Submission #76641889

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Source Code Expand

#line 2 "/home/shogo314/cpp_include/ou-library/segtree.hpp"

/**
 * @file segtree.hpp
 * @brief セグメント木
 */

#include <cassert>
#include <functional>
#include <ostream>
#include <vector>
#line 2 "/home/shogo314/cpp_include/ou-library/more_functional.hpp"

/**
 * @file more_functional.hpp
 * @brief 関数オブジェクトを定義する
 */

#include <limits>
#include <numeric>
#include <type_traits>

namespace more_functional {
template <typename S>
struct Max {
    const S operator()(const S& a, const S& b) const { return std::max(a, b); }
};
template <typename S>
struct Min {
    const S operator()(const S& a, const S& b) const { return std::min(a, b); }
};
template <typename S>
struct MinMax {
    const std::pair<S, S> operator()(const std::pair<S, S>& a, const std::pair<S, S>& b) const { return {std::min(a.first, b.first), std::max(a.second, b.second)}; }
};
template <typename S, std::enable_if_t<std::is_integral_v<S>>* = nullptr>
struct Gcd {
    constexpr S operator()(const S& a, const S& b) const { return std::gcd(a, b); }
};
template <typename S>
struct Zero {
    S operator()() const { return S(0); }
};
template <typename S>
struct One {
    S operator()() const { return S(1); }
};
template <typename S>
struct None {
    S operator()() const { return S{}; }
};
template <typename S, std::enable_if_t<std::is_scalar_v<S>>* = nullptr>
struct MaxLimit {
    constexpr S operator()() const { return std::numeric_limits<S>::max(); }
};
template <typename S, std::enable_if_t<std::is_scalar_v<S>>* = nullptr>
struct MinLimit {
    constexpr S operator()() const { return std::numeric_limits<S>::lowest(); }
};
template <typename S, std::enable_if_t<std::is_scalar_v<S>>* = nullptr>
struct MaxMinLimit {
    constexpr std::pair<S, S> operator()() const { return {std::numeric_limits<S>::max(), std::numeric_limits<S>::lowest()}; }
};
template <typename S>
struct Div {
    S operator()(const S& a) const { return S(1) / a; }
};
}  // namespace more_functional
#line 13 "/home/shogo314/cpp_include/ou-library/segtree.hpp"

/**
 * @brief セグメント木のCRTP基底クラス
 * 
 * @tparam S モノイドの型
 * @tparam ActualSegTree 派生クラス
 */
template <typename S, typename ActualSegTree>
class SegTreeBase {
    S op(const S& a, const S& b) const { return static_cast<const ActualSegTree&>(*this).op(a, b); }
    S e() const { return static_cast<const ActualSegTree&>(*this).e(); }

    int n, sz, height;
    std::vector<S> data;
    void update(int k) { data[k] = op(data[2 * k], data[2 * k + 1]); }

    class SegTreeReference {
        SegTreeBase& segtree;
        int k;
    public:
        SegTreeReference(SegTreeBase& segtree, int k) : segtree(segtree), k(k) {}
        SegTreeReference& operator=(const S& x) {
            segtree.set(k, x);
            return *this;
        }
        operator S() const { return segtree.get(k); }
    };

protected:
    void construct_data() {
        sz = 1;
        height = 0;
        while (sz < n) {
            sz <<= 1;
            height++;
        }
        data.assign(sz * 2, e());
    }
    void initialize(const std::vector<S>& v) {
        for (int i = 0; i < n; i++) data[sz + i] = v[i];
        for (int i = sz - 1; i > 0; i--) update(i);
    }

public:
    // Warning: 継承先のコンストラクタでconstruct_data()を必ず呼び出す！
    SegTreeBase(int n = 0) : n(n) {}

    /**
     * @brief 指定された要素の値を返す
     * 
     * @param k インデックス
     * @return S 値
     */
    S get(int k) const {
        assert(0 <= k && k < n);
        return data[sz + k];
    }
    /**
     * @brief 指定された要素の値を返す
     * 
     * @param k インデックス
     * @return S 値
     */
    S operator[] (int k) const { return get(k); }
    /**
     * @brief 指定された要素への参照を返す
     * 
     * @param k 
     * @return SegTreeReference 要素への参照 代入されるとset()が呼ばれる
     */
    SegTreeReference operator[] (int k) { return SegTreeReference(*this, k); }

    /**
     * @brief 内容を出力する
     * 
     * @tparam CharT 出力ストリームの文字型
     * @tparam Traits 出力ストリームの文字型特性
     * @param os 出力ストリーム
     * @param rhs セグメント木
     * @return std::basic_ostream<CharT, Traits>& 出力ストリーム 
     */
    template <class CharT, class Traits>
    friend std::basic_ostream<CharT, Traits>& operator<<(std::basic_ostream<CharT, Traits>& os, const SegTreeBase& rhs) {
        for(int i = 0; i < rhs.n; i++) {
            if(i != 0) os << CharT(' ');
            os << rhs[i];
        }
        return os;
    }

    /**
     * @brief 指定された要素の値をxに更新する
     * 
     * @param k インデックス
     * @param x 新しい値
     */
    void set(int k, const S& x) {
        assert(0 <= k && k < n);
        k += sz;
        data[k] = x;
        for (int i = 1; i <= height; i++) update(k >> i);
    }
    /**
     * @brief 指定された要素の値にxを作用させる
     * 
     * @param k インデックス
     * @param x 作用素
     */
    void apply(int k, const S& x) { set(k, op(get(k), x)); }

    /**
     * @brief [l, r)の区間の総積を返す
     * 
     * @param l 半開区間の開始
     * @param r 半開区間の終端 0<=l<=r<=n
     * @return S 総積
     */
    S prod(int l, int r) const {
        assert(0 <= l && l <= r && r <= n);
        S left_prod = e(), right_prod = e();
        l += sz;
        r += sz;
        while (l < r) {
            if (l & 1) left_prod = op(left_prod, data[l++]);
            if (r & 1) right_prod = op(data[--r], right_prod);
            l >>= 1;
            r >>= 1;
        }
        return op(left_prod, right_prod);
    }
    /**
     * @brief すべての要素の総積を返す
     * 
     * @return S 総積
     */
    S all_prod() const { return data[1]; }

    /**
     * @brief (r = l or f(prod([l, r))) = true) and (r = n or f(prod([l, r+1))) = false)となるrを返す
     * fが単調なら、f(prod([l, r))) = trueとなる最大のr
     * 
     * @tparam F
     * @param l 半開区間の開始 0<=l<=n
     * @param f 判定関数 f(e) = true
     * @return int
     */
    template <typename F>
    int max_right(int l, F f) const {
        assert(f(e()));
        assert(0 <= l && l <= n);
        if (l == n) return n;
        l += sz;
        while (l % 2 == 0) l >>= 1;
        S sum = e();
        while(f(op(sum, data[l]))) {
            sum = op(sum, data[l]);
            l++;
            while (l % 2 == 0) l >>= 1;
            if (l == 1) return n;
        }
        while (l < sz) {
            if (!f(op(sum, data[l * 2]))) l *= 2;
            else {
                sum = op(sum, data[l * 2]);
                l = l * 2 + 1;
            }
        }
        return l - sz;
    }
    /**
     * @brief (l = 0 or f(prod([l, r))) = true) and (l = r or f(prod([l-1, r))) = false)となるlを返す
     * fが単調なら、f(prod([l, r))) = trueとなる最小のl
     * 
     * @tparam F
     * @param r 半開区間の終端 0<=r<=n
     * @param f 判定関数 f(e) = true
     * @return int
     */
    template <typename F>
    int min_left(int r, F f) const {
        assert(f(e()));
        assert(0 <= r && r <= n);
        if (r == 0) return 0;
        r += sz;
        while (r % 2 == 0) r >>= 1;
        S sum = e();
        while(f(op(data[r-1], sum))) {
            sum = op(data[r-1], sum);
            r--;
            while (r % 2 == 0) r >>= 1;
            if (r == 1) return 0;
        }
        while (r < sz) {
            if (!f(op(data[r * 2 - 1], sum))) r *= 2;
            else {
                sum = op(data[r * 2 - 1], sum);
                r = r * 2 - 1;
            }
        }
        return r - sz;
    }
};

/**
 * @brief 積のファンクタが静的な場合のセグメント木の実装
 * 
 * @tparam S モノイドの型
 * @tparam Op 積のファンクタ
 * @tparam E 積の単位元を返すファンクタ
 */
template <typename S, typename Op, typename E>
class StaticSegTree : public SegTreeBase<S, StaticSegTree<S, Op, E>> {
    using BaseType = SegTreeBase<S, StaticSegTree<S, Op, E>>;

    inline static Op operator_object;
    inline static E identity_object;
public:
    S op(const S& a, const S& b) const { return operator_object(a, b); }
    S e() const { return identity_object(); }

    /**
     * @brief デフォルトコンストラクタ
     * 
    */
    StaticSegTree() = default;
    /**
     * @brief コンストラクタ
     * 
     * @param n 要素数
     */
    explicit StaticSegTree(int n) : BaseType(n) {
        this->construct_data();
    }
    /**
     * @brief コンストラクタ
     * 
     * @param v 初期の要素
     */
    explicit StaticSegTree(const std::vector<S>& v) : StaticSegTree(v.size()) {
        this->initialize(v);
    }
};

/**
 * @brief コンストラクタで関数オブジェクトを与えることで積を定義するセグメント木の実装
 * テンプレート引数を省略することができ、ラムダ式が使える
 * 
 * @tparam S モノイドの型
 * @tparam Op 積の関数オブジェクトの型
 */
template <typename S, typename Op>
class SegTree : public SegTreeBase<S, SegTree<S, Op>> {
    using BaseType = SegTreeBase<S, SegTree<S, Op>>;

    Op operator_object;
    S identity;

public:
    S op(const S& a, const S& b) const { return operator_object(a, b); }
    S e() const { return identity; }

    /**
     * @brief デフォルトコンストラクタ
    */
    SegTree() = default;
    /**
     * @brief コンストラクタ
     * 
     * @param n 要素数
     * @param op 積の関数オブジェクト
     * @param identity 単位元
     */
    explicit SegTree(int n, Op op, const S& identity) : BaseType(n), operator_object(std::move(op)), identity(identity) {
        this->construct_data();
    }
    /**
     * @brief コンストラクタ
     * 
     * @param v 初期の要素
     * @param op 積の関数オブジェクト
     * @param identity 単位元
     */
    explicit SegTree(const std::vector<S>& v, Op op, const S& identity) : SegTree(v.size(), std::move(op), identity) {
        this->initialize(v);
    }
};

/**
 * @brief RangeMaxQuery
 * 
 * @tparam S 型
 */
template <typename S>
using RMaxQ = StaticSegTree<S, more_functional::Max<S>, more_functional::MinLimit<S>>;
/**
 * @brief RangeMinQuery
 * 
 * @tparam S 型
 */
template <typename S>
using RMinQ = StaticSegTree<S, more_functional::Min<S>, more_functional::MaxLimit<S>>;
/**
 * @brief RangeSumQuery
 * 
 * @tparam S 型
 */
template <typename S>
using RSumQ = StaticSegTree<S, std::plus<S>, more_functional::None<S>>;
/**
 * @brief RangeProdQuery
 *
 * @tparam S 型
 */
template <typename S>
using RProdQ = StaticSegTree<S, std::multiplies<S>, more_functional::One<S>>;
/**
 * @brief RangeXorQuery
 *
 * @tparam S 型
 */
template <typename S>
using RXorQ = StaticSegTree<S, std::bit_xor<S>, more_functional::Zero<S>>;
/**
 * @brief RangeGcdQuery
 *
 * @tparam S 型
 */
template <typename S>
using RGcdQ = StaticSegTree<S, more_functional::Gcd<S>, more_functional::Zero<S>>;

namespace segtree {
    template <typename T>
    using TemplateS = typename T::S;
    template <typename T>
    struct TemplateOp {
        TemplateS<T> operator()(const TemplateS<T>& a, const TemplateS<T>& b) const {
            return T().op(a, b);
        }
    };
    template <typename T>
    struct TemplateE {
        TemplateS<T> operator()() const {
            return T().e();
        }
    };
}
template <typename T>
using TemplateSegTree = StaticSegTree<
    segtree::TemplateS<T>,
    segtree::TemplateOp<T>,
    segtree::TemplateE<T>
>;
#line 2 "/home/shogo314/cpp_include/sh-library/base/all"
#include <bits/stdc++.h>
#line 5 "/home/shogo314/cpp_include/sh-library/base/container_func.hpp"
#include <initializer_list>
#line 5 "/home/shogo314/cpp_include/sh-library/base/traits.hpp"

#define HAS_METHOD(func_name)                                                              \
    namespace detail {                                                                     \
    template <class T, class = void>                                                       \
    struct has_##func_name##_impl : std::false_type {};                                    \
    template <class T>                                                                     \
    struct has_##func_name##_impl<T, std::void_t<decltype(std::declval<T>().func_name())>> \
        : std::true_type {};                                                               \
    }                                                                                      \
    template <class T>                                                                     \
    struct has_##func_name : detail::has_##func_name##_impl<T>::type {};                   \
    template <class T>                                                                     \
    inline constexpr bool has_##func_name##_v = has_##func_name<T>::value;

#define HAS_METHOD_ARG(func_name)                                                                              \
    namespace detail {                                                                                         \
    template <class T, typename U, class = void>                                                               \
    struct has_##func_name##_impl : std::false_type {};                                                        \
    template <class T, typename U>                                                                             \
    struct has_##func_name##_impl<T, U, std::void_t<decltype(std::declval<T>().func_name(std::declval<U>()))>> \
        : std::true_type {};                                                                                   \
    }                                                                                                          \
    template <class T, typename U>                                                                             \
    struct has_##func_name : detail::has_##func_name##_impl<T, U>::type {};                                    \
    template <class T, typename U>                                                                             \
    inline constexpr bool has_##func_name##_v = has_##func_name<T, U>::value;

HAS_METHOD(repr)
HAS_METHOD(type_str)
HAS_METHOD(initializer_str)
HAS_METHOD(max)
HAS_METHOD(min)
HAS_METHOD(reversed)
HAS_METHOD(sorted)
HAS_METHOD(sum)
HAS_METHOD(product)
HAS_METHOD(product_xor)
HAS_METHOD_ARG(count)
HAS_METHOD_ARG(find)
HAS_METHOD_ARG(lower_bound)
HAS_METHOD_ARG(upper_bound)

#define ENABLE_IF_T_IMPL(expr) std::enable_if_t<expr, std::nullptr_t> = nullptr
#define ENABLE_IF_T(...) ENABLE_IF_T_IMPL((__VA_ARGS__))

template <class C>
using mem_value_type = typename C::value_type;
template <class C>
using mem_difference_type = typename C::difference_type;

namespace detail {
template <class T, class = void>
struct is_sorted_container_impl : std::false_type {};
template <class T>
struct is_sorted_container_impl<std::set<T>> : std::true_type {};
template <class T>
struct is_sorted_container_impl<std::multiset<T>> : std::true_type {};
}  // namespace detail
template <class T>
struct is_sorted_container : detail::is_sorted_container_impl<T>::type {};
template <class T>
inline constexpr bool is_sorted_container_v = is_sorted_container<T>::value;
#line 9 "/home/shogo314/cpp_include/sh-library/base/container_func.hpp"

#define METHOD_EXPAND(func)                                        \
    template <typename T, ENABLE_IF_T(has_##func##_v<T>)>          \
    inline constexpr auto func(const T &t) -> decltype(t.func()) { \
        return t.func();                                           \
    }

#define METHOD_AND_FUNC_ARG_EXPAND(func)                                     \
    template <typename T, typename U, ENABLE_IF_T(has_##func##_v<T, U>)>     \
    inline constexpr auto func(const T &t, const U &u)                       \
        -> decltype(t.func(u)) {                                             \
        return t.func(u);                                                    \
    }                                                                        \
    template <typename T, typename U, ENABLE_IF_T(not has_##func##_v<T, U>)> \
    inline constexpr auto func(const T &t, const U &u)                       \
        -> decltype(std::func(t.begin(), t.end(), u)) {                      \
        return std::func(t.begin(), t.end(), u);                             \
    }

METHOD_EXPAND(reversed)
template <class C, ENABLE_IF_T(not has_reversed_v<C>)>
inline constexpr C reversed(C t) {
    std::reverse(t.begin(), t.end());
    return t;
}

METHOD_EXPAND(sorted)
template <class C, ENABLE_IF_T(not has_sorted_v<C>)>
inline constexpr C sorted(C t, bool reverse = false) {
    std::sort(t.begin(), t.end());
    if (reverse) std::reverse(t.begin(), t.end());
    return t;
}
template <class C, class F, ENABLE_IF_T(not has_sorted_v<C> and std::is_invocable_r_v<bool, F, mem_value_type<C>, mem_value_type<C>>)>
inline constexpr C sorted(C t, F f) {
    std::sort(t.begin(), t.end(), f);
    return t;
}

template <class C>
inline constexpr void sort(C &t, bool reverse = false) {
    std::sort(t.begin(), t.end());
    if (reverse) std::reverse(t.begin(), t.end());
}
template <class C, class F, ENABLE_IF_T(std::is_invocable_r_v<bool, F, mem_value_type<C>, mem_value_type<C>>)>
inline constexpr void sort(C &t, F f) {
    std::sort(t.begin(), t.end(), f);
}
template <class C, class F, ENABLE_IF_T(std::is_invocable_v<F, mem_value_type<C>>)>
inline constexpr void sort_by_key(C &t, F f) {
    std::sort(t.begin(), t.end(), [&](const mem_value_type<C> &left, const mem_value_type<C> &right) {
        return f(left) < f(right);
    });
}

template <class C>
inline constexpr void reverse(C &t) {
    std::reverse(t.begin(), t.end());
}

METHOD_EXPAND(max)
template <class C, ENABLE_IF_T(not has_max_v<C> and is_sorted_container_v<C>)>
inline constexpr mem_value_type<C> max(const C &v) {
    assert(v.begin() != v.end());
    return *v.rbegin();
}
template <class C, ENABLE_IF_T(not has_max_v<C> and not is_sorted_container_v<C>)>
inline constexpr mem_value_type<C> max(const C &v) {
    assert(v.begin() != v.end());
    return *std::max_element(v.begin(), v.end());
}
template <typename T>
inline constexpr T max(const std::initializer_list<T> &v) {
    return std::max(v);
}

METHOD_EXPAND(min)
template <class C, ENABLE_IF_T(not has_max_v<C> and is_sorted_container_v<C>)>
inline constexpr mem_value_type<C> min(const C &v) {
    assert(v.begin() != v.end());
    return *v.begin();
}
template <class C, ENABLE_IF_T(not has_max_v<C> and not is_sorted_container_v<C>)>
inline constexpr mem_value_type<C> min(const C &v) {
    assert(v.begin() != v.end());
    return *std::min_element(v.begin(), v.end());
}
template <typename T>
inline constexpr T min(const std::initializer_list<T> &v) {
    return std::min(v);
}

METHOD_EXPAND(sum)
template <class C, ENABLE_IF_T(not has_sum_v<C>)>
inline constexpr mem_value_type<C> sum(const C &v) {
    return std::accumulate(v.begin(), v.end(), mem_value_type<C>{});
}
template <typename T>
inline constexpr T sum(const std::initializer_list<T> &v) {
    return std::accumulate(v.begin(), v.end(), T{});
}

METHOD_EXPAND(product)
template <class C, ENABLE_IF_T(not has_product_v<C>)>
inline constexpr mem_value_type<C> product(const C &v) {
    return std::accumulate(v.begin(), v.end(), mem_value_type<C>{1}, std::multiplies<mem_value_type<C>>());
}
template <typename T>
inline constexpr T product(const std::initializer_list<T> &v) {
    return std::accumulate(v.begin(), v.end(), T{1}, std::multiplies<T>());
}

METHOD_EXPAND(product_xor)
template <class C, ENABLE_IF_T(not has_product_xor_v<C>)>
inline constexpr mem_value_type<C> product_xor(const C &v) {
    return std::accumulate(v.begin(), v.end(), mem_value_type<C>{0}, std::bit_xor<mem_value_type<C>>());
}
template <typename T>
inline constexpr T product_xor(const std::initializer_list<T> &v) {
    return std::accumulate(v.begin(), v.end(), T{0}, std::bit_xor<T>());
}

template <class C>
inline constexpr mem_value_type<C> maximum_subarray(const C &v) {
    assert(not v.empty());
    auto itr = v.begin();
    mem_value_type<C> tmp = *itr++;
    mem_value_type<C> res = tmp;
    while (itr != v.end()) {
        tmp += *itr;
        if (tmp < *itr) tmp = *itr;
        if (res < tmp) res = tmp;
        ++itr;
    }
    return res;
}
template <class C>
inline constexpr mem_value_type<C> maximum_subarray(const C &v, mem_value_type<C> init) {
    mem_value_type<C> res = init, tmp = init;
    for (const auto &a : v) {
        tmp += a;
        if (tmp < init) tmp = init;
        if (res < tmp) res = tmp;
    }
    return res;
}

METHOD_AND_FUNC_ARG_EXPAND(count)
METHOD_AND_FUNC_ARG_EXPAND(find)
METHOD_AND_FUNC_ARG_EXPAND(lower_bound)
METHOD_AND_FUNC_ARG_EXPAND(upper_bound)

template <class C, typename T>
inline constexpr bool contains(const C &c, const T &t) {
    return find(c, t) != c.end();
}

template <class C>
inline constexpr mem_value_type<C> gcd(const C &v) {
    mem_value_type<C> init(0);
    for (const auto &e : v) init = std::gcd(init, e);
    return init;
}

template <class C>
inline constexpr mem_value_type<C> average(const C &v) {
    assert(v.size());
    return sum(v) / v.size();
}

template <class C>
inline constexpr mem_value_type<C> median(const C &v) {
    assert(not v.empty());
    std::vector<size_t> u(v.size());
    std::iota(u.begin(), u.end(), 0);
    std::sort(u.begin(), u.end(), [&](size_t a, size_t b) {
        return v[a] < v[b];
    });
    if (v.size() & 1) {
        return v[u[v.size() / 2]];
    }
    // C++20
    // return std::midpoint(v[u[v.size() / 2]], v[u[v.size() / 2 - 1]]);
    return (v[u[v.size() / 2]] + v[u[v.size() / 2 - 1]]) / 2;
}

template <class C, typename U>
inline constexpr std::ptrdiff_t index(const C &v, const U &x) {
    return std::distance(v.begin(), find(v, x));
}

template <class C, ENABLE_IF_T(std::is_integral_v<mem_value_type<C>>)>
inline constexpr mem_value_type<C> mex(const C &v) {
    std::vector<bool> b(v.size() + 1);
    for (const auto &a : v) {
        if (0 <= a and a < b.size()) {
            b[a] = true;
        }
    }
    mem_value_type<C> ret;
    for (size_t i = 0; i < b.size(); i++) {
        if (not b[i]) {
            ret = i;
            break;
        }
    }
    return ret;
}

template <class C>
inline constexpr mem_difference_type<C> bisect_left(const C &v, const mem_value_type<C> &x) {
    return std::distance(v.begin(), lower_bound(v, x));
}
template <class C>
inline constexpr mem_difference_type<C> bisect_right(const C &v, const mem_value_type<C> &x) {
    return std::distance(v.begin(), upper_bound(v, x));
}
#line 6 "/home/shogo314/cpp_include/sh-library/base/functions.hpp"

template <typename T1, typename T2>
inline constexpr bool chmin(T1 &a, T2 b) {
    if (a > b) {
        a = b;
        return true;
    }
    return false;
}

template <typename T1, typename T2>
inline constexpr bool chmax(T1 &a, T2 b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}

inline constexpr long long max(const long long &t1, const long long &t2) {
    return std::max<long long>(t1, t2);
}

inline constexpr long long min(const long long &t1, const long long &t2) {
    return std::min<long long>(t1, t2);
}

using std::abs;
using std::gcd;
using std::lcm;
using std::size;

template <typename T>
constexpr T extgcd(const T &a, const T &b, T &x, T &y) {
    T d = a;
    if (b != 0) {
        d = extgcd(b, a % b, y, x);
        y -= (a / b) * x;
    } else {
        x = 1;
        y = 0;
    }
    return d;
}

template <typename M, typename N, class F, ENABLE_IF_T(std::is_integral_v<std::common_type_t<M, N>> and std::is_invocable_r_v<bool, F, std::common_type_t<M, N>>)>
inline constexpr std::common_type_t<M, N> binary_search(const M &ok, const N &ng, F f) {
    std::common_type_t<M, N> _ok = ok, _ng = ng;
    while (std::abs(_ok - _ng) > 1) {
        std::common_type_t<M, N> mid = (_ok + _ng) / 2;
        if (f(mid)) {
            _ok = mid;
        } else {
            _ng = mid;
        }
    }
    return _ok;
}

template <typename M, typename N, class F, ENABLE_IF_T(not std::is_integral_v<std::common_type_t<M, N>> and std::is_invocable_r_v<bool, F, std::common_type_t<M, N>>)>
inline constexpr std::common_type_t<M, N> binary_search(const M &ok, const N &ng, F f) {
    std::common_type_t<M, N> _ok = ok, _ng = ng;
    for (int i = 0; i < 100; i++) {
        std::common_type_t<M, N> mid = (_ok + _ng) / 2;
        if (f(mid)) {
            _ok = mid;
        } else {
            _ng = mid;
        }
    }
    return _ok;
}

/**
 * 0 <= x < a
 */
inline constexpr bool inrange(long long x, long long a) {
    return 0 <= x and x < a;
}
/**
 * a <= x < b
 */
inline constexpr bool inrange(long long x, long long a, long long b) {
    return a <= x and x < b;
}
/**
 * 0 <= x < a and 0 <= y < b
 */
inline constexpr bool inrect(long long x, long long y, long long a, long long b) {
    return 0 <= x and x < a and 0 <= y and y < b;
}
#line 8 "/home/shogo314/cpp_include/sh-library/base/io.hpp"

namespace tuple_io {
template <typename Tuple, size_t I, typename CharT, typename Traits>
std::basic_istream<CharT, Traits>& read_tuple(std::basic_istream<CharT, Traits>& is, Tuple& t) {
    is >> std::get<I>(t);
    if constexpr (I + 1 < std::tuple_size_v<Tuple>) {
        return read_tuple<Tuple, I + 1>(is, t);
    }
    return is;
}
template <typename Tuple, size_t I, typename CharT, typename Traits>
std::basic_ostream<CharT, Traits>& write_tuple(std::basic_ostream<CharT, Traits>& os, const Tuple& t) {
    os << std::get<I>(t);
    if constexpr (I + 1 < std::tuple_size_v<Tuple>) {
        os << CharT(' ');
        return write_tuple<Tuple, I + 1>(os, t);
    }
    return os;
}
};  // namespace tuple_io

template <typename T1, typename T2, typename CharT, typename Traits>
std::basic_istream<CharT, Traits>& operator>>(std::basic_istream<CharT, Traits>& is, std::pair<T1, T2>& p) {
    is >> p.first >> p.second;
    return is;
}
template <typename... Types, typename CharT, typename Traits>
std::basic_istream<CharT, Traits>& operator>>(std::basic_istream<CharT, Traits>& is, std::tuple<Types...>& p) {
    return tuple_io::read_tuple<std::tuple<Types...>, 0>(is, p);
}
template <typename T, size_t N, typename CharT, typename Traits>
std::basic_istream<CharT, Traits>& operator>>(std::basic_istream<CharT, Traits>& is, std::array<T, N>& a) {
    for (auto& e : a) is >> e;
    return is;
}
template <typename T, typename CharT, typename Traits>
std::basic_istream<CharT, Traits>& operator>>(std::basic_istream<CharT, Traits>& is, std::vector<T>& v) {
    for (auto& e : v) is >> e;
    return is;
}

template <typename T1, typename T2, typename CharT, typename Traits>
std::basic_ostream<CharT, Traits>& operator<<(std::basic_ostream<CharT, Traits>& os, const std::pair<T1, T2>& p) {
    os << p.first << CharT(' ') << p.second;
    return os;
}
template <typename... Types, typename CharT, typename Traits>
std::basic_ostream<CharT, Traits>& operator<<(std::basic_ostream<CharT, Traits>& os, const std::tuple<Types...>& p) {
    return tuple_io::write_tuple<std::tuple<Types...>, 0>(os, p);
}
template <typename T, size_t N, typename CharT, typename Traits>
std::basic_ostream<CharT, Traits>& operator<<(std::basic_ostream<CharT, Traits>& os, const std::array<T, N>& a) {
    for (size_t i = 0; i < N; ++i) {
        if (i) os << CharT(' ');
        os << a[i];
    }
    return os;
}
template <typename T, typename CharT, typename Traits>
std::basic_ostream<CharT, Traits>& operator<<(std::basic_ostream<CharT, Traits>& os, const std::vector<T>& v) {
    for (size_t i = 0; i < v.size(); ++i) {
        if (i) os << CharT(' ');
        os << v[i];
    }
    return os;
}
template <typename T, typename CharT, typename Traits>
std::basic_ostream<CharT, Traits>& operator<<(std::basic_ostream<CharT, Traits>& os, const std::set<T>& s) {
    for (auto itr = s.begin(); itr != s.end(); ++itr) {
        if (itr != s.begin()) os << CharT(' ');
        os << *itr;
    }
    return os;
}

/**
 * @brief 空行出力
 */
void print() { std::cout << '\n'; }
/**
 * @brief 出力して改行
 *
 * @tparam T 型
 * @param x 出力する値
 */
template <typename T>
void print(const T& x) { std::cout << x << '\n'; }
/**
 * @brief 空白区切りで出力して改行
 *
 * @tparam T 1つ目の要素の型
 * @tparam Tail 2つ目以降の要素の型
 * @param x 1つ目の要素
 * @param tail 2つ目以降の要素
 */
template <typename T, typename... Tail>
void print(const T& x, const Tail&... tail) {
    std::cout << x << ' ';
    print(tail...);
}

/**
 * @brief 空行出力
 */
void err() { std::cerr << std::endl; }
/**
 * @brief 出力して改行
 *
 * @tparam T 型
 * @param x 出力する値
 */
template <typename T>
void err(const T& x) { std::cerr << x << std::endl; }
/**
 * @brief 空白区切りで出力して改行
 *
 * @tparam T 1つ目の要素の型
 * @tparam Tail 2つ目以降の要素の型
 * @param x 1つ目の要素
 * @param tail 2つ目以降の要素
 */
template <typename T, typename... Tail>
void err(const T& x, const Tail&... tail) {
    std::cerr << x << ' ';
    err(tail...);
}
#line 3 "/home/shogo314/cpp_include/sh-library/base/type_alias.hpp"

using ll = long long;
using ull = unsigned long long;
using ld = long double;

template <typename T>
using vec = std::vector<T>;
template <typename T, int N>
using ary = std::array<T, N>;
using str = std::string;
using std::deque;
using std::list;
using std::map;
using std::multimap;
using std::multiset;
using std::pair;
using std::set;

using pl = pair<ll, ll>;
using pd = pair<ld, ld>;

template <typename T>
using vv = vec<vec<T>>;
template <typename T>
using vvv = vec<vec<vec<T>>>;
using vl = vec<ll>;
using vvl = vv<ll>;
using vvvl = vvv<ll>;
using vs = vec<str>;
using vc = vec<char>;
using vi = vec<int>;
using vb = vec<bool>;

template <typename T1, typename T2>
using vp = vec<pair<T1, T2>>;
using vpl = vec<pl>;
using vvpl = vv<pl>;
using vd = vec<ld>;
using vpd = vec<pd>;

template <int N>
using al = ary<ll, N>;
template <int N1, int N2>
using aal = ary<ary<ll, N2>, N1>;
template <int N>
using val = vec<al<N>>;
template <int N>
using avl = ary<vl,N>;

template <typename T>
using ml = std::map<ll, T>;
using mll = std::map<ll, ll>;
using sl = std::set<ll>;
using spl = set<pl>;
template <int N>
using sal = set<al<N>>;
template <int N>
using asl = ary<sl,N>;

template <typename T>
using heap_max = std::priority_queue<T, std::vector<T>, std::less<T>>;
template <typename T>
using heap_min = std::priority_queue<T, std::vector<T>, std::greater<T>>;
#line 3 "/home/shogo314/cpp_include/sh-library/base/macro.hpp"

#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")

#define all(obj) (obj).begin(), (obj).end()

#define CONCAT_IMPL(x, y) __CONCAT(x, y)
#define UNIQUE_ID(base) CONCAT_IMPL(base, __COUNTER__)

#define GET_MACRO(_1, _2, _3, _4, NAME, ...) NAME

#define rep4(i, a, n, t) for (long long i = static_cast<long long>(a), i##_loop_end = static_cast<long long>(n), i##_loop_step = static_cast<long long>(t); i < i##_loop_end; i += i##_loop_step)
#define rep3(i, a, n) for (long long i = static_cast<long long>(a), i##_loop_end = static_cast<long long>(n); i < i##_loop_end; ++i)
#define rep2(i, n) rep3(i, 0, n)
#define rep1(n) rep2(UNIQUE_ID(loop_counter_), n)
#define rep(...) GET_MACRO(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)

#define repd4(i, a, n, t) for (long long i = static_cast<long long>(n) - 1, i##_loop_end = static_cast<long long>(a), i##_loop_step = static_cast<long long>(t); i >= i##_loop_end; i -= i##_loop_step)
#define repd3(i, a, n) for (long long i = static_cast<long long>(n) - 1, i##_loop_end = static_cast<long long>(a); i >= i##_loop_end; --i)
#define repd2(i, n) repd3(i, 0, n)
#define repd(...) GET_MACRO(__VA_ARGS__, repd4, repd3, repd2)(__VA_ARGS__)

#define rrep(i, n) rep(i, 1, (n) + 1)
#define rrepd(i, n) repd(i, 1, (n) + 1)

inline void scan(){}
template<class Head,class... Tail>
inline void scan(Head&head,Tail&... tail){std::cin>>head;scan(tail...);}
#define LL(...) ll __VA_ARGS__;scan(__VA_ARGS__)
#define STR(...) str __VA_ARGS__;scan(__VA_ARGS__)
#define IN(a, x) a x; std::cin >> x;
#define CHAR(x) char x; std::cin >> x;
#define VL(a,n) vl a(n); std::cin >> a;
#define AL(a,k) al<k> a; std::cin >> a;
#define AAL(a,n,m) aal<n,m> a; std::cin >> a;
#define VC(a,n) vc a(n); std::cin >> a;
#define VS(a,n) vs a(n); std::cin >> a;
#define VPL(a,n) vpl a(n); std::cin >> a;
#define VAL(a,n,k) val<k> a(n); std::cin >> a;
#define VVL(a,n,m) vvl a(n,vl(m)); std::cin >> a;
#define SL(a,n) sl a;{VL(b,n);a=sl(all(b));}

#define NO std::cout << "NO" << std::endl; return;
#define YES std::cout << "YES" << std::endl; return;
#define No std::cout << "No" << std::endl; return;
#define Yes std::cout << "Yes" << std::endl; return;
#define Takahashi std::cout << "Takahashi" << std::endl; return;
#define Aoki std::cout << "Aoki" << std::endl; return;
#line 7 "/home/shogo314/cpp_include/sh-library/base/vector_func.hpp"

#line 9 "/home/shogo314/cpp_include/sh-library/base/vector_func.hpp"

template <typename T>
std::vector<std::ptrdiff_t> sorted_idx(const std::vector<T> &v, bool reverse = false) {
    std::vector<std::ptrdiff_t> ret(v.size());
    std::iota(ret.begin(), ret.end(), 0);
    std::sort(ret.begin(), ret.end(), [&](std::ptrdiff_t i, std::ptrdiff_t j) {
        return v[i] < v[j];
    });
    if (reverse) std::reverse(ret.begin(), ret.end());
    return ret;
}

template <typename T>
inline std::vector<T> &operator++(std::vector<T> &v) {
    for (auto &e : v) e++;
    return v;
}
template <typename T>
inline std::vector<T> operator++(std::vector<T> &v, int) {
    auto res = v;
    for (auto &e : v) e++;
    return res;
}
template <typename T>
inline std::vector<T> &operator--(std::vector<T> &v) {
    for (auto &e : v) e--;
    return v;
}
template <typename T>
inline std::vector<T> operator--(std::vector<T> &v, int) {
    auto res = v;
    for (auto &e : v) e--;
    return res;
}

template <typename T, typename U, ENABLE_IF_T(std::is_convertible_v<U, T>)>
inline std::vector<T> &operator+=(std::vector<T> &v1, const std::vector<U> &v2) {
    if (v2.size() > v1.size()) {
        v1.resize(v2.size());
    }
    for (size_t i = 0; i < v2.size(); i++) {
        v1[i] += v2[i];
    }
    return v1;
}

template <typename T, typename U, ENABLE_IF_T(std::is_convertible_v<U, T>)>
inline std::vector<T> operator+(const std::vector<T> &v1, const std::vector<U> &v2) {
    std::vector<T> res(v1);
    return res += v2;
}

template <typename T, typename U, ENABLE_IF_T(std::is_convertible_v<U, T>)>
inline std::vector<T> &operator+=(std::vector<T> &v, const U &u) {
    for (T &e : v) {
        e += u;
    }
    return v;
}

template <typename T, typename U, ENABLE_IF_T(std::is_convertible_v<U, T>)>
inline std::vector<T> operator+(const std::vector<T> &v, const U &u) {
    std::vector<T> res(v);
    return res += u;
}

template <typename T, typename U, ENABLE_IF_T(std::is_convertible_v<U, T>)>
inline std::vector<T> operator+(const U &u, const std::vector<T> &v) {
    std::vector<T> res(v);
    return res += u;
}

template <typename T, typename U, ENABLE_IF_T(std::is_convertible_v<U, T>)>
inline std::vector<T> &operator*=(std::vector<T> &v1, const std::vector<U> &v2) {
    if (v2.size() > v1.size()) {
        v1.resize(v2.size());
    }
    for (size_t i = 0; i < v2.size(); i++) {
        v1[i] *= v2[i];
    }
    for (size_t i = v2.size(); i < v1.size(); i++) {
        v1[i] *= U(0);
    }
    return v1;
}

template <typename T, typename U, ENABLE_IF_T(std::is_convertible_v<U, T>)>
inline std::vector<T> operator*(const std::vector<T> &v1, const std::vector<U> &v2) {
    std::vector<T> res(v1);
    return res *= v2;
}

template <typename T, typename U, ENABLE_IF_T(std::is_convertible_v<U, T>)>
inline std::vector<T> &operator*=(std::vector<T> &v, const U &u) {
    for (T &e : v) {
        e *= u;
    }
    return v;
}

template <typename T, typename U, ENABLE_IF_T(std::is_convertible_v<U, T>)>
inline std::vector<T> operator*(const std::vector<T> &v, const U &u) {
    std::vector<T> res(v);
    return res *= u;
}

template <typename T, typename U, ENABLE_IF_T(std::is_convertible_v<U, T>)>
inline std::vector<T> operator*(const U &u, const std::vector<T> &v) {
    std::vector<T> res(v);
    return res *= u;
}

template <typename T, typename U>
inline std::vector<T> &assign(std::vector<T> &v1, const std::vector<U> &v2) {
    v1.assign(v2.begin(), v2.end());
    return v1;
}

template <typename T, typename U>
inline std::vector<T> &extend(std::vector<T> &v1, const std::vector<U> &v2) {
    v1.insert(v1.end(), v2.begin(), v2.end());
    return v1;
}

template <typename T, typename U, ENABLE_IF_T(std::is_convertible_v<U, T>)>
inline std::vector<T> &operator|=(std::vector<T> &v1, const std::vector<U> &v2) {
    return extend(v1, v2);
}

template <typename T, typename U, ENABLE_IF_T(std::is_integral_v<U>)>
inline std::vector<T> &operator|=(std::vector<T> &v, const U &u) {
    std::vector<T> w(v);
    v.clear();
    for (int i = 0; i < u; i++) {
        extend(v, w);
    }
    return v;
}

template <typename T, typename U, ENABLE_IF_T(std::is_integral_v<U>)>
inline std::vector<T> operator|(const std::vector<T> &v, const U &u) {
    std::vector<T> res(v);
    return res |= u;
}

template <typename T, typename U, ENABLE_IF_T(std::is_integral_v<U>)>
inline std::vector<T> operator|(const U &u, const std::vector<T> &v) {
    std::vector<T> res(v);
    return res |= u;
}

template <typename T>
inline std::vector<T> abs(const std::vector<T> &v) {
    std::vector<T> ret;
    ret.reserve(v.size());
    for (const T &e : v) ret.push_back(std::abs(e));
    return ret;
}

template <typename T>
std::vector<T> cumulative_sum(std::vector<T> v) {
    v.insert(v.begin(), T{});
    std::vector<T> ret(v.size());
    std::partial_sum(v.begin(), v.end(), ret.begin());
    return ret;
}

template <typename T, ENABLE_IF_T(std::is_integral_v<T>)>
std::vector<T> iota(T n) {
    assert(n >= 0);
    std::vector<T> ret(n);
    std::iota(ret.begin(), ret.end(), 0);
    return ret;
}

template <typename T>
std::vector<T> unique(const std::vector<T> &v) {
    std::vector<T> res(v);
    std::sort(res.begin(), res.end());
    res.erase(std::unique(res.begin(), res.end()), res.end());
    return res;
}

long long radix_convert(const std::vector<long long> &v, int base = 10) {
    long long res = 0;
    for (int i = v.size() - 1; i >= 0; i--) {
        res <<= base;
        res += v[i];
    }
    return res;
}

std::vector<long long> radix_convert(long long v, int base = 10) {
    std::vector<long long> res;
    while (v > 0) {
        res.push_back(v % base);
        v /= base;
    }
    std::reverse(res.begin(), res.end());
    return res;
}
#line 5 "/home/shogo314/cpp_include/sh-library/base/bit.hpp"

/**
 * @brief 2進数の文字列をlong longにする
 */
long long btoll(std::string s, char one = '1') {
    long long res = 0;
    for (char c : s) {
        res <<= 1;
        if (c == one) ++res;
    }
    return res;
}

#if __cplusplus < 202000L

/**
 * @brief 立っているビットを数える
 * __builtin_popcountll
 */
int popcount(long long a) {
    assert(a >= 0);
    return __builtin_popcountll((unsigned long long)a);
}
/**
 * @brief 左から連続した0のビットを数える
 * __builtin_clzll
 */
int countl_zero(long long a) {
    assert(a >= 0);
    return __builtin_clzll((unsigned long long)a);
}
/**
 * @brief 右から連続した0のビットを数える
 * __builtin_ctzll
 */
int countr_zero(long long a) {
    assert(a >= 0);
    return __builtin_ctzll((unsigned long long)a);
}

#else

#include <bit>
#define BIT_FUNC_EXPAND(func)                      \
    inline constexpr long long func(long long a) { \
        assert(a >= 0);                            \
        return std::func((unsigned long long)a);   \
    }

/**
 * @brief 立っているビットを数える
 */
BIT_FUNC_EXPAND(popcount)
/**
 * @brief 左から連続した0のビットを数える
 */
BIT_FUNC_EXPAND(countl_zero)
/**
 * @brief 左から連続した1のビットを数える
 */
BIT_FUNC_EXPAND(countl_one)
/**
 * @brief 右から連続した0のビットを数える
 */
BIT_FUNC_EXPAND(countr_zero)
/**
 * @brief 右から連続した1のビットを数える
 */
BIT_FUNC_EXPAND(countr_one)
/**
 * @brief 整数値を2の累乗値に切り上げる
 */
BIT_FUNC_EXPAND(bit_ceil)
/**
 * @brief 整数値を2の累乗値に切り下げる
 */
BIT_FUNC_EXPAND(bit_floor)
/**
 * @brief 値を表現するために必要なビット幅を求める
 */
BIT_FUNC_EXPAND(bit_width)

#endif
#line 3 "main.cpp"

void solve() {
    constexpr ll MAX = 1e6 + 1;
    LL(N, D);
    VAL(ST, N, 2);
    sort(ST);
    RSumQ<ll> seg0(MAX), seg1(MAX);
    ll ans = 0;
    for (auto [s, t] : ST) {
        while (seg0.all_prod()) {
            ll r = seg0.max_right(0, [](ll x) { return x == 0; });
            assert(r < MAX);
            assert(seg0.get(r) > 0);
            if (r < s + D) {
                seg0.apply(r, -1);
                seg1.apply(r, -r);
            } else {
                break;
            }
        }
        if (t < s + D)
            continue;
        if (seg0.all_prod()) {
            ans += seg1.prod(0, t) - seg0.prod(0, t) * (s + D - 1);
            ans += seg0.prod(t, MAX) * (t - (s + D) + 1);
        }
        seg0.apply(t, 1);
        seg1.apply(t, t);
    }
    print(ans);
}

int main() {
    std::cin.tie(nullptr);
    std::ios_base::sync_with_stdio(false);
    solve();
}

Submission Info

Judge Result