verify/ds/wavelet_matrix/dynamic_wavelet_matrix.test.cpp

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Last update: 2026-10-06 01:57:24+09:00
Problem: https://judge.yosupo.jp/problem/point_set_range_frequency

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Code

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

#include "../../../ds/wavelet_matrix/dynamic_wavelet_matrix.hpp"
#include "../../../utilities/fast_io.hpp"

#include <algorithm>
#include <cassert>
#include <cstdint>
#include <limits>
#include <optional>
#include <vector>

namespace {

using Matrix = m1une::ds::DynamicWaveletMatrix<int>;

std::uint64_t random_state = 0x123456789abcdef0ULL;

std::uint64_t random_value() {
    random_state ^= random_state << 7;
    random_state ^= random_state >> 9;
    return random_state;
}

int random_int() {
    return int(std::uint32_t(random_value()));
}

void check_queries(const Matrix& matrix, const std::vector<int>& values) {
    assert(matrix.size() == int(values.size()));
    assert(matrix.empty() == values.empty());
    for (int i = 0; i < int(values.size()); i++) {
        assert(matrix[i] == values[i]);
    }
    if (values.empty()) return;

    int left = int(random_value() % values.size());
    int right = left + 1 + int(random_value() % (values.size() - left));
    int value = random_int();
    int rank = int(std::count(
        values.begin() + left,
        values.begin() + right,
        value
    ));
    assert(matrix.rank(value, left, right) == rank);
    assert(
        matrix.rank(value, right) ==
        int(std::count(values.begin(), values.begin() + right, value))
    );

    int first_bound = random_int();
    int second_bound = random_int();
    int lower = std::min(first_bound, second_bound);
    int upper = std::max(first_bound, second_bound);
    int below = 0;
    int between = 0;
    for (int i = left; i < right; i++) {
        below += values[i] < upper;
        between += lower <= values[i] && values[i] < upper;
    }
    assert(matrix.range_freq(left, right, upper) == below);
    assert(matrix.range_freq(left, right, lower, upper) == between);

    std::vector<int> sorted(values.begin() + left, values.begin() + right);
    std::sort(sorted.begin(), sorted.end());
    int k = int(random_value() % sorted.size());
    assert(matrix.kth_smallest(left, right, k) == sorted[k]);
    assert(
        matrix.kth_largest(left, right, k) ==
        sorted[sorted.size() - 1 - k]
    );

    auto expected_previous = std::lower_bound(sorted.begin(), sorted.end(), upper);
    std::optional<int> previous;
    if (expected_previous != sorted.begin()) previous = *--expected_previous;
    assert(matrix.prev_value(left, right, upper) == previous);

    auto expected_next = std::lower_bound(sorted.begin(), sorted.end(), lower);
    std::optional<int> next;
    if (expected_next != sorted.end()) next = *expected_next;
    assert(matrix.next_value(left, right, lower) == next);
}

void test_randomized() {
    std::vector<int> edge_values = {
        std::numeric_limits<int>::min(),
        -1,
        0,
        1,
        std::numeric_limits<int>::max()
    };
    Matrix edge_matrix(edge_values);
    check_queries(edge_matrix, edge_values);

    std::vector<signed char> byte_values = {-128, 5, -1, 127};
    m1une::ds::DynamicWaveletMatrix<signed char> byte_matrix(byte_values);
    assert(byte_matrix.kth_smallest(0, 4, 1) == -1);
    byte_matrix.set(1, -100);
    byte_matrix.insert(2, 100);
    assert(
        byte_matrix.range_freq(0, 5, static_cast<signed char>(0)) == 3
    );

    using Unsigned = unsigned long long;
    std::vector<Unsigned> unsigned_values = {
        0,
        std::numeric_limits<Unsigned>::max(),
        Unsigned(1) << 63
    };
    m1une::ds::DynamicWaveletMatrix<Unsigned> unsigned_matrix(
        unsigned_values
    );
    assert(
        unsigned_matrix.kth_largest(0, 3, 0) ==
        std::numeric_limits<Unsigned>::max()
    );
    unsigned_matrix.clear();
    assert(unsigned_matrix.empty());

    for (int trial = 0; trial < 120; trial++) {
        int initial_size = int(random_value() % 50);
        std::vector<int> values(initial_size);
        for (int& value : values) value = random_int();
        Matrix matrix(values);

        for (int operation = 0; operation < 250; operation++) {
            int type = int(random_value() % 5);
            if (values.empty()) type = 0;
            if (type == 0) {
                int position = int(random_value() % (values.size() + 1));
                int value = random_int();
                values.insert(values.begin() + position, value);
                matrix.insert(position, value);
            } else if (type == 1) {
                int position = int(random_value() % values.size());
                int expected = values[position];
                values.erase(values.begin() + position);
                assert(matrix.erase(position) == expected);
            } else if (type == 2) {
                int position = int(random_value() % values.size());
                int value = random_int();
                values[position] = value;
                matrix.set(position, value);
            } else if (type == 3) {
                int value = random_int();
                values.push_back(value);
                matrix.push_back(value);
            }
            check_queries(matrix, values);
        }
    }

    std::vector<int> values(900);
    for (int& value : values) value = random_int();
    Matrix matrix(values);
    for (int operation = 0; operation < 4000; operation++) {
        int from = int(random_value() % values.size());
        int to = int(random_value() % values.size());
        int value = values[from];
        values.erase(values.begin() + from);
        assert(matrix.erase(from) == value);
        values.insert(values.begin() + to, value);
        matrix.insert(to, value);
        if (operation % 20 == 0) check_queries(matrix, values);
    }
}

}  // namespace

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

    test_randomized();

    int size = 0;
    int query_count = 0;
    fast_input >> size >> query_count;
    std::vector<int> values(size);
    for (int& value : values) fast_input >> value;
    Matrix matrix(values);
    while (query_count--) {
        int type = 0;
        fast_input >> type;
        if (type == 0) {
            int position = 0;
            int value = 0;
            fast_input >> position >> value;
            matrix.set(position, value);
        } else {
            int left = 0;
            int right = 0;
            int value = 0;
            fast_input >> left >> right >> value;
            fast_output << matrix.rank(value, left, right) << '\n';
        }
    }
}

#line 1 "verify/ds/wavelet_matrix/dynamic_wavelet_matrix.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/point_set_range_frequency"

#line 1 "ds/wavelet_matrix/dynamic_wavelet_matrix.hpp"



#include <algorithm>
#include <array>
#include <bit>
#include <cassert>
#include <concepts>
#include <cstdint>
#include <limits>
#include <optional>
#include <type_traits>
#include <utility>
#include <vector>

namespace m1une {
namespace ds {

namespace dynamic_wavelet_matrix_detail {

// A dynamic bit vector stored as an implicit treap of small packed chunks.
class DynamicRankBitVector {
   public:
    struct AccessRankResult {
        bool value;
        int ones_before;
    };

    struct EraseRankResult {
        bool value;
        int ones_before;
    };

    struct RankPair {
        int left_ones;
        int right_ones;
    };

   private:
    static constexpr int word_bits = 64;
    static constexpr int chunk_words = 4;
    static constexpr int chunk_capacity = word_bits * chunk_words;
    static constexpr int minimum_chunk_size = chunk_capacity / 2;

    struct Node {
        std::array<std::uint64_t, chunk_words> bits{};
        std::uint32_t priority = 0;
        int left = 0;
        int right = 0;
        int subtree_size = 0;
        int subtree_ones = 0;
        std::uint16_t length = 0;
        std::uint16_t chunk_ones = 0;
    };

    std::vector<Node> _nodes;
    std::vector<int> _free_nodes;
    int _root = 0;
    std::uint32_t _random_state = 1;

    int size_of(int node) const {
        return _nodes[node].subtree_size;
    }

    int ones_of(int node) const {
        return _nodes[node].subtree_ones;
    }

    std::uint32_t next_priority() {
        _random_state ^= _random_state << 13;
        _random_state ^= _random_state >> 17;
        _random_state ^= _random_state << 5;
        if (_random_state == 0) _random_state = 1;
        return _random_state;
    }

    void update(int node) {
        if (node == 0) return;
        _nodes[node].subtree_size =
            size_of(_nodes[node].left) + int(_nodes[node].length) +
            size_of(_nodes[node].right);
        _nodes[node].subtree_ones =
            ones_of(_nodes[node].left) + int(_nodes[node].chunk_ones) +
            ones_of(_nodes[node].right);
    }

    bool local_get(int node, int position) const {
        return (_nodes[node].bits[position / word_bits] >>
                (position % word_bits)) &
               1U;
    }

    void local_set(int node, int position, bool value) {
        std::uint64_t mask =
            std::uint64_t(1) << (position % word_bits);
        std::uint64_t& word = _nodes[node].bits[position / word_bits];
        if (value) {
            word |= mask;
        } else {
            word &= ~mask;
        }
    }

    int local_rank1(int node, int right) const {
        int full_words = right / word_bits;
        int result = 0;
        for (int word = 0; word < full_words; word++) {
            result += std::popcount(_nodes[node].bits[word]);
        }
        int remainder = right % word_bits;
        if (remainder != 0) {
            result += std::popcount(
                _nodes[node].bits[full_words] &
                ((std::uint64_t(1) << remainder) - 1)
            );
        }
        return result;
    }

    void clear_unused_bits(int node) {
        int length = _nodes[node].length;
        int word = length / word_bits;
        int remainder = length % word_bits;
        if (word < chunk_words) {
            if (remainder == 0) {
                _nodes[node].bits[word] = 0;
            } else {
                _nodes[node].bits[word] &=
                    (std::uint64_t(1) << remainder) - 1;
                word++;
            }
            for (; word < chunk_words; word++) {
                _nodes[node].bits[word] = 0;
            }
        }
    }

    void local_insert(int node, int position, bool value) {
        Node& current = _nodes[node];
        assert(0 <= position && position <= current.length);
        assert(current.length < chunk_capacity);

        int first_word = position / word_bits;
        int offset = position % word_bits;
        for (int word = chunk_words - 1; word > first_word; word--) {
            current.bits[word] =
                (current.bits[word] << 1) |
                (current.bits[word - 1] >> (word_bits - 1));
        }
        std::uint64_t lower_mask =
            offset == 0 ? 0 : (std::uint64_t(1) << offset) - 1;
        current.bits[first_word] =
            (current.bits[first_word] & lower_mask) |
            ((current.bits[first_word] & ~lower_mask) << 1);
        if (value) {
            current.bits[first_word] |= std::uint64_t(1) << offset;
        }
        current.length++;
        current.chunk_ones += value;
        clear_unused_bits(node);
        update(node);
    }

    bool local_erase(int node, int position) {
        Node& current = _nodes[node];
        assert(0 <= position && position < current.length);
        bool value = local_get(node, position);
        int first_word = position / word_bits;
        int offset = position % word_bits;
        std::uint64_t lower_mask =
            offset == 0 ? 0 : (std::uint64_t(1) << offset) - 1;
        std::uint64_t shifted =
            offset == word_bits - 1
                ? 0
                : (current.bits[first_word] >> (offset + 1)) << offset;
        std::uint64_t carry =
            first_word + 1 < chunk_words
                ? (current.bits[first_word + 1] & 1U) << (word_bits - 1)
                : 0;
        current.bits[first_word] =
            (current.bits[first_word] & lower_mask) | shifted | carry;
        for (int word = first_word + 1; word < chunk_words; word++) {
            std::uint64_t next_carry =
                word + 1 < chunk_words
                    ? (current.bits[word + 1] & 1U) << (word_bits - 1)
                    : 0;
            current.bits[word] = (current.bits[word] >> 1) | next_carry;
        }
        current.length--;
        current.chunk_ones -= value;
        clear_unused_bits(node);
        update(node);
        return value;
    }

    int new_node() {
        int node;
        if (_free_nodes.empty()) {
            node = int(_nodes.size());
            _nodes.emplace_back();
        } else {
            node = _free_nodes.back();
            _free_nodes.pop_back();
            _nodes[node] = Node();
        }
        _nodes[node].priority = next_priority();
        return node;
    }

    int new_node(const std::vector<std::uint8_t>& bits, int first, int last) {
        int node = new_node();
        _nodes[node].length = std::uint16_t(last - first);
        for (int position = first; position < last; position++) {
            if (bits[position]) {
                local_set(node, position - first, true);
                _nodes[node].chunk_ones++;
            }
        }
        update(node);
        return node;
    }

    void recycle_node(int node) {
        assert(node != 0);
        _nodes[node] = Node();
        _free_nodes.push_back(node);
    }

    int merge(int left, int right) {
        if (left == 0 || right == 0) return left != 0 ? left : right;
        if (_nodes[left].priority > _nodes[right].priority) {
            _nodes[left].right = merge(_nodes[left].right, right);
            update(left);
            return left;
        }
        _nodes[right].left = merge(left, _nodes[right].left);
        update(right);
        return right;
    }

    int rotate_right(int tree) {
        int result = _nodes[tree].left;
        _nodes[tree].left = _nodes[result].right;
        _nodes[result].right = tree;
        update(tree);
        update(result);
        return result;
    }

    int rotate_left(int tree) {
        int result = _nodes[tree].right;
        _nodes[tree].right = _nodes[result].left;
        _nodes[result].left = tree;
        update(tree);
        update(result);
        return result;
    }

    int extract_leftmost(int tree, int& extracted) {
        if (_nodes[tree].left == 0) {
            extracted = tree;
            int result = _nodes[tree].right;
            _nodes[tree].right = 0;
            update(tree);
            return result;
        }
        _nodes[tree].left = extract_leftmost(_nodes[tree].left, extracted);
        update(tree);
        return tree;
    }

    int extract_rightmost(int tree, int& extracted) {
        if (_nodes[tree].right == 0) {
            extracted = tree;
            int result = _nodes[tree].left;
            _nodes[tree].left = 0;
            update(tree);
            return result;
        }
        _nodes[tree].right = extract_rightmost(_nodes[tree].right, extracted);
        update(tree);
        return tree;
    }

    void assign_concatenation(
        int destination,
        int first,
        int second,
        int begin,
        int length
    ) {
        std::array<std::uint64_t, chunk_words> bits{};
        int ones = 0;
        int first_length = _nodes[first].length;
        for (int position = 0; position < length; position++) {
            int source_position = begin + position;
            bool value = source_position < first_length
                             ? local_get(first, source_position)
                             : local_get(
                                   second,
                                   source_position - first_length
                               );
            if (value) {
                bits[position / word_bits] |=
                    std::uint64_t(1) << (position % word_bits);
                ones++;
            }
        }
        _nodes[destination].bits = bits;
        _nodes[destination].length = std::uint16_t(length);
        _nodes[destination].chunk_ones = std::uint16_t(ones);
        update(destination);
    }

    int rebalance(int node) {
        if (_nodes[node].length >= minimum_chunk_size) return node;

        if (_nodes[node].right != 0) {
            int neighbor = 0;
            _nodes[node].right =
                extract_leftmost(_nodes[node].right, neighbor);
            int total = _nodes[node].length + _nodes[neighbor].length;
            if (total <= chunk_capacity) {
                assign_concatenation(node, node, neighbor, 0, total);
                recycle_node(neighbor);
            } else {
                int left_length = total / 2;
                std::array<std::uint8_t, chunk_capacity * 2> values{};
                for (int i = 0; i < _nodes[node].length; i++) {
                    values[i] = local_get(node, i);
                }
                int old_length = _nodes[node].length;
                for (int i = 0; i < _nodes[neighbor].length; i++) {
                    values[old_length + i] = local_get(neighbor, i);
                }
                std::vector<std::uint8_t> packed(values.begin(), values.begin() + total);
                assign_from_values(node, packed, 0, left_length);
                assign_from_values(neighbor, packed, left_length, total);
                _nodes[node].right = merge(neighbor, _nodes[node].right);
            }
            update(node);
            return node;
        }

        if (_nodes[node].left != 0) {
            int neighbor = 0;
            _nodes[node].left =
                extract_rightmost(_nodes[node].left, neighbor);
            int total = _nodes[neighbor].length + _nodes[node].length;
            std::array<std::uint8_t, chunk_capacity * 2> values{};
            for (int i = 0; i < _nodes[neighbor].length; i++) {
                values[i] = local_get(neighbor, i);
            }
            int neighbor_length = _nodes[neighbor].length;
            for (int i = 0; i < _nodes[node].length; i++) {
                values[neighbor_length + i] = local_get(node, i);
            }
            std::vector<std::uint8_t> packed(values.begin(), values.begin() + total);
            if (total <= chunk_capacity) {
                assign_from_values(node, packed, 0, total);
                recycle_node(neighbor);
            } else {
                int left_length = total / 2;
                assign_from_values(neighbor, packed, 0, left_length);
                assign_from_values(node, packed, left_length, total);
                _nodes[node].left = merge(_nodes[node].left, neighbor);
            }
            update(node);
        }
        return node;
    }

    void assign_from_values(
        int node,
        const std::vector<std::uint8_t>& values,
        int first,
        int last
    ) {
        _nodes[node].bits.fill(0);
        _nodes[node].length = std::uint16_t(last - first);
        _nodes[node].chunk_ones = 0;
        for (int i = first; i < last; i++) {
            if (values[i]) {
                local_set(node, i - first, true);
                _nodes[node].chunk_ones++;
            }
        }
        update(node);
    }

    int prefix_rank1_impl(int tree, int right) const {
        int result = 0;
        while (tree != 0 && right != 0) {
            int left_size = size_of(_nodes[tree].left);
            if (right <= left_size) {
                tree = _nodes[tree].left;
                continue;
            }
            result += ones_of(_nodes[tree].left);
            right -= left_size;
            int take = std::min(right, int(_nodes[tree].length));
            result += local_rank1(tree, take);
            right -= take;
            if (right == 0) break;
            tree = _nodes[tree].right;
        }
        return result;
    }

    RankPair rank1_pair_impl(int tree, int left, int right) const {
        if (left == right) {
            int ones = prefix_rank1_impl(tree, left);
            return RankPair{ones, ones};
        }
        if (tree == 0 || right == 0) return RankPair{0, 0};

        int left_size = size_of(_nodes[tree].left);
        int chunk_end = left_size + _nodes[tree].length;
        if (right <= left_size) {
            return rank1_pair_impl(_nodes[tree].left, left, right);
        }
        if (chunk_end <= left) {
            int base =
                ones_of(_nodes[tree].left) + _nodes[tree].chunk_ones;
            RankPair result = rank1_pair_impl(
                _nodes[tree].right,
                left - chunk_end,
                right - chunk_end
            );
            result.left_ones += base;
            result.right_ones += base;
            return result;
        }

        int left_ones;
        if (left <= left_size) {
            left_ones = prefix_rank1_impl(_nodes[tree].left, left);
        } else {
            left_ones = ones_of(_nodes[tree].left) +
                        local_rank1(tree, left - left_size);
        }

        int right_ones;
        if (right <= chunk_end) {
            right_ones = ones_of(_nodes[tree].left) +
                         local_rank1(tree, right - left_size);
        } else {
            right_ones = ones_of(_nodes[tree].left) +
                         _nodes[tree].chunk_ones +
                         prefix_rank1_impl(
                             _nodes[tree].right,
                             right - chunk_end
                         );
        }
        return RankPair{left_ones, right_ones};
    }

    int insert_impl(
        int tree,
        int position,
        bool value,
        int& ones_before
    ) {
        if (tree == 0) {
            int node = new_node();
            local_insert(node, 0, value);
            return node;
        }

        int left_size = size_of(_nodes[tree].left);
        int length = _nodes[tree].length;
        if (position < left_size) {
            _nodes[tree].left = insert_impl(
                _nodes[tree].left,
                position,
                value,
                ones_before
            );
            update(tree);
            if (_nodes[_nodes[tree].left].priority >
                _nodes[tree].priority) {
                tree = rotate_right(tree);
            }
            return tree;
        }
        if (position > left_size + length) {
            ones_before +=
                ones_of(_nodes[tree].left) + _nodes[tree].chunk_ones;
            _nodes[tree].right = insert_impl(
                _nodes[tree].right,
                position - left_size - length,
                value,
                ones_before
            );
            update(tree);
            if (_nodes[_nodes[tree].right].priority >
                _nodes[tree].priority) {
                tree = rotate_left(tree);
            }
            return tree;
        }

        int local_position = position - left_size;
        ones_before += ones_of(_nodes[tree].left) +
                       local_rank1(tree, local_position);
        if (length < chunk_capacity) {
            local_insert(tree, local_position, value);
            return tree;
        }

        std::vector<std::uint8_t> values(chunk_capacity);
        for (int i = 0; i < chunk_capacity; i++) {
            values[i] = local_get(tree, i);
        }
        int right_chunk = new_node();
        int middle = chunk_capacity / 2;
        assign_from_values(tree, values, 0, middle);
        assign_from_values(right_chunk, values, middle, chunk_capacity);
        if (local_position <= middle) {
            local_insert(tree, local_position, value);
        } else {
            local_insert(right_chunk, local_position - middle, value);
        }

        int old_right = _nodes[tree].right;
        _nodes[tree].right = 0;
        update(tree);
        return merge(merge(tree, right_chunk), old_right);
    }

    int erase_impl(
        int tree,
        int position,
        EraseRankResult& result
    ) {
        int left_size = size_of(_nodes[tree].left);
        int length = _nodes[tree].length;
        if (position < left_size) {
            _nodes[tree].left = erase_impl(
                _nodes[tree].left,
                position,
                result
            );
            update(tree);
            return tree;
        }
        if (position >= left_size + length) {
            result.ones_before +=
                ones_of(_nodes[tree].left) + _nodes[tree].chunk_ones;
            _nodes[tree].right = erase_impl(
                _nodes[tree].right,
                position - left_size - length,
                result
            );
            update(tree);
            return tree;
        }

        int local_position = position - left_size;
        result.ones_before += ones_of(_nodes[tree].left) +
                              local_rank1(tree, local_position);
        result.value = local_erase(tree, local_position);
        if (_nodes[tree].length == 0) {
            int merged = merge(_nodes[tree].left, _nodes[tree].right);
            recycle_node(tree);
            return merged;
        }
        return rebalance(tree);
    }

    void update_subtree(int tree) {
        if (tree == 0) return;
        update_subtree(_nodes[tree].left);
        update_subtree(_nodes[tree].right);
        update(tree);
    }

    void build(const std::vector<std::uint8_t>& bits) {
        _nodes.clear();
        _nodes.emplace_back();
        _free_nodes.clear();
        _root = 0;
        _nodes.reserve(bits.size() / minimum_chunk_size + 2);

        std::vector<int> stack;
        for (int first = 0; first < int(bits.size()); first += chunk_capacity) {
            int last = std::min(first + chunk_capacity, int(bits.size()));
            int node = new_node(bits, first, last);
            int left = 0;
            while (!stack.empty() &&
                   _nodes[stack.back()].priority < _nodes[node].priority) {
                left = stack.back();
                stack.pop_back();
            }
            _nodes[node].left = left;
            if (!stack.empty()) _nodes[stack.back()].right = node;
            stack.push_back(node);
        }
        if (!stack.empty()) _root = stack.front();
        update_subtree(_root);
    }

   public:
    DynamicRankBitVector() : _nodes(1) {}

    explicit DynamicRankBitVector(
        const std::vector<std::uint8_t>& bits,
        std::uint32_t seed = 1
    ) : _random_state(seed == 0 ? 1 : seed) {
        build(bits);
    }

    int size() const {
        return size_of(_root);
    }

    bool get(int position) const {
        return access_with_rank(position).value;
    }

    AccessRankResult access_with_rank(int position) const {
        assert(0 <= position && position < size());
        int ones_before = 0;
        int tree = _root;
        while (tree != 0) {
            int left_size = size_of(_nodes[tree].left);
            if (position < left_size) {
                tree = _nodes[tree].left;
            } else if (position < left_size + _nodes[tree].length) {
                int local_position = position - left_size;
                ones_before += ones_of(_nodes[tree].left) +
                               local_rank1(tree, local_position);
                return AccessRankResult{
                    local_get(tree, local_position),
                    ones_before
                };
            } else {
                ones_before +=
                    ones_of(_nodes[tree].left) + _nodes[tree].chunk_ones;
                position -= left_size + _nodes[tree].length;
                tree = _nodes[tree].right;
            }
        }
        assert(false);
        return AccessRankResult{false, 0};
    }

    int rank1(int right) const {
        assert(0 <= right && right <= size());
        return prefix_rank1_impl(_root, right);
    }

    RankPair rank1_pair(int left, int right) const {
        assert(0 <= left && left <= right && right <= size());
        return rank1_pair_impl(_root, left, right);
    }

    void insert(int position, bool value) {
        insert_with_rank(position, value);
    }

    int insert_with_rank(int position, bool value) {
        assert(0 <= position && position <= size());
        int ones_before = 0;
        _root = insert_impl(_root, position, value, ones_before);
        return ones_before;
    }

    bool erase(int position) {
        return erase_with_rank(position).value;
    }

    EraseRankResult erase_with_rank(int position) {
        assert(0 <= position && position < size());
        EraseRankResult result{false, 0};
        _root = erase_impl(_root, position, result);
        return result;
    }
};

}  // namespace dynamic_wavelet_matrix_detail

// A dynamic wavelet matrix for integral sequences.
template <std::integral T>
requires(!std::same_as<std::remove_cv_t<T>, bool>)
class DynamicWaveletMatrix {
   public:
    using value_type = T;
    using unsigned_type = std::make_unsigned_t<T>;

   private:
    static constexpr int bit_width =
        std::numeric_limits<unsigned_type>::digits;
    static constexpr unsigned_type sign_mask = [] {
        if constexpr (std::signed_integral<T>) {
            return unsigned_type(1) << (bit_width - 1);
        } else {
            return unsigned_type(0);
        }
    }();

    int _size = 0;
    std::vector<dynamic_wavelet_matrix_detail::DynamicRankBitVector> _matrix;
    std::array<int, bit_width> _zero_count{};

    static unsigned_type encode(T value) {
        unsigned_type bits;
        if constexpr (std::signed_integral<T>) {
            bits = std::bit_cast<unsigned_type>(value);
        } else {
            bits = value;
        }
        return bits ^ sign_mask;
    }

    static T decode(unsigned_type key) {
        unsigned_type bits = key ^ sign_mask;
        if constexpr (std::signed_integral<T>) {
            return std::bit_cast<T>(bits);
        } else {
            return bits;
        }
    }

    static bool bit(unsigned_type key, int level) {
        return (key >> (bit_width - 1 - level)) & unsigned_type(1);
    }

    void insert_encoded(int position, unsigned_type key) {
        for (int level = 0; level < bit_width; level++) {
            if (bit(key, level)) {
                int ones_before =
                    _matrix[level].insert_with_rank(position, true);
                int next_position = _zero_count[level] + ones_before;
                position = next_position;
            } else {
                int ones_before =
                    _matrix[level].insert_with_rank(position, false);
                int next_position = position - ones_before;
                _zero_count[level]++;
                position = next_position;
            }
        }
        _size++;
    }

    void erase_encoded(int position) {
        for (int level = 0; level < bit_width; level++) {
            auto erased = _matrix[level].erase_with_rank(position);
            int next_position;
            if (erased.value) {
                next_position = _zero_count[level] + erased.ones_before;
            } else {
                next_position = position - erased.ones_before;
                _zero_count[level]--;
            }
            position = next_position;
        }
        _size--;
    }

    int count_less_encoded(int left, int right, unsigned_type upper) const {
        int result = 0;
        for (int level = 0; level < bit_width; level++) {
            auto ranks = _matrix[level].rank1_pair(left, right);
            int left_ones = ranks.left_ones;
            int right_ones = ranks.right_ones;
            if (bit(upper, level)) {
                result += (right - left) - (right_ones - left_ones);
                left = _zero_count[level] + left_ones;
                right = _zero_count[level] + right_ones;
            } else {
                left -= left_ones;
                right -= right_ones;
            }
        }
        return result;
    }

   public:
    DynamicWaveletMatrix() : _matrix(bit_width) {}

    explicit DynamicWaveletMatrix(const std::vector<T>& values)
        : _size(int(values.size())) {
        std::vector<unsigned_type> current(_size);
        std::vector<unsigned_type> next(_size);
        for (int i = 0; i < _size; i++) current[i] = encode(values[i]);

        _matrix.reserve(bit_width);
        for (int level = 0; level < bit_width; level++) {
            std::vector<std::uint8_t> bits(_size);
            int zeros = 0;
            for (int i = 0; i < _size; i++) {
                bits[i] = bit(current[i], level);
                zeros += !bits[i];
            }
            _zero_count[level] = zeros;
            int zero_position = 0;
            int one_position = zeros;
            for (int i = 0; i < _size; i++) {
                if (bits[i]) {
                    next[one_position++] = current[i];
                } else {
                    next[zero_position++] = current[i];
                }
            }
            _matrix.emplace_back(
                bits,
                std::uint32_t(0x9e3779b9U + level * 0x85ebca6bU)
            );
            current.swap(next);
        }
    }

    int size() const {
        return _size;
    }

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

    void clear() {
        *this = DynamicWaveletMatrix();
    }

    T access(int position) const {
        assert(0 <= position && position < _size);
        unsigned_type key = 0;
        for (int level = 0; level < bit_width; level++) {
            auto accessed = _matrix[level].access_with_rank(position);
            if (accessed.value) {
                key |= unsigned_type(1) << (bit_width - 1 - level);
                position = _zero_count[level] + accessed.ones_before;
            } else {
                position -= accessed.ones_before;
            }
        }
        return decode(key);
    }

    T operator[](int position) const {
        return access(position);
    }

    void insert(int position, T value) {
        assert(0 <= position && position <= _size);
        insert_encoded(position, encode(value));
    }

    void push_back(T value) {
        insert(_size, value);
    }

    T erase(int position) {
        assert(0 <= position && position < _size);
        T value = access(position);
        erase_encoded(position);
        return value;
    }

    void set(int position, T value) {
        assert(0 <= position && position < _size);
        if (access(position) == value) return;
        erase_encoded(position);
        insert_encoded(position, encode(value));
    }

    int rank(T value, int right) const {
        assert(0 <= right && right <= _size);
        return rank(value, 0, right);
    }

    int rank(T value, int left, int right) const {
        assert(0 <= left && left <= right && right <= _size);
        unsigned_type key = encode(value);
        for (int level = 0; level < bit_width; level++) {
            auto ranks = _matrix[level].rank1_pair(left, right);
            int left_ones = ranks.left_ones;
            int right_ones = ranks.right_ones;
            if (bit(key, level)) {
                left = _zero_count[level] + left_ones;
                right = _zero_count[level] + right_ones;
            } else {
                left -= left_ones;
                right -= right_ones;
            }
        }
        return right - left;
    }

    T kth_smallest(int left, int right, int k) const {
        assert(0 <= left && left <= right && right <= _size);
        assert(0 <= k && k < right - left);
        unsigned_type key = 0;
        for (int level = 0; level < bit_width; level++) {
            auto ranks = _matrix[level].rank1_pair(left, right);
            int left_ones = ranks.left_ones;
            int right_ones = ranks.right_ones;
            int left_zeros = left - left_ones;
            int right_zeros = right - right_ones;
            int zeros = right_zeros - left_zeros;
            if (k < zeros) {
                left = left_zeros;
                right = right_zeros;
            } else {
                k -= zeros;
                key |= unsigned_type(1) << (bit_width - 1 - level);
                left = _zero_count[level] + left_ones;
                right = _zero_count[level] + right_ones;
            }
        }
        return decode(key);
    }

    T kth_largest(int left, int right, int k) const {
        assert(0 <= left && left <= right && right <= _size);
        assert(0 <= k && k < right - left);
        return kth_smallest(left, right, right - left - 1 - k);
    }

    int range_freq(int left, int right, T upper) const {
        assert(0 <= left && left <= right && right <= _size);
        return count_less_encoded(left, right, encode(upper));
    }

    int range_freq(int left, int right, T lower, T upper) const {
        assert(0 <= left && left <= right && right <= _size);
        if (upper <= lower) return 0;
        return range_freq(left, right, upper) -
               range_freq(left, right, lower);
    }

    std::optional<T> prev_value(int left, int right, T upper) const {
        assert(0 <= left && left <= right && right <= _size);
        int count = range_freq(left, right, upper);
        if (count == 0) return std::nullopt;
        return kth_smallest(left, right, count - 1);
    }

    std::optional<T> next_value(int left, int right, T lower) const {
        assert(0 <= left && left <= right && right <= _size);
        int count = range_freq(left, right, lower);
        if (count == right - left) return std::nullopt;
        return kth_smallest(left, right, count);
    }
};

}  // namespace ds
}  // namespace m1une


#line 1 "utilities/fast_io.hpp"



#line 6 "utilities/fast_io.hpp"
#include <cerrno>
#include <charconv>
#include <cstddef>
#include <cstdio>
#include <cstdlib>
#line 12 "utilities/fast_io.hpp"
#include <cstring>
#include <iterator>
#include <string>
#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 5 "verify/ds/wavelet_matrix/dynamic_wavelet_matrix.test.cpp"

#line 12 "verify/ds/wavelet_matrix/dynamic_wavelet_matrix.test.cpp"

namespace {

using Matrix = m1une::ds::DynamicWaveletMatrix<int>;

std::uint64_t random_state = 0x123456789abcdef0ULL;

std::uint64_t random_value() {
    random_state ^= random_state << 7;
    random_state ^= random_state >> 9;
    return random_state;
}

int random_int() {
    return int(std::uint32_t(random_value()));
}

void check_queries(const Matrix& matrix, const std::vector<int>& values) {
    assert(matrix.size() == int(values.size()));
    assert(matrix.empty() == values.empty());
    for (int i = 0; i < int(values.size()); i++) {
        assert(matrix[i] == values[i]);
    }
    if (values.empty()) return;

    int left = int(random_value() % values.size());
    int right = left + 1 + int(random_value() % (values.size() - left));
    int value = random_int();
    int rank = int(std::count(
        values.begin() + left,
        values.begin() + right,
        value
    ));
    assert(matrix.rank(value, left, right) == rank);
    assert(
        matrix.rank(value, right) ==
        int(std::count(values.begin(), values.begin() + right, value))
    );

    int first_bound = random_int();
    int second_bound = random_int();
    int lower = std::min(first_bound, second_bound);
    int upper = std::max(first_bound, second_bound);
    int below = 0;
    int between = 0;
    for (int i = left; i < right; i++) {
        below += values[i] < upper;
        between += lower <= values[i] && values[i] < upper;
    }
    assert(matrix.range_freq(left, right, upper) == below);
    assert(matrix.range_freq(left, right, lower, upper) == between);

    std::vector<int> sorted(values.begin() + left, values.begin() + right);
    std::sort(sorted.begin(), sorted.end());
    int k = int(random_value() % sorted.size());
    assert(matrix.kth_smallest(left, right, k) == sorted[k]);
    assert(
        matrix.kth_largest(left, right, k) ==
        sorted[sorted.size() - 1 - k]
    );

    auto expected_previous = std::lower_bound(sorted.begin(), sorted.end(), upper);
    std::optional<int> previous;
    if (expected_previous != sorted.begin()) previous = *--expected_previous;
    assert(matrix.prev_value(left, right, upper) == previous);

    auto expected_next = std::lower_bound(sorted.begin(), sorted.end(), lower);
    std::optional<int> next;
    if (expected_next != sorted.end()) next = *expected_next;
    assert(matrix.next_value(left, right, lower) == next);
}

void test_randomized() {
    std::vector<int> edge_values = {
        std::numeric_limits<int>::min(),
        -1,
        0,
        1,
        std::numeric_limits<int>::max()
    };
    Matrix edge_matrix(edge_values);
    check_queries(edge_matrix, edge_values);

    std::vector<signed char> byte_values = {-128, 5, -1, 127};
    m1une::ds::DynamicWaveletMatrix<signed char> byte_matrix(byte_values);
    assert(byte_matrix.kth_smallest(0, 4, 1) == -1);
    byte_matrix.set(1, -100);
    byte_matrix.insert(2, 100);
    assert(
        byte_matrix.range_freq(0, 5, static_cast<signed char>(0)) == 3
    );

    using Unsigned = unsigned long long;
    std::vector<Unsigned> unsigned_values = {
        0,
        std::numeric_limits<Unsigned>::max(),
        Unsigned(1) << 63
    };
    m1une::ds::DynamicWaveletMatrix<Unsigned> unsigned_matrix(
        unsigned_values
    );
    assert(
        unsigned_matrix.kth_largest(0, 3, 0) ==
        std::numeric_limits<Unsigned>::max()
    );
    unsigned_matrix.clear();
    assert(unsigned_matrix.empty());

    for (int trial = 0; trial < 120; trial++) {
        int initial_size = int(random_value() % 50);
        std::vector<int> values(initial_size);
        for (int& value : values) value = random_int();
        Matrix matrix(values);

        for (int operation = 0; operation < 250; operation++) {
            int type = int(random_value() % 5);
            if (values.empty()) type = 0;
            if (type == 0) {
                int position = int(random_value() % (values.size() + 1));
                int value = random_int();
                values.insert(values.begin() + position, value);
                matrix.insert(position, value);
            } else if (type == 1) {
                int position = int(random_value() % values.size());
                int expected = values[position];
                values.erase(values.begin() + position);
                assert(matrix.erase(position) == expected);
            } else if (type == 2) {
                int position = int(random_value() % values.size());
                int value = random_int();
                values[position] = value;
                matrix.set(position, value);
            } else if (type == 3) {
                int value = random_int();
                values.push_back(value);
                matrix.push_back(value);
            }
            check_queries(matrix, values);
        }
    }

    std::vector<int> values(900);
    for (int& value : values) value = random_int();
    Matrix matrix(values);
    for (int operation = 0; operation < 4000; operation++) {
        int from = int(random_value() % values.size());
        int to = int(random_value() % values.size());
        int value = values[from];
        values.erase(values.begin() + from);
        assert(matrix.erase(from) == value);
        values.insert(values.begin() + to, value);
        matrix.insert(to, value);
        if (operation % 20 == 0) check_queries(matrix, values);
    }
}

}  // namespace

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

    test_randomized();

    int size = 0;
    int query_count = 0;
    fast_input >> size >> query_count;
    std::vector<int> values(size);
    for (int& value : values) fast_input >> value;
    Matrix matrix(values);
    while (query_count--) {
        int type = 0;
        fast_input >> type;
        if (type == 0) {
            int position = 0;
            int value = 0;
            fast_input >> position >> value;
            matrix.set(position, value);
        } else {
            int left = 0;
            int right = 0;
            int value = 0;
            fast_input >> left >> right >> value;
            fast_output << matrix.rank(value, left, right) << '\n';
        }
    }
}

m1une's library

This documentation is automatically generated by online-judge-tools/verification-helper

verify/ds/wavelet_matrix/dynamic_wavelet_matrix.test.cpp

Depends on

Code