/**
 * date   : 2026-10-10 03:11:17
 * author : yamadanull
 */

// ===== BEGIN INCLUDE: ../../template/template.hpp =====

#include <bits/stdc++.h>
using namespace std;

// ===== BEGIN INCLUDE: util.hpp =====
namespace yamada {
using ll = long long;
using i32 = int;
using u32 = unsigned int;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
using lld = long double;

template <typename T>
using vc = vector<T>;
template <typename T>
using vvc = vector<vector<T>>;
template <typename T>
using vvvc = vector<vector<vector<T>>>;
template <typename T>
using vvvvc = vector<vector<vector<vector<T>>>>;
using vint = vector<int>;
using vl = vector<long long>;
using vd = vector<double>;
using vs = vector<string>;
using vvl = vector<vector<long long>>;
using vvvl = vector<vector<vector<long long>>>;
using vvvvl = vector<vector<vector<vector<long long>>>>;
template <typename T>
using minpq = priority_queue<T, vector<T>, greater<T>>;
template <typename T>
using maxpq = priority_queue<T, vector<T>, less<T>>;

template <typename T, typename U>
struct pr : pair<T, U> {
	template <typename... Args>
	pr(Args... args) : pair<T, U>(args...) {}

	using pair<T, U>::first;
	using pair<T, U>::second;

	pr &operator+=(const pr &r) { first += r.first; second += r.second; return *this; }
	pr &operator-=(const pr &r) { first -= r.first; second -= r.second; return *this; }
	pr &operator*=(const pr &r) { first *= r.first; second *= r.second; return *this; }
	template <typename S>
	pr &operator*=(const S &r) { first *= r, second *= r; return *this; }
	pr operator+(const pr &r) const { return pr(*this) += r; }
	pr operator-(const pr &r) const { return pr(*this) -= r; }
	pr operator*(const pr &r) const { return pr(*this) *= r; }
	template <typename S>
	pr operator*(const S &r) const { return pr(*this) *= r; }
	pr operator-() const { return pr{-first, -second}; }
};

using pint = pr<int, int>;
using pl = pr<ll, ll>;
using vp = vc<pl>;
using vvp = vvc<pl>;

template <typename T>
int len(const T &t) { return t.size(); }

constexpr int inf = 1001001001;
constexpr long long infLL = 4004004004004004004LL;

template <typename T, typename U>
inline bool amin(T &x, U y) { return (y < x) ? (x = y, true) : false; }
template <typename T, typename U>
inline bool amax(T &x, U y) { return (x < y) ? (x = y, true) : false; }

template <typename T, typename U>
pair<T, U> mkp(const T &t, const U &u) { return make_pair(t, u); }
template <typename... Args>
tuple<Args...> mkt(const Args&... args) { return make_tuple(args...); }

template <typename T>
inline long long Sum(const vector<T> &v) { return accumulate(v.begin(), v.end(), T(0)); }

template <typename T>
int lb(const vector<T> &v, const T &a) { return ranges::lower_bound(v, a) - v.begin(); }
template <typename T>
int ub(const vector<T> &v, const T &a) { return ranges::upper_bound(v, a) - v.begin(); }

constexpr long long TEN(int n) {
	long long ret = 1, x = 10;
	for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1);
	return ret;
}

template <typename T>
vector<T> mkrui(const vector<T> &v, const bool rev = false) {
	vector<T> ret(v.size() + 1);
	if (rev) {
		for (int i = (int)v.size() - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1];
	} else {
		for (int i = 0; i < (int)v.size(); i++) ret[i + 1] = ret[i] + v[i];
	}
	return ret;
};

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

template <typename F>
vector<int> mkord(int N, const F &f) {
	vector<int> ord = views::iota(0, N) | ranges::to<vector>();
	ranges::sort(ord, f);
	return ord;
}

template <typename T>
vector<int> mkinv(const vector<T> &v) {
	vector<int> inv(ranges::max(v) + 1, -1);
	for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;
	return inv;
}

vector<int> mkiota(int N) { return views::iota(0, N) | ranges::to<vector>(); }

vector<int> p_mrg(const vector<int> &f, const vector<int> &g) { // g o f
	return f | views::transform([&](auto a) { return g[a]; }) | ranges::to<vector>();
}

template <typename T> // f: old_idx -> new_idx
vector<T> p_shf(const vector<T>& A, const vector<int>& f, const bool inv = false) {
	int n = A.size();
	vector<T> ret(n);
	if (!inv) for (int i = 0; i < n; i++) ret[f[i]] = A[i];
	else for (int i = 0; i < n; i++) ret[i] = A[f[i]];
	return ret;
}

template <typename T>
T mkrev(const T &v) { return v | views::reverse | ranges::to<vector>(); }

template <typename C>
bool nxp(C &v) { return ranges::next_permutation(v).found; }
template <typename F>
void nxp(int N, F f) {
	auto a = views::iota(0, N) | ranges::to<vector>();
	do { f(a); } while (nxp(a));
}

// i 要素目 : [0, A[i])
template <typename F>
void Product(const vector<int> &A, const F& f) {
	vector<int> cur;
	auto dfs = [&](this auto dfs, int i) -> void {
		if (i == (int)A.size()) { f(cur); return; }
		for (int j = 0; j < A[i]; j++) cur.emplace_back(j), dfs(i + 1), cur.pop_back();
	}; dfs(0);
}
// i 要素目 : [0, M)
template <typename F>
void Product(const int N, const int M, const F& f) { vector<int> A(N, M); Product(A, f); }

template <typename T, typename U>
vector<U> Digit(T a, const U &x, int siz = -1) {
	vector<U> ret;
	while (a > 0) {
		ret.emplace_back(a % x);
		a /= x;
	}
	if (siz >= 0) ret.resize(siz);
	return ret;
}

// F : function(void(T&)), mod を取る操作
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I, const function<void(T &)> &f) {
	T res = I;
	for (; n; f(a = a * a), n >>= 1) {
		if (n & 1) f(res = res * a);
	}
	return res;
}
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I = T{1}) {
	return Power(a, n, I, function<void(T &)>{[](T &) -> void {}});
}

template <typename T>
vector<T> Transpose(const vector<T> &A) {
	if (A.empty()) return {};
	return views::iota(0, (int)A[0].size()) | views::transform([&](auto j) {
		return A | views::transform([&](auto&& a) { return a[j]; }) | ranges::to<T>();
	}) | ranges::to<vector<T>>();
}

template <typename T>
vector<T> RotateGrid(const vector<T> &A) {
	if (A.empty()) return {};
	return views::iota(0, (int)A[0].size()) | views::transform([&](auto j) {
		return A | views::transform([&](auto&& a) { return a[j]; }) | ranges::to<T>();
	}) | views::reverse | ranges::to<vector<T>>();
}

template <typename T, typename F>
T bisect(T ok, T bad, F pred) {
	if (ok == bad) return ok;
	while (bad - ok > 1) { T mid = ok + (bad - ok) / 2; (pred(mid) ? ok : bad) = mid; } 
	return bad;
}

template <typename T, typename F>
T bisect_double(T ok, T bad, F pred, int iter = 100) {
	if (ok == bad) return ok;
	while (iter--) { T mid = ok + (bad - ok) / 2; (pred(mid) ? ok : bad) = mid; } 
	return bad;
}

template <typename T0, typename T1, typename T2>
bool inLR(T0 L, T1 x, T2 R){ return L <= x && x < R; }
bool YESNO(bool b) { cout << (b ? "YES\n" : "NO\n"); return b; }
bool YesNo(bool b) { cout << (b ? "Yes\n" : "No\n"); return b; }
bool yesno(bool b) { cout << (b ? "yes\n" : "no\n"); return b; }

long long Isqrt(long long n) {
	if (n <= 0) return 0;
	long long x = sqrt(n);
	while ((x + 1) * (x + 1) <= n) x++;
	while (x * x > n) x--;
	return x;
}

template <typename T>
struct CumulativeSum {
	vector<T> S;
	CumulativeSum(vector<T> &A) : S(A.size() + 1) {
		for (int i = 0; i < (int)A.size(); i++) S[i + 1] = S[i] + A[i];
	}
	T query(int l, int r) { return (l <= r ? S[r] - S[l] : T(0)); }
	T query() { return S.back(); }
	inline T operator()(int l, int r) { return query(l, r); }
	inline T operator()() { return query(); }
};

// 速度よりオーバーフロー対策優先
template <typename T>
T Floor(T a, T b) { assert(b != 0); if (b < 0) a = -a, b = -b; return a / b - (a % b < 0); }
template <typename T>
T Under(T a, T b) { assert(b != 0); if (b < 0) a = -a, b = -b; return a / b - (a % b <= 0); }
template <typename T>
T Ceil (T a, T b) { assert(b != 0); if (b < 0) a = -a, b = -b; return a / b + (a % b > 0); }
template <typename T>
T Over (T a, T b) { assert(b != 0); if (b < 0) a = -a, b = -b; return a / b + (a % b >= 0); }
template <typename T>
T Modulo(T a, T b) { assert(b > 0); T c = a % b; return c < 0 ? c + b : c; }

template <typename T>
pair<T, T> DivMod(T a, T b) {
	assert(b > 0);
	T q = a / b, r = a % b;
	if (r < 0) --q, r += b;
	return {q, r};
}

string rds() { string S; cin >> S; return S; }
int rdi() { int x; cin >> x; return x; }
char rdc() { char c; cin >> c; return c; }
long long rdl() { long long x; cin >> x; return x; }

template <typename mint, int iter = 1000>
string tof(const mint &a) {
	for (int deno = 1; deno <= iter; deno++) {
		mint inv = ((mint)deno).inverse();
		for (int nume = 0; nume <= iter; nume++) {
			mint val = inv * nume;
			if (val == a) {
				if (deno == 1) return to_string(nume);
				return to_string(nume) + "/" + to_string(deno);
			}
			else if (-val == a) {
				if (deno == 1) return to_string(-nume);
				return to_string(-nume) + "/" + to_string(deno);
			}
		}
	}
	return "!NF";
}

} // namespace yamada
// ===== END INCLUDE: util.hpp =====
// ===== BEGIN INCLUDE: bitop.hpp =====
namespace yamada {
__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {
	return __builtin_popcountll(a);
}
inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; }
template <typename T>
inline int gbit(const T &a, int i) { return (a >> i) & 1; }
template <typename T>
inline void sbit(T &a, int i, bool b) { if (gbit(a, i) != b) a ^= T(1) << i; }
constexpr long long PW(int n) { return 1LL << n; }
constexpr long long MSK(int n) { return (1LL << n) - 1; }

string tog(int msk, int N) {
	return views::iota(0, N) | views::transform([&](auto i) {
		return msk >> i & 1 ? '#' : '.';
	}) | ranges::to<string>();
}
}  // namespace yamada
// ===== END INCLUDE: bitop.hpp =====
// ===== BEGIN INCLUDE: io.hpp =====
namespace yamada {
istream &operator>>(istream &is, __int128_t &x) {
	string S; is >> S;
	x = 0;
	bool f{};
	for (auto &c : S) {
		if (c == '-') { f = 1; continue; }
		x *= 10;
		x += c - '0';
	}
	if (f) x = -x;
	return is;
}
istream &operator>>(istream &is, __uint128_t &x) {
	string S; is >> S;
	x = 0;
	for (auto &c : S) {
		x *= 10;
		x += c - '0';
	}
	return is;
}
ostream &operator<<(ostream &os, __int128_t x) {
	if (x == 0) return os << 0;
	if (x < 0) os << '-', x = -x;
	string S;
	while (x) S.push_back('0' + x % 10), x /= 10;
	ranges::reverse(S);
	return os << S;
}
ostream &operator<<(ostream &os, __uint128_t x) {
	if (x == 0) return os << 0;
	string S;
	while (x) S.push_back('0' + x % 10), x /= 10;
	ranges::reverse(S);
	return os << S;
}

template <class T> // tuple / pair / array
concept TupleLike = requires { tuple_size<remove_cvref_t<T>>::value; };
template <class R> // vector / set / ranges::view など（set は入力不可）
concept ListLike = ranges::input_range<R> && !convertible_to<R, string_view> && !TupleLike<R>;

template <TupleLike T> ostream& operator<<(ostream&, const T&);
template <TupleLike T> istream& operator>>(istream&, T&&);
template <ListLike  R> ostream& operator<<(ostream&, const R&);
template <ListLike  R> istream& operator>>(istream&, R&&);

template <TupleLike T>
ostream& operator<<(ostream& os, const T& t) {
	bool f{};
	apply([&](const auto&... x) {
		(..., (os << (exchange(f, 1) ? " " : "") << x));
	}, t);
	return os;
}
template <TupleLike T>
istream& operator>>(istream& is, T&& t) {
	apply([&](auto&... x) { (..., (is >> x)); }, t);
	return is;
}
template <ListLike R>
ostream& operator<<(ostream& os, const R& a) {
	bool f{};
	for (const auto& x : a) os << (exchange(f, 1) ? " " : "") << x;
	return os;
}
template <ListLike R>
istream& operator>>(istream& is, R&& a) {
	for (auto&& x : a) is >> x;
	return is;
}

template <class... T>
void IN(T&&... x) { (cin >> ... >> x); }
template <class... T>
void OUT (const T&... x) { bool f{}; (..., (cout << (exchange(f, 1) ? " " : "") << x)); cout << '\n'; }
template <class... T> // "Flush after OUT"
void FOUT(const T&... x) { bool f{}; (..., (cout << (exchange(f, 1) ? " " : "") << x)); cout << endl; }
template <class... T> // "WithOUT ln"
void WOUT(const T&... x) { bool f{}; (..., (cout << (exchange(f, 1) ? " " : "") << x)); }

struct IoSetupYamada {
	IoSetupYamada() {
		cin.tie(nullptr);
		ios::sync_with_stdio(false);
		cout << fixed << setprecision(15);
		cerr << fixed << setprecision(7);
	}
} iosetupyamada;

namespace DebugImpl {

void dump(const char&   t) { cerr << t; }
void dump(const string& t) { cerr << t; }
void dump(const bool&   t) { cerr << (t ? "true" : "false"); }
void dump(__int128_t    t) { cerr << t; }
void dump(__uint128_t   t) { cerr << t; }

template <integral T>
void dump(const T& t) {
	string res;
	if (t == yamada::inf) res = "inf";
	if constexpr (is_signed<T>::value) {
		if (t == -yamada::inf) res = "-inf";
	}
	if constexpr (sizeof(T) == 8) {
		if (t == yamada::infLL) res = "inf";
		if constexpr (is_signed<T>::value) {
			if (t == -yamada::infLL) res = "-inf";
		}
	}
	if (res.empty()) res = to_string(t);
	cerr << res;
}

template <typename T>
requires (!ListLike<T> && !TupleLike<T> && !integral<T>)
void dump(const T& t) { cerr << t; }

template <ListLike  R> void dump(const R&);
template <TupleLike T> void dump(const T&);

template <ListLike R>
void dump(const R& a) {
	bool f{};
	for (const auto& x : a) {
		cerr << (exchange(f, 1) ? ", " : "[ ");
		dump(x);
	}
	cerr << " ]";
}

template <TupleLike T>
void dump(const T& t) {
	bool f{};
	apply([&](const auto&... x) {
		(..., (cerr << (exchange(f, 1) ? ", " : "( "), dump(x)));
	}, t);
	cerr << " )";
}

template <class... T>
void trace(const T&... x) {
	bool f{};
	(..., (cerr << (exchange(f, 1) ? ", " : " "), dump(x)));
	cerr << endl;
}

}  // namespace DebugImpl

}  // namespace yamada


#ifdef yamadaDebug
#define ERR(...) \
	do { \
		std::cerr << "## " << #__VA_ARGS__ << " = "; \
		yamada::DebugImpl::trace(__VA_ARGS__); \
	} while (0)
#else
#define ERR(...) (void(0))
#endif
// ===== END INCLUDE: io.hpp =====
// ===== BEGIN INCLUDE: ranges.hpp =====
namespace yamada {
constexpr auto All = ranges::all_of; // of なし (Python に合わせている）
constexpr auto Any = ranges::any_of; // 同上
constexpr auto BinarySearch = ranges::binary_search;
constexpr auto Contains = ranges::contains;
constexpr auto Copy = ranges::copy;
constexpr auto Count = ranges::count;
constexpr auto CountIf = ranges::count_if;
constexpr auto Fill = ranges::fill;
constexpr auto Find = ranges::find;
constexpr auto FindIf = ranges::find_if;
constexpr auto FoldLeft = ranges::fold_left;
constexpr auto FoldRight = ranges::fold_right;
constexpr auto IsSorted = ranges::is_sorted;
constexpr auto IsSortedUntil = ranges::is_sorted_until;
constexpr auto LowerBound = ranges::lower_bound;
constexpr auto Max = ranges::max;
constexpr auto MaxElement = ranges::max_element;
constexpr auto Min = ranges::min;
constexpr auto MinElement = ranges::min_element;
constexpr auto MinMax = ranges::minmax;
constexpr auto MinMaxElement = ranges::minmax_element;
constexpr auto Reverse = ranges::reverse;
constexpr auto Rotate = ranges::rotate;
constexpr auto Sort = ranges::sort;
constexpr auto UpperBound = ranges::upper_bound;

template <int K>
constexpr auto Adjacent = views::adjacent<K>;
constexpr auto Chunk = views::chunk;
constexpr auto Drop = views::drop;
constexpr auto DropWhile = views::drop_while;
constexpr auto Enumerate = views::enumerate;
constexpr auto Filter = views::filter;
constexpr auto Join = views::join;
constexpr auto Slide = views::slide;
constexpr auto Stride = views::stride;
constexpr auto Take = views::take;
constexpr auto TakeWhile = views::take_while;
constexpr auto Zip = views::zip;

constexpr auto Rev = views::reverse; // ranges の方と混同しない
constexpr auto Transform = views::transform; // ranges の方は多分使わない
constexpr auto Iota = views::iota; // ranges の方は多分使わない

constexpr auto rtov = ranges::to<vector>();
constexpr auto rtos = ranges::to<string>();

namespace rg = ranges;
namespace vw = views;
using namespace placeholders;
} // namespace yamada
// ===== END INCLUDE: ranges.hpp =====
// ===== BEGIN INCLUDE: macro.hpp =====
#define FOR_E1(x, v) for (auto&& x : v)
#define FOR_E2(x, y, v) for (auto&& [x, y] : v)
#define FOR_E3(x, y, z, v) for (auto&& [x, y, z] : v)
#define FOR_E4(x, y, z, w, v) for (auto&& [x, y, z, w] : v)
#define OVERLOAD5(a, b, c, d, e, f, ...) f
#define FOR_E(...) OVERLOAD5(__VA_ARGS__, FOR_E4, FOR_E3, FOR_E2, FOR_E1)(__VA_ARGS__)

#define FOR1(a) for (long long _ = 0; _ < (long long)(a); ++_)
#define FOR2(i, a) for (long long i = 0; i < (long long)(a); ++i)
#define FOR3(i, a, b) for (long long i = a; i < (long long)(b); ++i)
#define FOR4(i, a, b, c) for (long long i = a; i < (long long)(b); i += c)
#define OVERLOAD4(a, b, c, d, e, ...) e
#define FOR(...) OVERLOAD4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)

#define FOR_R1(a) for (long long i = (long long)(a)-1; i >= 0LL; --i)
#define FOR_R2(i, a) for (long long i = (long long)(a)-1; i >= 0LL; --i)
#define FOR_R3(i, a, b) for (long long i = (long long)(b)-1; i >= (long long)(a); --i)
#define OVERLOAD3(a, b, c, d, ...) d
#define FOR_R(...) OVERLOAD3(__VA_ARGS__, FOR_R3, FOR_R2, FOR_R1)(__VA_ARGS__)

#define eb emplace_back
#define pb push_back
#define fi first
#define se second

#define VV(type, name, h, ...) \
	vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define VVV(type, name, h, w, ...) \
	vector<vector<vector<type>>> name( \
			h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define VVVV(type, name, a, b, c, ...) \
	vector<vector<vector<vector<type>>>> name( \
			a, vector<vector<vector<type>>>( \
				b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))

#define CHAR(...) char __VA_ARGS__; IN(__VA_ARGS__)
#define INT(...) int __VA_ARGS__; IN(__VA_ARGS__)
#define LL(...) long long __VA_ARGS__; IN(__VA_ARGS__)
#define STR(...) std::string __VA_ARGS__; IN(__VA_ARGS__)
#define ZIN(...) for (auto&& [__VA_ARGS__] : std::views::zip(__VA_ARGS__)) IN(__VA_ARGS__)
#define DIE(...) do { yamada::OUT(__VA_ARGS__); return; } while (0)
// ===== END INCLUDE: macro.hpp =====

namespace yamada {
void solve();
}
int main() { yamada::solve(); }
// ===== END INCLUDE: ../../template/template.hpp =====
// ===== BEGIN INCLUDE: ../../monoid/add-max.hpp =====

// ===== BEGIN INCLUDE: add.hpp =====

namespace MONOID {

template <typename E>
struct Add {
	using value_type = E;
	static constexpr value_type O(const value_type& x, const value_type& y) noexcept { return x + y; }
	static constexpr value_type inverse(const value_type &x) noexcept { return -x; }
	static constexpr value_type power(const value_type& x, long long n) noexcept { return value_type(n) * x; }
	static constexpr value_type I() { return value_type(0); }
	static constexpr bool COMMUTATIVE = true;
};

} // namespace monoid
// ===== END INCLUDE: add.hpp =====
// ===== BEGIN INCLUDE: max.hpp =====

#include <algorithm>
#include <limits>

namespace MONOID {

template <typename E, E MNF = std::numeric_limits<E>::min()>
struct Max {
	using value_type = E;
	static constexpr value_type O(const value_type& x, const value_type& y) { return std::max(x, y); }
	static constexpr value_type I() { return MNF; }
	static constexpr bool COMMUTATIVE = true;
};

} // namespace monoid
// ===== END INCLUDE: max.hpp =====

namespace ACTED_MONOID {

template <typename E, E MNF = std::numeric_limits<E>::min()>
struct Add_Max {
	using Monoid_X = MONOID::Max<E, MNF>;
	using Monoid_A = MONOID::Add<E>;
	using X = typename Monoid_X::value_type; // E
	using A = typename Monoid_A::value_type; // E
	static constexpr X O(const X& x, const A& a, const long long) {
		return x == MNF ? x : x + a;
	}
};

} // namespace ACTED_MONOID

// ===== END INCLUDE: ../../monoid/add-max.hpp =====
// ===== BEGIN INCLUDE: ../../segment-tree/dynamic-segment-tree.hpp =====

// ===== BEGIN INCLUDE: ../data-structure/node-pool.hpp =====

// マルチテストケースに弱いので static で確保すること
template <typename Node>
struct NodePool {
	struct Slot {
		union alignas(Node) {
			Slot* next;
			unsigned char storage[sizeof(Node)];
		};
	};
	using Ptr = Node*;

	static constexpr int CHUNK_SIZE = 1 << 12;

	std::vector<std::unique_ptr<Slot[]>> chunks;
	Slot* cur = nullptr;
	int cur_used = 0;
	Slot* free_head = nullptr;

	NodePool() { alloc_chunk(); }

	template <typename... Args>
	Ptr create(Args&&... args) {
		Slot* s = new_slot();
		return ::new (s) Node(std::forward<Args>(args)...);
	}

	Ptr clone(const Ptr x) {
		assert(x);
		Slot* s = new_slot();
		return ::new (s) Node(*x);  // コピーコンストラクタ呼び出し
	}

	void destroy(Ptr x) {
		if (!x) return;
		x->~Node();
		auto s = reinterpret_cast<Slot*>(x);
		s->next = free_head;
		free_head = s;
	}

	void reset() {
		free_head = nullptr;
		if (!chunks.empty()) {
			cur = chunks[0].get();
			cur_used = 0;
		}
	}

	private:
	void alloc_chunk() {
		chunks.emplace_back(std::make_unique<Slot[]>(CHUNK_SIZE));
		cur = chunks.back().get();
		cur_used = 0;
	}

	Slot* new_slot() {
		if (free_head) {
			Slot* s = free_head;
			free_head = free_head->next;
			return s;
		}
		if (cur_used == CHUNK_SIZE) alloc_chunk();
		return &cur[cur_used++];
	}
};
// ===== END INCLUDE: ../data-structure/node-pool.hpp =====

template <typename AM, bool PERSISTENT = false>
struct DynamicLazySegmentTree {
	using MX = typename AM::Monoid_X;
	using MA = typename AM::Monoid_A;
	using X = typename MX::value_type;
	using A = typename MA::value_type;
	using ll = long long;
	struct Node {
		Node *l, *r;
		X sum;
		A laz;
	};

	NodePool<Node> pool;
	const ll L0, R0;
	using Ptr = Node *;
	using I = function<X(ll, ll)>;
	I init;
	Ptr cur_root;

	DynamicLazySegmentTree(ll L0, ll R0, I init = [](ll, ll) -> X { return MX::I(); })
		: L0(L0), R0(R0), init(init), cur_root(new_root()) {}
	template <typename T>
	DynamicLazySegmentTree(const std::vector<T> &dat)
		: L0(0), R0(dat.size()), init([](ll, ll) -> X { return MX::I(); }), cur_root(my_new(dat)) {}

	X prod(Ptr root, ll l, ll r) {
		if (l == r || !root) return MX::I();
		assert(L0 <= l && l < r && r <= R0);
		X sum = MX::I();
		_prod(root, L0, R0, l, r, sum, MA::I());
		return sum;
	}
	X prod(ll l, ll r) { return prod(cur_root, l, r); }
	X prod(Ptr root) { return root ? root->sum : MX::I(); }
	X prod() { return prod(cur_root); }
	template <typename... Args>
	X operator()(Args... args) { return prod(args...); }
	template <typename... Args>
	X operator[](Args... args) { return get_val(args...); }

	X get_val(ll i) { return get_val(cur_root, i); }
	A get_laz(ll i) { return get_laz(cur_root, i); }
	Ptr set_val(ll i, const X &sum) { return set_val(cur_root, i, sum); }
	Ptr multiply(ll i, const X &sum) { return multiply(cur_root, i, sum); }
	Ptr apply(ll l, ll r, const A &laz) { return apply(cur_root, l, r, laz); }
	template <typename G>
	ll max_right(ll L, G check) { return max_right(cur_root, L, check); }
	template <typename G>
	ll min_left(ll R, G check) { return min_left(cur_root, R, check); }

	X get_val(Ptr root, ll i) {
		ll L = L0, R = R0;
		while (L + 1 < R) {
			push(root, L, R);
			ll M = (L + R) / 2;
			if (i < M) {
				if (!root->l) return init(i, i + 1);
				root = root->l, R = M;
			}
			else {
				if (!root->r) return init(i, i + 1);
				root = root->r, L = M;
			}
		}
		return root->sum;
	}

	A get_laz(Ptr root, ll i) {
		if (!root) return MA::I();
		A laz = MA::I();
		_get_laz(root, L0, R0, i, laz);
		return laz;
	}

	Ptr set_val(Ptr root, ll i, const X &sum) {
		assert(root && L0 <= i && i < R0);
		return cur_root = _set_val(root, L0, R0, i, sum);
	}

	Ptr multiply(Ptr root, ll i, const X &sum) {
		assert(root && L0 <= i && i < R0);
		return cur_root = _multiply(root, L0, R0, i, sum);
	}

	Ptr apply(Ptr root, ll l, ll r, const A &laz) {
		if (l == r) return root;
		assert(root && L0 <= l && l < r && r <= R0);
		return cur_root = _apply(root, L0, R0, l, r, laz);
	}

	template <typename G>
	ll max_right(Ptr root, ll L, G check) {
		assert(root && L0 <= L && L <= R0 && check(MX::I()));
		X sum = MX::I();
		return _max_right(root, check, L0, R0, L, sum);
	}

	template <typename G>
	ll min_left(Ptr root, ll R, G check) {
		assert(root && L0 <= R && R <= R0 && check(MX::I()));
		X sum = MX::I();
		return _min_left(root, check, L0, R0, R, sum);
	}

	// memo(idx, val)
	template <typename MEMO>
	void enumerate(Ptr root, MEMO memo) {
		auto dfs = [&](auto &dfs, Ptr u, ll l, ll r, A laz) -> void {
			if (!u) return;
			if (r - l == 1) {
				memo(l, AM::O(u->sum, laz, 1));
				return;
			}
			ll m = (l + r) / 2;
			laz = MA::O(u->laz, laz);
			dfs(dfs, u->l, l, m, laz);
			dfs(dfs, u->r, m, r, laz);
		};
		dfs(dfs, root, L0, R0, MA::I());
	}

	// u[l:r) を apply(v[l:r), laz) で上書きしたものを返す
	Ptr copy_interval(Ptr u, Ptr v, ll l, ll r, A laz = MA::I()) {
		static_assert(PERSISTENT);
		if (u == v) return u;
		u = clone(u);
		_copy_interval(u, v, L0, R0, l, r, laz);
		return u;
	}

	private:
	Ptr new_root() { return my_new(L0, R0); }

	Ptr my_new(const X sum) {
		Ptr u = pool.create();
		u->l = u->r = nullptr;
		u->sum = sum, u->laz = MA::I();
		return u;
	}

	Ptr my_new(ll l, ll r) { return my_new(init(l, r)); }
	Ptr my_new() { return my_new(L0, R0); }
	void my_del(Ptr u) { delete u; }

	Ptr clone(Ptr u) {
		if constexpr (!PERSISTENT) return u;
		if (!u) return u;
		return pool.clone(u);
	}

	void push(Ptr u, ll l, ll r) {
		assert(r - l >= 2);
		ll m = (l + r) / 2;
		if (u->laz == MA::I()) return;
		u->l = (u->l ? clone(u->l) : my_new(l, m));
		u->r = (u->r ? clone(u->r) : my_new(m, r));
		u->l->sum = AM::O(u->l->sum, u->laz, m - l);
		u->r->sum = AM::O(u->r->sum, u->laz, r - m);
		u->l->laz = MA::O(u->l->laz, u->laz);
		u->r->laz = MA::O(u->r->laz, u->laz);
		u->laz = MA::I();
	}

	void _copy_interval(Ptr u, Ptr v, ll l, ll r, ll ql, ll qr, A laz) {
		// u[ql, qr) <- apply(v[ql, qr), laz)
		// u is already updated
		assert(u);
		ql = std::max(ql, l);
		qr = std::min(qr, r);
		if (ql >= qr) return;
		if (l == ql && r == qr) { // terminus
			if (v) {
				u->sum = AM::O(v->sum, laz, r - l);
				u->laz = MA::O(v->laz, laz);
				u->l = v->l, u->r = v->r;
			}
			else {
				u->sum = AM::O(init(l, r), laz, r - l);
				u->laz = laz;
				u->l = nullptr, u->r = nullptr;
			}
			return;
		}
		// push
		ll m = (l + r) / 2;
		u->l = (u->l ? clone(u->l) : my_new());
		u->r = (u->r ? clone(u->r) : my_new());
		u->l->sum = AM::O(u->l->sum, u->laz, m - l);
		u->l->laz = MA::O(u->l->laz, u->laz);
		u->r->sum = AM::O(u->r->sum, u->laz, r - m);
		u->r->laz = MA::O(u->r->laz, u->laz);
		u->laz = MA::I();
		if (v) laz = MA::O(v->laz, laz);
		_copy_interval(u->l, (v && v->l ? v->l : nullptr), l, m, ql, qr, laz);
		_copy_interval(u->r, (v && v->r ? v->r : nullptr), m, r, ql, qr, laz);
		u->sum = MX::O(u->l->sum, u->r->sum);
	}

	template <typename T>
	Ptr my_new(const std::vector<T> &dat) {
		assert(L0 == 0 && R0 == dat.size());
		auto dfs = [&](auto &dfs, ll l, ll r) -> Ptr {
			if (l == r) return nullptr;
			if (r == l + 1) return my_new(X(dat[l]));
			ll m = (l + r) / 2;
			Ptr l_root = dfs(dfs, l, m), r_root = dfs(dfs, m, r);
			X sum = MX::O(l_root->sum, r_root->sum);
			Ptr cur_root = my_new(sum);
			cur_root->l = l_root, cur_root->r = r_root;
			return cur_root;
		};
		return dfs(dfs, 0, dat.size());
	}

	Ptr _set_val(Ptr u, ll l, ll r, ll i, const X &sum) {
		if (r == l + 1) {
			u = clone(u);
			u->sum = sum;
			u->laz = MA::I();
			return u;
		}
		push(u, l, r);
		ll m = (l + r) / 2;
		if (!u->l) u->l = my_new(l, m);
		if (!u->r) u->r = my_new(m, r);

		u = clone(u);
		if (i < m) {
			u->l = _set_val(u->l, l, m, i, sum);
		} else {
			u->r = _set_val(u->r, m, r, i, sum);
		}
		u->sum = MX::O(u->l->sum, u->r->sum);
		return u;
	}

	Ptr _multiply(Ptr u, ll l, ll r, ll i, const X &sum) {
		if (r == l + 1) {
			u = clone(u);
			u->sum = MX::O(u->sum, sum);
			u->laz = MA::I();
			return u;
		}
		push(u, l, r);
		ll m = (l + r) / 2;
		if (!u->l) u->l = my_new(l, m);
		if (!u->r) u->r = my_new(m, r);

		u = clone(u);
		if (i < m) {
			u->l = _multiply(u->l, l, m, i, sum);
		} else {
			u->r = _multiply(u->r, m, r, i, sum);
		}
		u->sum = MX::O(u->l->sum, u->r->sum);
		return u;
	}

	void _prod(Ptr u, ll l, ll r, ll ql, ll qr, X &sum, A laz) {
		ql = std::max(ql, l);
		qr = std::min(qr, r);
		if (ql >= qr) return;
		if (!u) {
			sum = MX::O(sum, AM::O(init(ql, qr), laz, qr - ql));
			return;
		}
		if (l == ql && r == qr) {
			sum = MX::O(sum, AM::O(u->sum, laz, qr - ql));
			return;
		}
		ll m = (l + r) / 2;
		laz = MA::O(u->laz, laz);
		_prod(u->l, l, m, ql, qr, sum, laz);
		_prod(u->r, m, r, ql, qr, sum, laz);
	}

	Ptr _apply(Ptr u, ll l, ll r, ll ql, ll qr, const A &laz) {
		if (!u) u = my_new(l, r);
		ql = std::max(ql, l);
		qr = std::min(qr, r);
		if (ql >= qr) return u;
		if (l == ql && r == qr) {
			u = clone(u);
			u->sum = AM::O(u->sum, laz, qr - ql);
			u->laz = MA::O(u->laz, laz);
			return u;
		}
		push(u, l, r);
		ll m = (l + r) / 2;
		u = clone(u);
		u->l = _apply(u->l, l, m, ql, qr, laz);
		u->r = _apply(u->r, m, r, ql, qr, laz);
		u->sum = MX::O(u->l->sum, u->r->sum);
		return u;
	}

	template <typename G>
	ll _max_right(Ptr u, const G &check, ll l, ll r, ll ql, X &sum) {
		if (r <= ql) return r;
		if (!u) u = my_new(l, r);
		ql = std::max(ql, l);
		if (l == ql && check(MX::O(sum, u->sum))) {
			sum = MX::O(sum, u->sum);
			return r;
		}
		if (r == l + 1) return l;
		push(u, l, r);
		ll m = (l + r) / 2;
		ll k = _max_right(u->l, check, l, m, ql, sum);
		if (k < m) return k;
		return _max_right(u->r, check, m, r, ql, sum);
	}

	template <typename G>
	ll _min_left(Ptr u, const G &check, ll l, ll r, ll qr, X &sum) {
		if (qr <= l) return l;
		if (!u) u = my_new(l, r);
		qr = std::min(qr, r);
		if (r == qr && check(MX::O(u->sum, sum))) {
			sum = MX::O(u->sum, sum);
			return l;
		}
		if (r == l + 1) return r;
		push(u, l, r);
		ll m = (l + r) / 2;
		ll k = _min_left(u->r, check, m, r, qr, sum);
		if (m < k) return k;
		return _min_left(u->l, check, l, m, qr, sum);
	}

	void _get_laz(Ptr u, ll l, ll r, ll i, A &laz) {
		if (!u) return;
		laz = MA::O(u->laz, laz);
		if (r == l + 1) return;
		ll m = (l + r) / 2;
		if (i < m) return _get_laz(u->l, l, m, i, laz);
		_get_laz(u->r, m, r, i, laz);
	}
};
// ===== END INCLUDE: ../../segment-tree/dynamic-segment-tree.hpp =====

void yamada::solve()
{
	auto[N,D,A,B]=[&]()->tuple<i128,i128,vc<i128>,vc<i128>>{
		LL(N,D);
		vc<i128> X(N),Y(N); ZIN(X,Y);
		Sort(Zip(Y,X));
		vc<i128> A,B;
		for(i128 l=0,r=0; l<N; l=r){
			while(r<N && Y[l]==Y[r])++r;
			i128 a=0;
			FOR(i,l,r)a+=X[i];
			A.eb(a);
			B.eb(Y[l]);
		}
		N=len(A);
		return{N,D,A,B};
	}();
	ERR(A); ERR(B);

	using SEG=DynamicLazySegmentTree<ACTED_MONOID::Add_Max<i128,-infLL>>;

	SEG seg(0,D+1,[](i128 l,i128){return -l;});
	FOR_E(a,b,Zip(A,B))seg.apply(b%D+1,D+1,a);

	// f(l,r)=sum (k:[l,r)) (cnt[k%D] - 1)
	// f(0,i)=seg[i] (i<D)
	auto f=[&](this auto f,i128 l,i128 r)->i128{
		if(l/D==(r-1)/D)return seg[(r-1)%D+1]-seg[l%D];
		if(l%D==0 && r%D==0)return (r-l)/D*seg[D];
		i128 m0=(l/D+1)*D;
		i128 m1=(r/D)*D;
		return f(l,m0)+f(m0,m1)+f(m1,r);
	};
	// g(L,l,r): max (k:[l,r)) (f(L,k))
	auto g=[&](this auto g,i128 L,i128 l,i128 r)->i128{
		assert(r-l<=D);
		if(l/D==(r-1)/D){
			return seg(l%D,(r-1)%D+1)+f(0,l/D*D)-f(0,L);
		}
		i128 m=(l/D+1)*D;
		return max(g(L,l,m),g(L,m,r));
	};

	i128 cur=0; FOR_E(a,b,Zip(A,B))cur+=Ceil<i128>(b,D)*a;
	i128 ans=cur;

	FOR(m,N){ // [0,m) を０にした状態
		i128 L=(m==0? 0:B[m-1]);
		i128 R=B[m];
		amin(ans,cur);
		amin(ans,cur-g(L+1,L+1,min(L+D,R)+1));
		amin(ans,cur-g(L+1,max(L,R-D)+1,R+1));

		cur-=f(L+1,R+1);
		seg.apply(B[m]%D+1,D+1,-A[m]);
	}
	amin(ans,cur);
	amin(ans,Max(B));
	OUT(ans);
}