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:heavy_check_mark: verify/ds/dynamic_array/dynamic_lazy_monoid_array_range_ap.test.cpp

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Code

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

#include "../../../ds/dynamic_array/dynamic_lazy_monoid_array.hpp"

#include <algorithm>
#include <cassert>
#include "../../../utilities/fast_io.hpp"
#include <numeric>
#include <random>
#include <utility>
#include <vector>

#include "../../../acted_monoid/range_ap_add_range_sum.hpp"

using AM = m1une::acted_monoid::RangeApAddRangeSum<long long>;
using Node = AM::value_type;
using Array = m1une::ds::DynamicLazyMonoidArray<AM>;

std::vector<long long> sums(std::vector<Node> a) {
    std::vector<long long> res;
    res.reserve(a.size());
    for (Node x : a) res.push_back(x.sum);
    return res;
}

long long sum_range(const std::vector<long long>& a, int l, int r) {
    return std::accumulate(a.begin() + l, a.begin() + r, 0LL);
}

void assert_all_ranges(Array& a, const std::vector<long long>& expected) {
    assert(sums(a.to_vector()) == expected);
    assert(a.all_prod().sum == sum_range(expected, 0, int(expected.size())));
    for (int l = 0; l <= int(expected.size()); l++) {
        for (int r = l; r <= int(expected.size()); r++) {
            assert(a.prod(l, r).sum == sum_range(expected, l, r));
        }
    }
}

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

    {
        Array a(std::vector<long long>{0, 0, 0, 0});
        a.apply(1, 4, {2, 3});
        a.insert(2, AM::make(100));
        assert_all_ranges(a, {0, 3, 100, 5, 7});

        a.apply(1, 5, {10, 0});
        assert_all_ranges(a, {0, 3, 110, 25, 37});
    }
    {
        Array a(std::vector<long long>{0, 0, 0, 0, 0});
        a.apply(0, 5, {1, 0});
        a.insert(2, AM::make(100));
        assert_all_ranges(a, {0, 1, 100, 2, 3, 4});
    }
    {
        Array a(std::vector<long long>{0, 0, 0, 0});
        a.apply(0, 4, {1, 0});
        a.reverse();
        a.insert(1, AM::make(9));
        a.apply(1, 4, {2, 1});
        assert_all_ranges(a, {3, 10, 5, 6, 0});
    }
    {
        Array a(std::vector<long long>{1, 2, 3});
        a.erase(1);
        Array copied = a;
        a.insert(1, AM::make(9));
        copied.insert(1, AM::make(8));
        assert_all_ranges(a, {1, 9, 3});
        assert_all_ranges(copied, {1, 8, 3});

        copied.erase(1);
        Array moved = std::move(copied);
        moved.insert(1, AM::make(7));
        assert(copied.empty());
        assert_all_ranges(moved, {1, 7, 3});
    }

    std::mt19937 rng(3);
    Array a;
    std::vector<long long> expected;
    for (int step = 0; step < 500; step++) {
        int op = int(rng() % 6);
        if (op == 0 || expected.empty()) {
            int pos = int(rng() % (expected.size() + 1));
            long long value = int(rng() % 101) - 50;
            a.insert(pos, AM::make(value));
            expected.insert(expected.begin() + pos, value);
        } else if (op == 1) {
            int pos = int(rng() % expected.size());
            a.erase(pos);
            expected.erase(expected.begin() + pos);
        } else if (op == 2) {
            int l = int(rng() % (expected.size() + 1));
            int r = int(rng() % (expected.size() + 1));
            if (l > r) std::swap(l, r);
            long long coef = int(rng() % 11) - 5;
            long long add = int(rng() % 21) - 10;
            a.apply(l, r, {coef, add});
            for (int i = l; i < r; i++) expected[i] += coef * (i - l) + add;
        } else if (op == 3) {
            int l = int(rng() % (expected.size() + 1));
            int r = int(rng() % (expected.size() + 1));
            if (l > r) std::swap(l, r);
            a.reverse(l, r);
            std::reverse(expected.begin() + l, expected.begin() + r);
        } else if (op == 4) {
            int l = int(rng() % (expected.size() + 1));
            int m = int(rng() % (expected.size() + 1));
            int r = int(rng() % (expected.size() + 1));
            if (l > m) std::swap(l, m);
            if (m > r) std::swap(m, r);
            if (l > m) std::swap(l, m);
            a.rotate(l, m, r);
            std::rotate(expected.begin() + l, expected.begin() + m, expected.begin() + r);
        } else {
            int pos = int(rng() % expected.size());
            long long value = int(rng() % 101) - 50;
            a.set(pos, AM::make(value));
            expected[pos] = value;
        }
        assert_all_ranges(a, expected);
    }

    long long x, y;
    fast_input >> x >> y;
    fast_output << x + y << '\n';
}
#line 1 "verify/ds/dynamic_array/dynamic_lazy_monoid_array_range_ap.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"

#line 1 "ds/dynamic_array/dynamic_lazy_monoid_array.hpp"



#include <cassert>
#include <chrono>
#include <concepts>
#include <cstdint>
#include <initializer_list>
#include <type_traits>
#include <utility>
#include <vector>

#line 1 "acted_monoid/concept.hpp"



#line 5 "acted_monoid/concept.hpp"

namespace m1une {
namespace acted_monoid {

// Concept defining the requirements for an Acted Monoid.
template <typename AM>
concept IsActedMonoid = requires(typename AM::value_type a, typename AM::value_type b, typename AM::operator_type f,
                                 typename AM::operator_type g) {
    // 1. Value Monoid
    typename AM::value_type;
    { AM::id() } -> std::same_as<typename AM::value_type>;
    { AM::op(a, b) } -> std::same_as<typename AM::value_type>;

    // 2. Operator Monoid
    typename AM::operator_type;
    { AM::op_id() } -> std::same_as<typename AM::operator_type>;
    { AM::op_comp(f, g) } -> std::same_as<typename AM::operator_type>;  // Composition order: f(g(x))

    // 3. Mapping: Operator x Value -> Value
    { AM::mapping(f, a) } -> std::same_as<typename AM::value_type>;
};

// Concept for acted monoids whose value monoid is a commutative group.
// The value operation must obey commutativity and inverse laws.
template <typename AM>
concept IsCommutativeActedGroup = IsActedMonoid<AM> && requires(typename AM::value_type a) {
    { AM::inv(a) } -> std::same_as<typename AM::value_type>;
};

}  // namespace acted_monoid
}  // namespace m1une


#line 14 "ds/dynamic_array/dynamic_lazy_monoid_array.hpp"

namespace m1une {
namespace ds {

template <m1une::acted_monoid::IsActedMonoid ActedMonoid>
struct DynamicLazyMonoidArray {
    using T = typename ActedMonoid::value_type;
    using F = typename ActedMonoid::operator_type;

   private:
    static constexpr bool value_commutative = [] {
        if constexpr (requires { ActedMonoid::commutative; }) {
            return bool(ActedMonoid::commutative);
        } else {
            return false;
        }
    }();

    struct EmptyReverseProduct {};
    using ReverseProduct = std::conditional_t<value_commutative, EmptyReverseProduct, T>;

    static constexpr bool count_stored_in_value = requires(const T& value) {
        { ActedMonoid::size(value) } -> std::convertible_to<int>;
    };

    struct EmptyCount {};
    using Count = std::conditional_t<count_stored_in_value, EmptyCount, int>;

    static ReverseProduct make_reverse_product(const T& value) {
        if constexpr (value_commutative) {
            return {};
        } else {
            return value;
        }
    }

    static Count make_count(int count) {
        if constexpr (count_stored_in_value) {
            return {};
        } else {
            return count;
        }
    }

    struct Node {
        T val;
        T prod;
        [[no_unique_address]] ReverseProduct rprod;
        F lazy;
        std::uint32_t priority : 30;
        std::uint32_t rev : 1;
        std::uint32_t has_lazy : 1;
        [[no_unique_address]] Count count;
        int l, r;

        Node()
            : val(ActedMonoid::id()),
              prod(ActedMonoid::id()),
              rprod(make_reverse_product(prod)),
              lazy(ActedMonoid::op_id()),
              priority(0),
              rev(false),
              has_lazy(false),
              count(make_count(0)),
              l(0),
              r(0) {}

        Node(T value, int node_priority)
            : val(std::move(value)),
              prod(val),
              rprod(make_reverse_product(val)),
              lazy(ActedMonoid::op_id()),
              priority(std::uint32_t(node_priority)),
              rev(false),
              has_lazy(false),
              count(make_count(1)),
              l(0),
              r(0) {}
    };

    std::vector<Node> pool;
    int root;
    int free_head;
    std::uint32_t rng_state;

    int node_count(int t) const {
        if constexpr (count_stored_in_value) {
            return int(ActedMonoid::size(pool[t].prod));
        } else {
            return pool[t].count;
        }
    }

    void set_node_count(int t, int count) {
        if constexpr (!count_stored_in_value) {
            pool[t].count = count;
        }
    }

    template <typename U>
    static T make_value(const U& value) {
        if constexpr (requires(U x) { ActedMonoid::make(x); }) {
            return ActedMonoid::make(value);
        } else {
            return static_cast<T>(value);
        }
    }

    static T mapping_at(const F& f, const T& value, long long ord) {
        if constexpr (requires(F g, T x, long long i) { ActedMonoid::mapping(g, x, i); }) {
            return ActedMonoid::mapping(f, value, ord);
        } else {
            return ActedMonoid::mapping(f, value);
        }
    }

    static F shift_operator(const F& f, long long ord) {
        if constexpr (requires(F g, long long i) { ActedMonoid::op_shift(g, i); }) {
            return ActedMonoid::op_shift(f, ord);
        } else {
            return f;
        }
    }

    static F reverse_operator(const F& f, long long size) {
        if constexpr (requires(F g, long long n) { ActedMonoid::op_reverse(g, n); }) {
            return ActedMonoid::op_reverse(f, size);
        } else {
            return f;
        }
    }

    int new_node(T value) {
        int priority = next_priority();
        if (free_head) {
            int res = free_head;
            free_head = pool[res].l;
            pool[res] = Node(std::move(value), priority);
            return res;
        }
        pool.push_back(Node(std::move(value), priority));
        return int(pool.size()) - 1;
    }

    void release_node(int t) {
        pool[t].l = free_head;
        free_head = t;
    }

    int next_priority() {
        rng_state ^= rng_state << 13;
        rng_state ^= rng_state >> 17;
        rng_state ^= rng_state << 5;
        return int(rng_state);
    }

    void update(int t) {
        if (!t) return;
        int l = pool[t].l;
        int r = pool[t].r;
        set_node_count(t, 1 + node_count(l) + node_count(r));
        pool[t].prod = ActedMonoid::op(ActedMonoid::op(pool[l].prod, pool[t].val), pool[r].prod);
        if constexpr (!value_commutative) {
            pool[t].rprod = ActedMonoid::op(ActedMonoid::op(pool[r].rprod, pool[t].val), pool[l].rprod);
        }
    }

    void all_apply(int t, const F& f) {
        if (!t) return;
        int left_count = node_count(pool[t].l);
        pool[t].val = mapping_at(f, pool[t].val, left_count);
        pool[t].prod = mapping_at(f, pool[t].prod, 0);
        if constexpr (!value_commutative) {
            pool[t].rprod = mapping_at(reverse_operator(f, node_count(t)), pool[t].rprod, 0);
        }
        pool[t].lazy = ActedMonoid::op_comp(f, pool[t].lazy);
        pool[t].has_lazy = true;
    }

    void apply_reverse(int t) {
        if (!t) return;
        std::swap(pool[t].l, pool[t].r);
        pool[t].rev = !pool[t].rev;
        if constexpr (!value_commutative) {
            std::swap(pool[t].prod, pool[t].rprod);
        }
        if (pool[t].has_lazy) {
            pool[t].lazy = reverse_operator(pool[t].lazy, node_count(t));
        }
    }

    void push(int t) {
        if (!t) return;
        if (pool[t].rev) {
            apply_reverse(pool[t].l);
            apply_reverse(pool[t].r);
            pool[t].rev = false;
        }
        if (pool[t].has_lazy) {
            all_apply(pool[t].l, pool[t].lazy);
            all_apply(pool[t].r, shift_operator(pool[t].lazy, node_count(pool[t].l) + 1));
            pool[t].lazy = ActedMonoid::op_id();
            pool[t].has_lazy = false;
        }
    }

    void split(int t, int pos, int& l, int& r) {
        if (!t) {
            l = r = 0;
            return;
        }
        if (pos == 0) {
            l = 0;
            r = t;
            return;
        }
        if (pos == node_count(t)) {
            l = t;
            r = 0;
            return;
        }
        push(t);
        int left_count = node_count(pool[t].l);
        if (pos == left_count) {
            l = pool[t].l;
            pool[t].l = 0;
            update(t);
            r = t;
            return;
        }
        if (pos == left_count + 1) {
            r = pool[t].r;
            pool[t].r = 0;
            update(t);
            l = t;
            return;
        }
        if (pos <= left_count) {
            split(pool[t].l, pos, l, pool[t].l);
            r = t;
        } else {
            split(pool[t].r, pos - left_count - 1, pool[t].r, r);
            l = t;
        }
        update(t);
    }

    int merge(int l, int r) {
        if (!l || !r) return l ? l : r;
        if (pool[l].priority > pool[r].priority) {
            push(l);
            if (pool[l].r) {
                pool[l].r = merge(pool[l].r, r);
            } else {
                pool[l].r = r;
            }
            update(l);
            return l;
        } else {
            push(r);
            if (pool[r].l) {
                pool[r].l = merge(l, pool[r].l);
            } else {
                pool[r].l = l;
            }
            update(r);
            return r;
        }
    }

    void split_three(int t, int ql, int qr, int& a, int& b, int& c) {
        if (ql == qr) {
            split(t, ql, a, c);
            b = 0;
            return;
        }
        if (ql == 0 && qr == node_count(t)) {
            a = c = 0;
            b = t;
            return;
        }
        push(t);
        int left_count = node_count(pool[t].l);
        if (qr <= left_count) {
            split_three(pool[t].l, ql, qr, a, b, pool[t].l);
            c = t;
            update(t);
        } else if (left_count < ql) {
            split_three(pool[t].r, ql - left_count - 1, qr - left_count - 1, pool[t].r, b, c);
            a = t;
            update(t);
        } else {
            split(pool[t].l, ql, a, pool[t].l);
            split(pool[t].r, qr - left_count - 1, pool[t].r, c);
            b = t;
            update(t);
        }
    }

    int merge_three(int a, int b, int c) {
        if (!a) return merge(b, c);
        if (!b) return merge(a, c);
        if (!c) return merge(a, b);
        std::uint32_t pa = pool[a].priority;
        std::uint32_t pb = pool[b].priority;
        std::uint32_t pc = pool[c].priority;
        if (pb >= pa && pb >= pc) {
            push(b);
            pool[b].l = merge(a, pool[b].l);
            pool[b].r = merge(pool[b].r, c);
            update(b);
            return b;
        }
        if (pa >= pc) {
            push(a);
            pool[a].r = merge_three(pool[a].r, b, c);
            update(a);
            return a;
        }
        push(c);
        pool[c].l = merge_three(a, b, pool[c].l);
        update(c);
        return c;
    }

    int insert_node(int t, int pos, int node) {
        if (!t) return node;
        if (pool[node].priority > pool[t].priority) {
            split(t, pos, pool[node].l, pool[node].r);
            update(node);
            return node;
        }
        push(t);
        int left_count = node_count(pool[t].l);
        if (pos <= left_count) {
            pool[t].l = insert_node(pool[t].l, pos, node);
        } else {
            pool[t].r = insert_node(pool[t].r, pos - left_count - 1, node);
        }
        update(t);
        return t;
    }

    int erase_node(int t, int pos) {
        push(t);
        int left_count = node_count(pool[t].l);
        if (pos < left_count) {
            pool[t].l = erase_node(pool[t].l, pos);
            update(t);
            return t;
        }
        if (pos == left_count) {
            int res = merge(pool[t].l, pool[t].r);
            release_node(t);
            return res;
        }
        pool[t].r = erase_node(pool[t].r, pos - left_count - 1);
        update(t);
        return t;
    }

    void set_node(int t, int pos, T value) {
        push(t);
        int left_count = node_count(pool[t].l);
        if (pos < left_count) {
            set_node(pool[t].l, pos, std::move(value));
        } else if (pos == left_count) {
            pool[t].val = std::move(value);
        } else {
            set_node(pool[t].r, pos - left_count - 1, std::move(value));
        }
        update(t);
    }

    void apply_node(int t, int pos, const F& f) {
        push(t);
        int left_count = node_count(pool[t].l);
        if (pos < left_count) {
            apply_node(pool[t].l, pos, f);
        } else if (pos == left_count) {
            pool[t].val = mapping_at(f, pool[t].val, 0);
        } else {
            apply_node(pool[t].r, pos - left_count - 1, f);
        }
        update(t);
    }

    void apply_range(int t, int ql, int qr, const F& f) {
        if (ql == 0 && qr == node_count(t)) {
            all_apply(t, f);
            return;
        }
        push(t);
        int left_count = node_count(pool[t].l);
        if (qr <= left_count) {
            apply_range(pool[t].l, ql, qr, f);
        } else if (left_count < ql) {
            apply_range(pool[t].r, ql - left_count - 1, qr - left_count - 1, f);
        } else {
            if (ql < left_count) {
                apply_range(pool[t].l, ql, left_count, f);
            }
            pool[t].val = mapping_at(f, pool[t].val, left_count - ql);
            if (left_count + 1 < qr) {
                apply_range(pool[t].r, 0, qr - left_count - 1,
                            shift_operator(f, left_count + 1 - ql));
            }
        }
        update(t);
    }

    T prod_range(int t, int ql, int qr) {
        if (ql == 0 && qr == node_count(t)) return pool[t].prod;
        push(t);
        int left_count = node_count(pool[t].l);
        if (qr <= left_count) {
            return prod_range(pool[t].l, ql, qr);
        }
        if (left_count < ql) {
            return prod_range(pool[t].r, ql - left_count - 1, qr - left_count - 1);
        }
        T res = pool[t].val;
        if (ql < left_count) {
            res = ActedMonoid::op(prod_range(pool[t].l, ql, left_count), res);
        }
        if (left_count + 1 < qr) {
            res = ActedMonoid::op(res, prod_range(pool[t].r, 0, qr - left_count - 1));
        }
        return res;
    }

    int find_node(int t, int pos) {
        while (t) {
            push(t);
            int left_count = node_count(pool[t].l);
            if (pos < left_count) {
                t = pool[t].l;
            } else if (pos == left_count) {
                return t;
            } else {
                pos -= left_count + 1;
                t = pool[t].r;
            }
        }
        return 0;
    }

    void dump_dfs(int t, std::vector<T>& res) {
        if (!t) return;
        push(t);
        dump_dfs(pool[t].l, res);
        res.push_back(pool[t].val);
        dump_dfs(pool[t].r, res);
        update(t);
    }

    void dump_range_dfs(int t, int ql, int qr, int offset, std::vector<T>& res) {
        if (!t || qr <= offset || offset + node_count(t) <= ql) return;
        push(t);
        int left_count = node_count(pool[t].l);
        int node_pos = offset + left_count;
        dump_range_dfs(pool[t].l, ql, qr, offset, res);
        if (ql <= node_pos && node_pos < qr) {
            res.push_back(pool[t].val);
        }
        dump_range_dfs(pool[t].r, ql, qr, node_pos + 1, res);
        update(t);
    }

    int clone_subtree_from(const DynamicLazyMonoidArray& other, int t) {
        if (!t) return 0;
        int res = int(pool.size());
        pool.push_back(other.pool[t]);
        pool[res].l = clone_subtree_from(other, other.pool[t].l);
        pool[res].r = clone_subtree_from(other, other.pool[t].r);
        return res;
    }

    void update_dfs(int t) {
        if (!t) return;
        update_dfs(pool[t].l);
        update_dfs(pool[t].r);
        update(t);
    }

    int build_cartesian(int first, int last) {
        if (first == last) return 0;
        std::vector<int> stack;
        stack.reserve(last - first);
        for (int i = first; i < last; i++) {
            int left_child = 0;
            while (!stack.empty() && pool[stack.back()].priority < pool[i].priority) {
                left_child = stack.back();
                stack.pop_back();
            }
            pool[i].l = left_child;
            if (!stack.empty()) {
                pool[stack.back()].r = i;
            }
            stack.push_back(i);
        }
        int res = stack.front();
        update_dfs(res);
        return res;
    }

    int build_from_vector(const std::vector<T>& v) {
        int first = int(pool.size());
        pool.reserve(pool.size() + v.size());
        for (const T& x : v) {
            new_node(x);
        }
        return build_cartesian(first, int(pool.size()));
    }

    int build_from_vector(std::vector<T>&& v) {
        int first = int(pool.size());
        pool.reserve(pool.size() + v.size());
        for (T& x : v) {
            new_node(std::move(x));
        }
        return build_cartesian(first, int(pool.size()));
    }

    template <typename U>
    int build_from_values(const std::vector<U>& v) {
        int first = int(pool.size());
        pool.reserve(pool.size() + v.size());
        for (const U& x : v) {
            new_node(make_value(x));
        }
        return build_cartesian(first, int(pool.size()));
    }

    void reset_to_empty() {
        pool.clear();
        pool.push_back(Node());
        root = 0;
        free_head = 0;
    }

   public:
    DynamicLazyMonoidArray()
        : root(0),
          free_head(0),
          rng_state(std::uint32_t(std::chrono::steady_clock::now().time_since_epoch().count())) {
        pool.push_back(Node());
        if (rng_state == 0) rng_state = 1;
    }

    DynamicLazyMonoidArray(const DynamicLazyMonoidArray& other)
        : pool(other.pool), root(other.root), free_head(other.free_head), rng_state(other.rng_state) {}

    DynamicLazyMonoidArray(DynamicLazyMonoidArray&& other) noexcept
        : pool(std::move(other.pool)), root(other.root), free_head(other.free_head), rng_state(other.rng_state) {
        other.reset_to_empty();
    }

    DynamicLazyMonoidArray& operator=(const DynamicLazyMonoidArray& other) {
        if (this != &other) {
            pool = other.pool;
            root = other.root;
            free_head = other.free_head;
            rng_state = other.rng_state;
        }
        return *this;
    }

    DynamicLazyMonoidArray& operator=(DynamicLazyMonoidArray&& other) noexcept {
        if (this != &other) {
            pool = std::move(other.pool);
            root = other.root;
            free_head = other.free_head;
            rng_state = other.rng_state;
            other.reset_to_empty();
        }
        return *this;
    }

    explicit DynamicLazyMonoidArray(int n) : DynamicLazyMonoidArray(n, ActedMonoid::id()) {}

    DynamicLazyMonoidArray(int n, const T& value) : DynamicLazyMonoidArray() {
        assert(0 <= n);
        pool.reserve(n + 1);
        int first = int(pool.size());
        for (int i = 0; i < n; i++) {
            new_node(value);
        }
        root = build_cartesian(first, int(pool.size()));
    }

    explicit DynamicLazyMonoidArray(const std::vector<T>& v) : DynamicLazyMonoidArray() {
        pool.reserve(v.size() + 1);
        root = build_from_vector(v);
    }

    explicit DynamicLazyMonoidArray(std::vector<T>&& v) : DynamicLazyMonoidArray() {
        pool.reserve(v.size() + 1);
        root = build_from_vector(std::move(v));
    }

    template <typename U>
        requires(!std::same_as<U, T>) && (requires(U x) { ActedMonoid::make(x); } || std::convertible_to<U, T>)
    explicit DynamicLazyMonoidArray(const std::vector<U>& v) : DynamicLazyMonoidArray() {
        pool.reserve(v.size() + 1);
        root = build_from_values(v);
    }

    DynamicLazyMonoidArray(std::initializer_list<T> init) : DynamicLazyMonoidArray() {
        pool.reserve(init.size() + 1);
        for (const T& x : init) push_back(x);
    }

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

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

    void clear() {
        reset_to_empty();
    }

    void insert(int pos, T value) {
        assert(0 <= pos && pos <= size());
        root = insert_node(root, pos, new_node(std::move(value)));
    }

    void insert(int pos, const std::vector<T>& v) {
        assert(0 <= pos && pos <= size());
        pool.reserve(pool.size() + v.size());
        int mid = build_from_vector(v);
        int l, r;
        split(root, pos, l, r);
        root = merge(merge(l, mid), r);
    }

    void insert(int pos, std::vector<T>&& v) {
        assert(0 <= pos && pos <= size());
        pool.reserve(pool.size() + v.size());
        int mid = build_from_vector(std::move(v));
        int l, r;
        split(root, pos, l, r);
        root = merge(merge(l, mid), r);
    }

    void insert(int pos, std::initializer_list<T> init) {
        insert(pos, std::vector<T>(init));
    }

    void insert(int pos, const DynamicLazyMonoidArray& other) {
        assert(0 <= pos && pos <= size());
        if (other.empty()) return;
        pool.reserve(pool.size() + other.size());
        int mid = clone_subtree_from(other, other.root);
        int l, r;
        split(root, pos, l, r);
        root = merge(merge(l, mid), r);
    }

    void push_back(T value) {
        insert(size(), std::move(value));
    }

    void push_front(T value) {
        insert(0, std::move(value));
    }

    void append(const std::vector<T>& v) {
        insert(size(), v);
    }

    void append(std::vector<T>&& v) {
        insert(size(), std::move(v));
    }

    void append(const DynamicLazyMonoidArray& other) {
        insert(size(), other);
    }

    void erase(int pos) {
        assert(0 <= pos && pos < size());
        root = erase_node(root, pos);
    }

    void erase(int l, int r) {
        assert(0 <= l && l <= r && r <= size());
        if (l == r) return;
        int a, b, c;
        split_three(root, l, r, a, b, c);
        root = merge(a, c);
    }

    void pop_back() {
        assert(!empty());
        erase(size() - 1);
    }

    void pop_front() {
        assert(!empty());
        erase(0);
    }

    T get(int pos) {
        assert(0 <= pos && pos < size());
        int t = find_node(root, pos);
        return pool[t].val;
    }

    T operator[](int pos) {
        return get(pos);
    }

    T front() {
        assert(!empty());
        return get(0);
    }

    T back() {
        assert(!empty());
        return get(size() - 1);
    }

    void set(int pos, T value) {
        assert(0 <= pos && pos < size());
        set_node(root, pos, std::move(value));
    }

    void reverse(int l, int r) {
        assert(0 <= l && l <= r && r <= size());
        if (l == r) return;
        int a, b, c;
        split_three(root, l, r, a, b, c);
        apply_reverse(b);
        root = merge_three(a, b, c);
    }

    void reverse() {
        apply_reverse(root);
    }

    void rotate(int l, int m, int r) {
        assert(0 <= l && l <= m && m <= r && r <= size());
        if (l == m || m == r) return;
        int a, b, c, d;
        split(root, l, a, b);
        split(b, m - l, b, c);
        split(c, r - m, c, d);
        root = merge(merge(a, c), merge(b, d));
    }

    void apply(int pos, const F& f) {
        assert(0 <= pos && pos < size());
        apply_node(root, pos, f);
    }

    void apply(int l, int r, const F& f) {
        assert(0 <= l && l <= r && r <= size());
        if (l == r) return;
        apply_range(root, l, r, f);
    }

    T prod(int l, int r) {
        assert(0 <= l && l <= r && r <= size());
        if (l == r) return ActedMonoid::id();
        return prod_range(root, l, r);
    }

    T all_prod() const {
        return pool[root].prod;
    }

    std::vector<T> to_vector() {
        std::vector<T> res;
        res.reserve(size());
        dump_dfs(root, res);
        return res;
    }

    std::vector<T> to_vector(int l, int r) {
        assert(0 <= l && l <= r && r <= size());
        std::vector<T> res;
        res.reserve(r - l);
        dump_range_dfs(root, l, r, 0, res);
        return res;
    }

    DynamicLazyMonoidArray split_off(int pos) {
        assert(0 <= pos && pos <= size());
        int l, r;
        split(root, pos, l, r);
        root = l;

        DynamicLazyMonoidArray res;
        res.pool.reserve(node_count(r) + 1);
        res.root = res.clone_subtree_from(*this, r);
        return res;
    }
};

}  // namespace ds
}  // namespace m1une


#line 4 "verify/ds/dynamic_array/dynamic_lazy_monoid_array_range_ap.test.cpp"

#include <algorithm>
#line 1 "utilities/fast_io.hpp"



#line 5 "utilities/fast_io.hpp"
#include <array>
#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 8 "verify/ds/dynamic_array/dynamic_lazy_monoid_array_range_ap.test.cpp"
#include <numeric>
#include <random>
#line 12 "verify/ds/dynamic_array/dynamic_lazy_monoid_array_range_ap.test.cpp"

#line 1 "acted_monoid/range_ap_add_range_sum.hpp"



#line 5 "acted_monoid/range_ap_add_range_sum.hpp"

namespace m1une {
namespace acted_monoid {

template <typename T>
struct RangeApAddRangeSumNode {
    T sum;
    long long size;
    T ord_sum;
};

template <typename T>
struct RangeApAddRangeSum {
    using value_type = RangeApAddRangeSumNode<T>;
    using operator_type = std::pair<T, T>;  // {a, b} for adding a * i + b
    static constexpr bool commutative = false;
    static constexpr bool operator_commutative = true;

    // Value Monoid (Sum)
    static constexpr value_type id() {
        return {T(0), 0, T(0)};
    }
    static constexpr value_type op(const value_type& a, const value_type& b) {
        return {a.sum + b.sum, a.size + b.size, a.ord_sum + b.ord_sum + T(a.size) * T(b.size)};
    }

    // Operator Monoid (Add)
    static constexpr operator_type op_id() {
        return {T(0), T(0)};
    }
    static constexpr operator_type op_comp(const operator_type& f, const operator_type& g) {
        return {f.first + g.first, f.second + g.second};
    }

    static constexpr value_type mapping(const operator_type& f, const value_type& x) {
        return mapping(f, x, 0);
    }

    static constexpr value_type mapping(const operator_type& f, const value_type& x, long long ord) {
        return {x.sum + f.first * (x.ord_sum + T(ord) * T(x.size)) + f.second * T(x.size), x.size, x.ord_sum};
    }

    static constexpr operator_type op_shift(const operator_type& f, long long ord) {
        return {f.first, f.second + f.first * T(ord)};
    }

    static constexpr operator_type op_reverse(const operator_type& f, long long size) {
        return {-f.first, f.second + f.first * T(size - 1)};
    }

    static constexpr value_type make(const T& val) {
        return {val, 1, T(0)};
    }
};

}  // namespace acted_monoid
}  // namespace m1une


#line 14 "verify/ds/dynamic_array/dynamic_lazy_monoid_array_range_ap.test.cpp"

using AM = m1une::acted_monoid::RangeApAddRangeSum<long long>;
using Node = AM::value_type;
using Array = m1une::ds::DynamicLazyMonoidArray<AM>;

std::vector<long long> sums(std::vector<Node> a) {
    std::vector<long long> res;
    res.reserve(a.size());
    for (Node x : a) res.push_back(x.sum);
    return res;
}

long long sum_range(const std::vector<long long>& a, int l, int r) {
    return std::accumulate(a.begin() + l, a.begin() + r, 0LL);
}

void assert_all_ranges(Array& a, const std::vector<long long>& expected) {
    assert(sums(a.to_vector()) == expected);
    assert(a.all_prod().sum == sum_range(expected, 0, int(expected.size())));
    for (int l = 0; l <= int(expected.size()); l++) {
        for (int r = l; r <= int(expected.size()); r++) {
            assert(a.prod(l, r).sum == sum_range(expected, l, r));
        }
    }
}

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

    {
        Array a(std::vector<long long>{0, 0, 0, 0});
        a.apply(1, 4, {2, 3});
        a.insert(2, AM::make(100));
        assert_all_ranges(a, {0, 3, 100, 5, 7});

        a.apply(1, 5, {10, 0});
        assert_all_ranges(a, {0, 3, 110, 25, 37});
    }
    {
        Array a(std::vector<long long>{0, 0, 0, 0, 0});
        a.apply(0, 5, {1, 0});
        a.insert(2, AM::make(100));
        assert_all_ranges(a, {0, 1, 100, 2, 3, 4});
    }
    {
        Array a(std::vector<long long>{0, 0, 0, 0});
        a.apply(0, 4, {1, 0});
        a.reverse();
        a.insert(1, AM::make(9));
        a.apply(1, 4, {2, 1});
        assert_all_ranges(a, {3, 10, 5, 6, 0});
    }
    {
        Array a(std::vector<long long>{1, 2, 3});
        a.erase(1);
        Array copied = a;
        a.insert(1, AM::make(9));
        copied.insert(1, AM::make(8));
        assert_all_ranges(a, {1, 9, 3});
        assert_all_ranges(copied, {1, 8, 3});

        copied.erase(1);
        Array moved = std::move(copied);
        moved.insert(1, AM::make(7));
        assert(copied.empty());
        assert_all_ranges(moved, {1, 7, 3});
    }

    std::mt19937 rng(3);
    Array a;
    std::vector<long long> expected;
    for (int step = 0; step < 500; step++) {
        int op = int(rng() % 6);
        if (op == 0 || expected.empty()) {
            int pos = int(rng() % (expected.size() + 1));
            long long value = int(rng() % 101) - 50;
            a.insert(pos, AM::make(value));
            expected.insert(expected.begin() + pos, value);
        } else if (op == 1) {
            int pos = int(rng() % expected.size());
            a.erase(pos);
            expected.erase(expected.begin() + pos);
        } else if (op == 2) {
            int l = int(rng() % (expected.size() + 1));
            int r = int(rng() % (expected.size() + 1));
            if (l > r) std::swap(l, r);
            long long coef = int(rng() % 11) - 5;
            long long add = int(rng() % 21) - 10;
            a.apply(l, r, {coef, add});
            for (int i = l; i < r; i++) expected[i] += coef * (i - l) + add;
        } else if (op == 3) {
            int l = int(rng() % (expected.size() + 1));
            int r = int(rng() % (expected.size() + 1));
            if (l > r) std::swap(l, r);
            a.reverse(l, r);
            std::reverse(expected.begin() + l, expected.begin() + r);
        } else if (op == 4) {
            int l = int(rng() % (expected.size() + 1));
            int m = int(rng() % (expected.size() + 1));
            int r = int(rng() % (expected.size() + 1));
            if (l > m) std::swap(l, m);
            if (m > r) std::swap(m, r);
            if (l > m) std::swap(l, m);
            a.rotate(l, m, r);
            std::rotate(expected.begin() + l, expected.begin() + m, expected.begin() + r);
        } else {
            int pos = int(rng() % expected.size());
            long long value = int(rng() % 101) - 50;
            a.set(pos, AM::make(value));
            expected[pos] = value;
        }
        assert_all_ranges(a, expected);
    }

    long long x, y;
    fast_input >> x >> y;
    fast_output << x + y << '\n';
}
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