transform_blocks = [&](const std::vector<Mint>& values, int block_count) {
        std::vector<AlignedUint32Buffer> blocks;
        blocks.reserve(block_count);
        for (int block = 0; block < block_count; block++) {
            const int begin = block * block_size;
            const int count = std::min(block_size, int(values.size()) - begin);
            AlignedUint32Buffer transformed(transform_size);
            if constexpr (std::is_same_v<Mint, math::ModInt<998244353>>) {
                static_assert(sizeof(Mint) == sizeof(uint32_t) &&
                              std::is_trivially_copyable_v<Mint>);
                std::memcpy(transformed.data(), values.data() + begin,
                            sizeof(uint32_t) * count);
            } else {
                for (int i = 0; i < count; i++)
                    transformed.data()[i] = values[begin + i].val();
            }
            std::memset(transformed.data() + count, 0,
                        sizeof(uint32_t) * (transform_size - count));
            fast998_v2::vector_dif(reinterpret_cast<__m256i*>(transformed.data()),
                                   vector_size, &transform);
            blocks.emplace_back(std::move(transformed));
        }
        return blocks;
    };

    std::vector<AlignedUint32Buffer> transformed_a = transform_blocks(a, a_blocks);
    std::vector<AlignedUint32Buffer> transformed_b = transform_blocks(b, b_blocks);
    const int result_size = int(a.size() + b.size() - 1);
    std::vector<Mint> result(result_size);
    AlignedUint32Buffer transformed_result(transform_size);
    for (int diagonal = 0; diagonal < a_blocks + b_blocks - 1; diagonal++) {
        std::memset(transformed_result.data(), 0, sizeof(uint32_t) * transform_size);
        const int first_a = std::max(0, diagonal - (b_blocks - 1));
        const int last_a = std::min(a_blocks - 1, diagonal);
        for (int a_block = first_a; a_block <= last_a; a_block++) {
            const int b_block = diagonal - a_block;
            fast998_v2::vector_convolution_accumulate(
                reinterpret_cast<__m256i*>(transformed_result.data()),
                reinterpret_cast<const __m256i*>(transformed_a[a_block].data()),
                reinterpret_cast<const __m256i*>(transformed_b[b_block].data()),
                vector_size, &transform);
        }
        fast998_v2::vector_dit<true>(
            reinterpret_cast<__m256i*>(transformed_result.data()), vector_size,
            &transform);

        const int output_offset = diagonal * block_size;
        const int output_count = std::min(transform_size, result_size - output_offset);
        for (int i = 0; i < output_count; i++) {
            uint32_t value = result[output_offset + i].val() + transformed_result.data()[i];
            if (value >= Mint::mod()) value -= Mint::mod();
            result[output_offset + i] = Mint::raw(value);
        }
    }
    return result;
}

#endif

template <class Mint>
std::vector<Mint> convolution_998244353_blocked(const std::vector<Mint>& a,
                                                const std::vector<Mint>& b,
                                                int transform_size = 1 << 23) {
#ifdef M1UNE_FPS_HAS_X86_SIMD
    if (transform_size >= 64 && __builtin_cpu_supports("avx2"))
        return convolution_998244353_blocked_simd(a, b, transform_size);
#endif
    return convolution_998244353_blocked_scalar(a, b, transform_size);
}

}  // namespace internal

template <class Mint>
std::vector<Mint> convolution(const std::vector<Mint>& a, const std::vector<Mint>& b) {
    if (a.empty() || b.empty()) return {};
    if (std::min(a.size(), b.size()) <= 32) return convolution_naive(a, b);

    const int result_size = int(a.size() + b.size() - 1);
    int n = 1;
    while (n < result_size) n <<= 1;
    if constexpr (internal::has_static_modulus<Mint>::value) {
        if constexpr (Mint::mod() == 998244353) {
            if (n > (1 << 23))
                return internal::convolution_998244353_blocked(a, b);
        }
        if ((Mint::mod() - 1) % uint32_t(n) == 0) return convolution_ntt(a, b);
    }

    using Mint1 = math::ModInt<167772161>;
    using Mint2 = math::ModInt<469762049>;
    using Mint3 = math::ModInt<754974721>;
    assert(n <= (1 << 24));

    [[maybe_unused]] const unsigned __int128 coefficient_bound =
        static_cast<unsigned __int128>(std::min(a.size(), b.size())) * (Mint::mod() - 1) *
        (Mint::mod() - 1);
    [[maybe_unused]] const unsigned __int128 crt_modulus =
        static_cast<unsigned __int128>(Mint1::mod()) * Mint2::mod() * Mint3::mod();
    assert(coefficient_bound < crt_modulus);

    auto converted_convolution = [&]<class OtherMint>() {
        std::vector<OtherMint> converted_a(a.size());
        std::vector<OtherMint> converted_b(b.size());
        for (int i = 0; i < int(a.size()); i++) converted_a[i] = OtherMint(a[i].val());
        for (int i = 0; i < int(b.size()); i++) converted_b[i] = OtherMint(b[i].val());
        return convolution_ntt(converted_a, converted_b);
    };
    std::vector<Mint1> c1 = converted_convolution.template operator()<Mint1>();
    std::vector<Mint2> c2 = converted_convolution.template operator()<Mint2>();
    std::vector<Mint3> c3 = converted_convolution.template operator()<Mint3>();
    static const uint64_t inverse_mod1_mod2 = Mint2(Mint1::mod()).inv().val();
    static const uint64_t mod1_mod3 = Mint1::mod() % Mint3::mod();
    static const uint64_t mod1_mod2_mod3 =
        mod1_mod3 * (Mint2::mod() % Mint3::mod()) % Mint3::mod();
    static const uint64_t inverse_mod1_mod2_mod3 = Mint3(uint32_t(mod1_mod2_mod3)).inv().val();

    const uint64_t target_mod = Mint::mod();
    const uint64_t mod1_target = Mint1::mod() % target_mod;
    const uint64_t mod1_mod2_target = mod1_target * (Mint2::mod() % target_mod) % target_mod;
    std::vector<Mint> result(result_size);
    for (int i = 0; i < result_size; i++) {
        const uint64_t r1 = c1[i].val();
        const uint64_t r2 = c2[i].val();
        const uint64_t r3 = c3[i].val();
        const uint64_t first =
            (r2 + Mint2::mod() - r1 % Mint2::mod()) % Mint2::mod() * inverse_mod1_mod2 %
            Mint2::mod();
        const uint64_t combined_mod3 =
            (r1 % Mint3::mod() + mod1_mod3 * (first % Mint3::mod())) % Mint3::mod();
        const uint64_t second =
            (r3 + Mint3::mod() - combined_mod3) % Mint3::mod() * inverse_mod1_mod2_mod3 %
            Mint3::mod();

        uint64_t value = r1 % target_mod;
        value = (value + mod1_target * (first % target_mod)) % target_mod;
        value = (value + mod1_mod2_target * (second % target_mod)) % target_mod;
        result[i] = Mint::raw(uint32_t(value));
    }
    return result;
}

}  // namespace fps
}  // namespace m1une

#ifdef M1UNE_FPS_HAS_X86_SIMD
#undef M1UNE_FPS_HAS_X86_SIMD
#endif


#line 9 "string/wildcard_pattern_matching.hpp"

namespace m1une {
namespace string {

namespace internal {

template <class Mint>
std::vector<Mint> wildcard_mismatch_scores(
    const std::string& text,
    const std::string& pattern,
    char wildcard
) {
    int n = int(text.size());
    int m = int(pattern.size());
    std::array<std::vector<Mint>, 3> text_powers;
    std::array<std::vector<Mint>, 3> pattern_powers;
    for (auto& powers : text_powers) powers.resize(n);
    for (auto& powers : pattern_powers) powers.resize(m);

    auto encode = [wildcard](char character) {
        if (character == wildcard) return 0;
        return int(static_cast<unsigned char>(character)) + 1;
    };
    for (int i = 0; i < n; i++) {
        Mint value = encode(text[i]);
        text_powers[0][i] = value;
        text_powers[1][i] = value * value;
        text_powers[2][i] = value * value * value;
    }
    for (int i = 0; i < m; i++) {
        Mint value = encode(pattern[m - 1 - i]);
        pattern_powers[0][i] = value;
        pattern_powers[1][i] = value * value;
        pattern_powers[2][i] = value * value * value;
    }

    std::vector<Mint> scores(n - m + 1);
    for (int power = 0; power < 3; power++) {
        std::vector<Mint> product = fps::convolution(
            text_powers[power],
            pattern_powers[2 - power]
        );
        Mint multiplier = power == 1 ? Mint(-2) : Mint(1);
        for (int start = 0; start <= n - m; start++) {
            scores[start] += multiplier * product[start + m - 1];
        }
    }
    return scores;
}

}  // namespace internal

// result[i] is true exactly when pattern matches text[i, i + pattern.size()).
// The wildcard character matches every character on either side.
inline std::vector<bool> wildcard_pattern_matching(
    const std::string& text,
    const std::string& pattern,
    char wildcard = '*'
) {
    int n = int(text.size());
    int m = int(pattern.size());
    if (m == 0) return std::vector<bool>(n + 1, true);
    if (n < m) return {};

    using Mint1 = math::ModInt<469762049>;
    using Mint2 = math::ModInt<754974721>;
    std::vector<Mint1> first_scores =
        internal::wildcard_mismatch_scores<Mint1>(text, pattern, wildcard);
    std::vector<Mint2> second_scores =
        internal::wildcard_mismatch_scores<Mint2>(text, pattern, wildcard);

    std::vector<bool> result(n - m + 1, false);
    for (int start = 0; start <= n - m; start++) {
        result[start] = first_scores[start].val() == 0 &&
                        second_scores[start].val() == 0;
    }
    return result;
}

}  // namespace string
}  // namespace m1une


#line 1 "string/z_algorithm.hpp"



#line 6 "string/z_algorithm.hpp"

namespace m1une {
namespace string {

// Returns z[i] = LCP(sequence, sequence[i..]).
template <class Sequence>
std::vector<int> z_algorithm(const Sequence& sequence) {
    int n = int(sequence.size());
    if (n == 0) return {};

    std::vector<int> z(n);
    z[0] = n;
    int left = 0;
    int right = 0;
    for (int i = 1; i < n; i++) {
        if (i < right) z[i] = std::min(right - i, z[i - left]);
        while (i + z[i] < n && sequence[z[i]] == sequence[i + z[i]]) {
            z[i]++;
        }
        if (right < i + z[i]) {
            left = i;
            right = i + z[i];
        }
    }
    return z;
}

}  // namespace string
}  // namespace m1une


#line 27 "string/all.hpp"


#line 4 "verify/string/string_algorithms.test.cpp"

#line 1 "utilities/fast_io.hpp"



#line 6 "utilities/fast_io.hpp"
#include <cerrno>
#include <charconv>
#line 9 "utilities/fast_io.hpp"
#include <cstdio>
#include <cstdlib>
#line 13 "utilities/fast_io.hpp"
#include <iterator>
#line 15 "utilities/fast_io.hpp"
#include <sys/stat.h>
#line 18 "utilities/fast_io.hpp"
#include <unistd.h>
#line 20 "utilities/fast_io.hpp"

namespace m1une {
namespace utilities {

struct FastOutput;

namespace internal {

// Shared with the convenience helpers in template.hpp.
inline FastOutput* standard_output_instance = nullptr;

// Detect std::begin(x), std::end(x).
template <class T, class = void>
struct is_range : std::false_type {};

template <class T>
struct is_range<T, std::void_t<
    decltype(std::begin(std::declval<T&>())),
    decltype(std::end(std::declval<T&>()))
>> : std::true_type {};

template <class T>
inline constexpr bool is_range_v = is_range<T>::value;

template <class T>
using range_reference_t = decltype(*std::begin(std::declval<T&>()));

template <class T>
using range_value_t = std::remove_cv_t<std::remove_reference_t<range_reference_t<T>>>;

template <class T, class = void>
struct range_stored_value {
    using type = range_value_t<T>;
};

template <class T>
struct range_stored_value<T, std::void_t<typename std::remove_cv_t<std::remove_reference_t<T>>::value_type>> {
    using type = typename std::remove_cv_t<std::remove_reference_t<T>>::value_type;
};

template <class T>
using range_stored_value_t = typename range_stored_value<T>::type;

// Treat strings and C strings as scalar output objects, not as ranges.
template <class T>
struct is_char_array : std::false_type {};

template <class T, std::size_t N>
struct is_char_array<T[N]>
    : std::bool_constant<std::is_same_v<std::remove_cv_t<T>, char>> {};

template <class T>
struct is_string_like
    : std::bool_constant<
          std::is_same_v<std::decay_t<T>, std::string>
          || std::is_same_v<std::decay_t<T>, const char*>
          || std::is_same_v<std::decay_t<T>, char*>
          || is_char_array<std::remove_reference_t<T>>::value
      > {};

template <class T>
inline constexpr bool is_string_like_v = is_string_like<T>::value;

// ModInt-like type: x.val() is printable, and x can be assigned from long long.
template <class T, class = void>
struct has_val_method : std::false_type {};

template <class T>
struct has_val_method<T, std::void_t<decltype(std::declval<const T&>().val())>>
    : std::true_type {};

template <class T>
inline constexpr bool has_val_method_v = has_val_method<T>::value;

template <class T, class = void>
struct has_static_mod_raw : std::false_type {};

template <class T>
struct has_static_mod_raw<
    T, std::void_t<decltype(T::mod()), decltype(T::raw(std::declval<uint32_t>()))>>
    : std::true_type {};

template <class T>
inline constexpr bool has_static_mod_raw_v = has_static_mod_raw<T>::value;

// libstdc++ before GCC 16 does not classify __int128 as an integral type in
// strict ISO modes such as -std=c++23. Keep the fast-I/O interface independent
// of that implementation detail.
template <class T>
inline constexpr bool is_integral_v =
    std::is_integral_v<T>
    || std::is_same_v<std::remove_cv_t<T>, __int128_t>
    || std::is_same_v<std::remove_cv_t<T>, __uint128_t>;

template <class T>
inline constexpr bool is_signed_v =
    std::is_signed_v<T>
    || std::is_same_v<std::remove_cv_t<T>, __int128_t>;

template <class T>
struct make_unsigned {
    using type = std::make_unsigned_t<T>;
};

template <>
struct make_unsigned<__int128_t> {
    using type = __uint128_t;
};

template <>
struct make_unsigned<__uint128_t> {
    using type = __uint128_t;
};

template <class T>
using make_unsigned_t = typename make_unsigned<std::remove_cv_t<T>>::type;

}  // namespace internal

struct FastInput {
    static constexpr int buffer_size = 1 << 20;

   private:
    std::FILE* _stream;
    char _buffer[buffer_size];
    int _position;
    int _length;
    int _file_descriptor;
    bool _streaming;

    bool refill() {
        _position = 0;
        if (_streaming) {
            ssize_t length;
            do {
                length = ::read(_file_descriptor, _buffer, buffer_size);
            } while (length < 0 && errno == EINTR);
            if (length <= 0) {
                _length = 0;
                return false;
            }
            _length = int(length);
        } else {
            _length = int(std::fread(_buffer, 1, buffer_size, _stream));
        }
        return _length != 0;
    }

    template <class T>
    bool read_integer_from_stream(T& value) {
        if (!skip_spaces()) return false;
        int c = read_char_raw();

        bool negative = false;
        if (c == '-') {
            negative = true;
            c = read_char_raw();
        }

        if constexpr (internal::is_signed_v<T>) {
            T result = 0;
            while ('0' <= c && c <= '9') {
                result = negative ? result * 10 - (c - '0')
                                  : result * 10 + (c - '0');
                c = read_char_raw();
            }
            value = result;
        } else {
            T result = 0;
            while ('0' <= c && c <= '9') {
                result = result * 10 + T(c - '0');
                c = read_char_raw();
            }
            value = negative ? T(0) - result : result;
        }
        return true;
    }

    bool prepare_number() {
        if (_length - _position >= 64) return true;
        const int remaining = _length - _position;
        if (remaining > 0) std::memmove(_buffer, _buffer + _position, remaining);
        const int added = int(std::fread(_buffer + remaining, 1, buffer_size - remaining, _stream));
        _position = 0;
        _length = remaining + added;
        if (_length < buffer_size) _buffer[_length] = '\0';
        return _length != 0;
    }

   public:
    explicit FastInput(std::FILE* stream = stdin)
        : _stream(stream),
          _position(0),
          _length(0),
          _file_descriptor(::fileno(stream)),
          _streaming([&] {
              struct stat status;
              return _file_descriptor >= 0
                     && ::fstat(_file_descriptor, &status) == 0
                     && !S_ISREG(status.st_mode);
          }()) {}

    FastInput(const FastInput&) = delete;
    FastInput& operator=(const FastInput&) = delete;

    int read_char_raw() {
        if (_position == _length && !refill()) return EOF;
        return _buffer[_position++];
    }

    bool skip_spaces() {
        int c = read_char_raw();
        while (c != EOF && c <= ' ') c = read_char_raw();
        if (c == EOF) return false;
        --_position;
        return true;
    }

    bool read(char& value) {
        if (!skip_spaces()) return false;
        value = char(read_char_raw());
        return true;
    }

    bool read(std::string& value) {
        if (!skip_spaces()) return false;
        value.clear();
        while (true) {
            const int begin = _position;
            while (_position < _length &&
                   static_cast<unsigned char>(_buffer[_position]) > ' ') {
                ++_position;
            }
            value.append(_buffer + begin, _position - begin);
            if (_position < _length) {
                ++_position;
                return true;
            }
            if (!refill()) return true;
        }
    }

    bool read(bool& value) {
        int x;
        if (!read(x)) return false;
        value = x != 0;
        return true;
    }

    template <class T>
    std::enable_if_t<
        internal::is_integral_v<T>
            && !std::is_same_v<std::remove_cv_t<T>, bool>
            && !std::is_same_v<std::remove_cv_t<T>, char>,
        bool
    >
    read(T& value) {
        if (_streaming) return read_integer_from_stream(value);
        if (!prepare_number()) return false;
        int c = static_cast<unsigned char>(_buffer[_position++]);
        while (c <= ' ') c = static_cast<unsigned char>(_buffer[_position++]);

        bool negative = false;
        if (c == '-') {
            negative = true;
            c = static_cast<unsigned char>(_buffer[_position++]);
        }

        if constexpr (internal::is_signed_v<T>) {
            T result = 0;
            while ('0' <= c && c <= '9') {
                const int first = c - '0';
                const int second = static_cast<unsigned char>(_buffer[_position]) - '0';
                if (0 <= second && second <= 9) {
                    result = negative ? result * 100 - (first * 10 + second)
                                      : result * 100 + (first * 10 + second);
                    ++_position;
                } else {
                    result = negative ? result * 10 - first : result * 10 + first;
                }
                c = static_cast<unsigned char>(_buffer[_position++]);
            }
            value = result;
        } else {
            T result = 0;
            while ('0' <= c && c <= '9') {
                const unsigned first = unsigned(c - '0');
                const int second = static_cast<unsigned char>(_buffer[_position]) - '0';
                if (0 <= second && second <= 9) {
                    result = result * 100 + T(first * 10 + unsigned(second));
                    ++_position;
                } else {
                    result = result * 10 + T(first);
                }
                c = static_cast<unsigned char>(_buffer[_position++]);
            }
            value = negative ? T(0) - result : result;
        }
        if (_position > _length) _position = _length;
        return true;
    }

    template <class T>
    std::enable_if_t<std::is_floating_point_v<T>, bool>
    read(T& value) {
        if (!skip_spaces()) return false;
        int c = read_char_raw();
        bool negative = false;
        if (c == '-' || c == '+') {
            negative = c == '-';
            c = read_char_raw();
        }

        long double result = 0;
        while ('0' <= c && c <= '9') {
            result = result * 10 + (c - '0');
            c = read_char_raw();
        }
        if (c == '.') {
            long double place = 0.1L;
            c = read_char_raw();
            while ('0' <= c && c <= '9') {
                result += (c - '0') * place;
                place *= 0.1L;
                c = read_char_raw();
            }
        }
        if (c == 'e' || c == 'E') {
            c = read_char_raw();
            bool exponent_negative = false;
            if (c == '-' || c == '+') {
                exponent_negative = c == '-';
                c = read_char_raw();
            }
            int exponent = 0;
            while ('0' <= c && c <= '9') {
                exponent = exponent * 10 + (c - '0');
                c = read_char_raw();
            }
            long double scale = 1;
            long double power = 10;
            while (exponent > 0) {
                if (exponent & 1) scale *= power;
                power *= power;
                exponent >>= 1;
            }
            result = exponent_negative ? result / scale : result * scale;
        }
        value = static_cast<T>(negative ? -result : result);
        return true;
    }

    template <class T>
    std::enable_if_t<
        internal::has_val_method_v<T>
            && !internal::is_integral_v<T>
            && !internal::is_range_v<T>,
        bool
    >
    read(T& value) {
        long long x;
        if (!read(x)) return false;
        if constexpr (internal::has_static_mod_raw_v<T>) {
            if (x >= 0 && uint64_t(x) < uint64_t(T::mod())) {
                value = T::raw(uint32_t(x));
            } else {
                value = T(x);
            }
        } else {
            value = T(x);
        }
        return true;
    }

    template <class First, class Second>
    bool read(std::pair<First, Second>& value) {
        if (!read(value.first)) return false;
        return read(value.second);
    }

    template <class Range>
    std::enable_if_t<
        internal::is_range_v<Range>
            && !internal::is_string_like_v<Range>,
        bool
    >
    read(Range& range) {
        using StoredValue = internal::range_stored_value_t<Range>;
        constexpr bool nested = internal::is_range_v<StoredValue>
                                && !internal::is_string_like_v<StoredValue>;

        for (auto&& value : range) {
            if constexpr (std::is_same_v<StoredValue, bool> && !nested) {
                bool x;
                if (!read(x)) return false;
                value = x;
            } else {
                if (!read(value)) return false;
            }
        }
        return true;
    }

    template <class First, class Second, class... Rest>
    bool read(First& first, Second& second, Rest&... rest) {
        if (!read(first)) return false;
        return read(second, rest...);
    }

    template <class T>
    FastInput& operator>>(T& value) {
        if (!read(value)) std::abort();
        return *this;
    }
};

struct FastOutput {
    static constexpr int buffer_size = 1 << 20;

   private:
    inline static const auto digit_quads = [] {
        std::array<char, 40000> result{};
        for (int i = 0; i < 10000; i++) {
            int value = i;
            for (int j = 3; j >= 0; j--) {
                result[4 * i + j] = char('0' + value % 10);
                value /= 10;
            }
        }
        return result;
    }();

    std::FILE* _stream;
    char _buffer[buffer_size];
    int _position;
    int _precision;
    std::chars_format _float_format;
    char _range_separator;
    std::string* _capture = nullptr;

    template <class T>
    std::string format_cell(const T& value) {
        std::string result;
        struct CaptureGuard {
            std::string*& target;
            std::string* previous;
            ~CaptureGuard() { target = previous; }
        } guard{_capture, _capture};
        _capture = &result;
        write(value);
        return result;
    }

    template <class Matrix>
    void write_aligned_matrix(const Matrix& matrix) {
        std::vector<std::vector<std::string>> rows;
        std::vector<std::size_t> widths;
        for (const auto& row : matrix) {
            auto& cells = rows.emplace_back();
            std::size_t column = 0;
            for (const auto& value : row) {
                cells.push_back(format_cell(value));
                if (column == widths.size()) widths.push_back(0);
                widths[column] = std::max(widths[column], cells.back().size());
                ++column;
            }
        }
        bool first = true;
        for (const auto& row : rows) {
            if (!first) write_char('\n');
            first = false;
            for (std::size_t column = 0; column < row.size(); ++column) {
                if (column != 0) write_char(_range_separator);
                for (std::size_t padding = row[column].size();
                     padding < widths[column]; ++padding) {
                    write_char(' ');
                }
                write(row[column]);
            }
        }
    }

   public:
    explicit FastOutput(std::FILE* stream = stdout)
        : _stream(stream),
          _position(0),
          _precision(6),
          _float_format(std::chars_format::general),
          _range_separator(' ') {
        if (_stream == stdout
            && internal::standard_output_instance == nullptr) {
            internal::standard_output_instance = this;
        }
    }

    FastOutput(const FastOutput&) = delete;
    FastOutput& operator=(const FastOutput&) = delete;

    ~FastOutput() {
        flush();
        if (internal::standard_output_instance == this) {
            internal::standard_output_instance = nullptr;
        }
    }

    void flush() {
        if (_position != 0) {
            std::fwrite(_buffer, 1, _position, _stream);
            _position = 0;
        }
        std::fflush(_stream);
    }

    void write_char(char c) {
        if (_capture != nullptr) {
            _capture->push_back(c);
            return;
        }
        if (_position == buffer_size) flush();
        _buffer[_position++] = c;
    }

    void write(const char* s) {
        while (*s != '\0') write_char(*s++);
    }

    void write(const std::string& s) {
        if (_capture != nullptr) {
            _capture->append(s);
            return;
        }
        std::size_t position = 0;
        while (position < s.size()) {
            if (_position == buffer_size) flush();
            const std::size_t copied =
                std::min<std::size_t>(buffer_size - _position, s.size() - position);
            std::memcpy(_buffer + _position, s.data() + position, copied);
            _position += int(copied);
            position += copied;
        }
    }

    void write(char c) {
        write_char(c);
    }

    void write(bool value) {
        write_char(value ? '1' : '0');
    }

    template <class T>
    std::enable_if_t<std::is_floating_point_v<T>>
    write(T value) {
        char digits[128];
        auto [end, error] = std::to_chars(
            digits,
            digits + sizeof(digits),
            value,
            _float_format,
            _precision
        );
        if (error != std::errc()) std::abort();
        for (const char* pointer = digits; pointer != end; pointer++) {
            write_char(*pointer);
        }
    }

    template <class T>
    std::enable_if_t<
        internal::is_integral_v<T>
            && !std::is_same_v<std::remove_cv_t<T>, bool>
            && !std::is_same_v<std::remove_cv_t<T>, char>
    >
    write(T value) {
        using Raw = std::remove_cv_t<T>;
        using Unsigned = internal::make_unsigned_t<Raw>;

        Unsigned magnitude;
        if constexpr (internal::is_signed_v<Raw>) {
            if (value < 0) {
                write_char('-');
                magnitude = Unsigned(0) - Unsigned(value);
            } else {
                magnitude = Unsigned(value);
            }
        } else {
            magnitude = value;
        }

        if (magnitude == 0) {
            write_char('0');
            return;
        }

        unsigned chunks[16];
        int count = 0;
        while (magnitude >= 10000) {
            const Unsigned quotient = magnitude / 10000;
            chunks[count++] = unsigned(magnitude - quotient * 10000);
            magnitude = quotient;
        }
        if (_capture == nullptr && _position > buffer_size - 64) flush();
        char captured[64];
        char* const begin = _capture != nullptr ? captured : _buffer + _position;
        char* destination = begin;
        const unsigned leading = unsigned(magnitude);
        const char* first = digit_quads.data() + 4 * leading;
        int skip = leading < 10 ? 3 : leading < 100 ? 2 : leading < 1000 ? 1 : 0;
        for (; skip < 4; skip++) *destination++ = first[skip];
        while (count--) {
            const char* digits = digit_quads.data() + 4 * chunks[count];
            std::memcpy(destination, digits, 4);
            destination += 4;
        }
        if (_capture != nullptr) {
            _capture->append(begin, destination - begin);
        } else {
            _position += int(destination - begin);
        }
    }

    template <class T>
    std::enable_if_t<
        internal::has_val_method_v<T>
            && !internal::is_integral_v<T>
            && !internal::is_range_v<T>
    >
    write(const T& value) {
        write(value.val());
    }

    template <class First, class Second>
    void write(const std::pair<First, Second>& value) {
        write(value.first);
        write_char(' ');
        write(value.second);
    }

    template <class Range>
    std::enable_if_t<
        internal::is_range_v<Range>
            && !internal::is_string_like_v<Range>
    >
    write(const Range& range) {
        using StoredValue = internal::range_stored_value_t<const Range>;
        constexpr bool nested = internal::is_range_v<StoredValue>
                                && !internal::is_string_like_v<StoredValue>;

        bool first = true;
        for (const auto& value : range) {
            if (!first) write_char(nested ? '\n' : _range_separator);
            first = false;
            if constexpr (std::is_same_v<StoredValue, bool> && !nested) {
                write(static_cast<bool>(value));
            } else {
                write(value);
            }
        }
    }

    template <class First, class... Rest>
    void print(const First& first, const Rest&... rest) {
        write(first);
        ((write_char(' '), write(rest)), ...);
    }

    void println() {
        write_char('\n');
    }

    void set_precision(int precision) {
        _precision = precision;
    }

    void set_fixed(int precision = 6) {
        _float_format = std::chars_format::fixed;
        _precision = precision;
    }

    void set_general(int precision = 6) {
        _float_format = std::chars_format::general;
        _precision = precision;
    }

    void set_range_separator(char separator) {
        _range_separator = separator;
    }

    template <class Matrix>
    void write_aligned(const Matrix& matrix) {
        using Row = internal::range_stored_value_t<const Matrix>;
        using Cell = internal::range_stored_value_t<const Row>;
        static_assert(internal::is_range_v<Row> && !internal::is_string_like_v<Row>,
                      "write_aligned requires a two-dimensional range");
        static_assert(!internal::is_range_v<Cell> || internal::is_string_like_v<Cell>,
                      "write_aligned requires scalar cells");
        write_aligned_matrix(matrix);
    }

    template <class Matrix>
    void println_aligned(const Matrix& matrix) {
        write_aligned(matrix);
        write_char('\n');
    }

    template <class... Args>
    void println(const Args&... args) {
        print(args...);
        write_char('\n');
    }

    template <class T>
    FastOutput& operator<<(const T& value) {
        write(value);
        return *this;
    }
};

}  // namespace utilities
}  // namespace m1une


#line 12 "verify/string/string_algorithms.test.cpp"

namespace {

void test_edge_cases() {
    std::string empty;
    assert(m1une::string::z_algorithm(empty).empty());
    assert(m1une::string::prefix_function(empty).empty());
    assert(m1une::string::suffix_array(empty).empty());
    assert(m1une::string::lcp_array(empty, std::vector<int>()).empty());
    assert(m1une::string::lyndon_factor_boundaries(empty) == std::vector<int>(1, 0));
    assert(m1une::string::lyndon_factorization(empty).empty());
    assert(m1une::string::minimum_cyclic_shift(empty) == 0);

    auto empty_palindromes = m1une::string::manacher(empty);
    assert(empty_palindromes.empty());
    assert(empty_palindromes.longest_length() == 0);
    assert(empty_palindromes.is_palindrome(0, 0));

    std::string text = "aaaa";
    assert(
        m1une::string::kmp_search(text, std::string("aa")) ==
        std::vector<int>({0, 1, 2})
    );
    assert(
        m1une::string::kmp_search(text, empty) ==
        std::vector<int>({0, 1, 2, 3, 4})
    );

    std::vector<int> values;
    values.push_back(2);
    values.push_back(-1);
    values.push_back(2);
    assert(
        m1une::string::suffix_array(values) ==
        std::vector<int>({1, 2, 0})
    );
    assert(
        m1une::string::z_algorithm(values) ==
        std::vector<int>({3, 0, 1})
    );
    assert(
        m1une::string::lyndon_factor_boundaries(values) ==
        std::vector<int>({0, 1, 3})
    );
    assert(m1une::string::minimum_cyclic_shift(values) == 1);

    std::string bytes;
    bytes.push_back(char(255));
    bytes.push_back(char(0));
    bytes.push_back(char(128));
    assert(
        m1une::string::suffix_array(bytes) ==
        std::vector<int>({1, 2, 0})
    );
}

void test_randomized() {
    std::uint64_t state = 31;
    auto random = [&state]() {
        state ^= state << 7;
        state ^= state >> 9;
        return state;
    };

    for (int trial = 0; trial < 1500; trial++) {
        int n = int(random() % 45);
        std::string text(n, 'a');
        for (char& character : text) character = char('a' + random() % 4);

        std::vector<int> z = m1une::string::z_algorithm(text);
        for (int i = 0; i < n; i++) {
            [[maybe_unused]] int expected = 0;
            while (
                i + expected < n &&
                text[expected] == text[i + expected]
            ) {
                expected++;
            }
            assert(z[i] == expected);
        }

        std::vector<int> prefix = m1une::string::prefix_function(text);
        for (int i = 0; i < n; i++) {
            [[maybe_unused]] int expected = 0;
            for (int length = 1; length <= i; length++) {
                if (
                    text.substr(0, length) ==
                    text.substr(i - length + 1, length)
                ) {
                    expected = length;
                }
            }
            assert(prefix[i] == expected);
        }

        int pattern_length = int(random() % 12);
        std::string pattern(pattern_length, 'a');
        for (char& character : pattern) character = char('a' + random() % 4);
        std::vector<int> expected_occurrences;
        for (int i = 0; i + pattern_length <= n; i++) {
            if (text.substr(i, pattern_length) == pattern) {
                expected_occurrences.push_back(i);
            }
        }
        assert(
            m1une::string::kmp_search(text, pattern) ==
            expected_occurrences
        );

        m1une::string::ManacherResult palindromes =
            m1une::string::manacher(text);
        int longest = 0;
        for (int left = 0; left <= n; left++) {
            for (int right = left; right <= n; right++) {
                bool expected = true;
                for (int offset = 0; offset < (right - left) / 2; offset++) {
                    if (text[left + offset] != text[right - 1 - offset]) {
                        expected = false;
                        break;
                    }
                }
                assert(palindromes.is_palindrome(left, right) == expected);
                if (expected) longest = std::max(longest, right - left);
            }
        }
        assert(palindromes.longest_length() == longest);

        std::vector<int> suffixes = m1une::string::suffix_array(text);
        std::vector<int> expected_suffixes(n);
        std::iota(expected_suffixes.begin(), expected_suffixes.end(), 0);
        std::sort(
            expected_suffixes.begin(),
            expected_suffixes.end(),
            [&text](int a, int b) {
                return text.substr(a) < text.substr(b);
            }
        );
        assert(suffixes == expected_suffixes);

        std::vector<int> lcp = m1une::string::lcp_array(text, suffixes);
        for (int i = 0; i + 1 < n; i++) {
            int expected = 0;
            while (
                suffixes[i] + expected < n &&
                suffixes[i + 1] + expected < n &&
                text[suffixes[i] + expected] ==
                    text[suffixes[i + 1] + expected]
            ) {
                expected++;
            }
            assert(lcp[i] == expected);
        }

        std::vector<std::pair<int, int>> lyndon_factors =
            m1une::string::lyndon_factorization(text);
        int minimum_shift = m1une::string::minimum_cyclic_shift(text);
        assert(
            (n == 0 && minimum_shift == 0) ||
            (0 <= minimum_shift && minimum_shift < n)
        );
        std::string restored;
        std::vector<std::string> factor_words;
        for (auto [left, right] : lyndon_factors) {
            assert(0 <= left && left < right && right <= n);
            std::string word = text.substr(left, right - left);
            restored += word;
            factor_words.push_back(word);
        }
        assert(restored == text);
        for (int i = 0; i + 1 < int(factor_words.size()); i++) {
            assert(!(factor_words[i] < factor_words[i + 1]));
        }
    }
}

}  // namespace

int main() {
    m1une::utilities::FastInput fast_input;
    m1une::utilities::FastOutput fast_output;

    test_edge_cases();
    test_randomized();

    long long a, b;
    fast_input >> a >> b;
    fast_output << a + b << '\n';
}
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