#1171136 (C++23) No.3589 Make Ends Meet (Hard)

• 問題: No.3589 Make Ends Meet (Hard)
• ユーザー: kwm_t
• 提出日時: 2026-07-11 12:01:04
• 言語: C++23 (gcc 15.2.0 + boost 1.90.0)
• 結果: AC
• 実行時間: 92 ms / 2,000 ms
• コード長: 19,092 bytes
• コンパイル時間: 7,443 ms
• コンパイル使用メモリ: 393,884 KB
• 実行使用メモリ: 20,736 KB
• 最終ジャッジ日時: 2026-07-11 12:01:20
• 合計ジャッジ時間: 11,231 ms
• ジャッジサーバーID （参考情報）: judge2_0 / judge1_0

ファイルパターン	結果
sample	AC * 3
other	AC * 47

ソースコード

#include <bits/stdc++.h>
#include <atcoder/all>
using namespace std;
using namespace atcoder;
// using mint = modint1000000007;
// const int mod = 1000000007;
using mint = modint998244353;
const int mod = 998244353;
// const int INF = 1e9;
// const long long LINF = 1e18;
#define rep(i, n) for (int i = 0; i < (n); ++i)
#define rep2(i, l, r) for (int i = (l); i < (r); ++i)
#define rrep(i, n) for (int i = (n)-1; i >= 0; --i)
#define rrep2(i, l, r) for (int i = (r)-1; i >= (l); --i)
#define all(x) (x).begin(), (x).end()
#define allR(x) (x).rbegin(), (x).rend()
#define P pair<int, int>
template<typename A, typename B> inline bool chmax(A& a, const B& b) { if (a < b) { a = b; return true; } return false; }
template<typename A, typename B> inline bool chmin(A& a, const B& b) { if (a > b) { a = b; return true; } return false; }
#ifndef KWM_T_MATH_MODINT_BINOM_HPP
#define KWM_T_MATH_MODINT_BINOM_HPP

#include <vector>
#include <cassert>

namespace kwm_t::math::modint {
/**
 * @brief 二項係数・順列・多項係数（modint用）
 *
 * 典型用途:
 *   nCk, nPk, 多項係数
 *
 * 計算量:
 *   前計算 O(N)
 *   クエリ O(1)
 *
 * @tparam Mint modint型 (例: atcoder::static_modint<MOD>)
 *
 * 制約 / 注意:
 *   - mod は素数
 *   - n < mod（階乗が0にならない範囲）
 *
 * 使用例:
 *   Binom<mint> C(2000000);
 *   C.com(n, k);
 *
 * verified:
 */
template <class Mint>
struct Binom {
	std::vector<Mint> fact, ifact;

	Binom(int n = 2000006) {
		init(n);
	}

	void init(int n) {
		fact.resize(n + 1);
		ifact.resize(n + 1);

		fact[0] = 1;
		for (int i = 1; i <= n; ++i) {
			fact[i] = fact[i - 1] * i;
		}

		ifact[n] = fact[n].inv();
		for (int i = n; i >= 1; --i) {
			ifact[i - 1] = ifact[i] * i;
		}
	}

	// nCk
	Mint com(int n, int k) const {
		if (k < 0 || k > n) return 0;
		return fact[n] * ifact[k] * ifact[n - k];
	}

	Mint operator()(int n, int k) const {
		return com(n, k);
	}

	// nPk
	Mint perm(int n, int k) const {
		if (k < 0 || k > n) return 0;
		return fact[n] * ifact[n - k];
	}

	// nCk (nが大きくkが小さい場合)
	Mint com_sub(long long n, long long k) const {
		if (k < 0 || k > n) return 0;
		if (n - k < k) k = n - k;
		assert(k < (int)fact.size());

		Mint res = ifact[k];
		for (long long i = 0; i < k; ++i) {
			res *= (n - i);
		}
		return res;
	}

	// 多項係数
	template <class... Ints>
	Mint multinomial(int n, const Ints&... ms) const {
		Mint res = fact[n];
		int sum = 0;

		for (int m : {ms...}) {
			if (m < 0 || m > n) return 0;
			res *= ifact[m];
			sum += m;
		}

		if (sum > n) return 0;
		res *= ifact[n - sum];
		return res;
	}

	// 1/x
	Mint inv(int x) const {
		if (x < (int)fact.size()) {
			return fact[x - 1] * ifact[x];
		}
		return Mint(x).inv();
	}

	// nCk の逆数
	Mint inv_com(int n, int k) const {
		if (k < 0 || k > n) return 0;
		return ifact[n] * fact[k] * fact[n - k];
	}
};

} // namespace kwm_t::math::modint

#endif // KWM_T_MATH_MODINT_BINOM_HPP

#ifndef KWM_T_MATH_FPS_FACTORIAL_HPP
#define KWM_T_MATH_FPS_FACTORIAL_HPP

#include <vector>

namespace kwm_t::math::fps {

/**
 * @brief 階乗・逆階乗テーブル
 *
 * fac[i]  = i!
 * finv[i] = (i!)^{-1}
 *
 * @tparam mint modint型
 */
template<typename mint>
struct Factorial {
	int n;
	std::vector<mint> fac, finv;

	explicit Factorial(int n = 0) : n(n), fac(n + 1, 1), finv(n + 1, 1) {
		if (n == 0) return;
		for (int i = 2; i <= n; ++i) fac[i] = fac[i - 1] * i;
		finv[n] = fac[n].inv();
		for (int i = n; i >= 1; --i) finv[i - 1] = finv[i] * i;
	}

	// nCk
	mint comb(int n, int k) const {
		if (k < 0 || n < k) return 0;
		return fac[n] * finv[k] * finv[n - k];
	}
	mint binom(int n, int k) const {
		return comb(n, k);
	}

	// nPk
	mint perm(int n, int k) const {
		if (k < 0 || n < k) return 0;
		return fac[n] * finv[n - k];
	}
};

} // namespace kwm_t::math::fps

#endif // KWM_T_MATH_FPS_FACTORIAL_HPP

#ifndef KWM_T_MATH_FPS_FPS_HPP
#define KWM_T_MATH_FPS_FPS_HPP

#include <vector>
#include <algorithm>
// #include "factorial.hpp"
#include "atcoder/convolution"

namespace kwm_t::math::fps {


template<class T>
struct FormalPowerSeries : std::vector<T> {
	FormalPowerSeries(const std::vector<T>& vec) : std::vector<T>(vec) {}

	using std::vector<T>::vector;
	using std::vector<T>::operator=;
	using F = FormalPowerSeries;
	using SparseFPS = std::vector<std::pair<int, T>>;

	F operator-() const {
		F res(*this);
		for (auto& e : res) e = -e;
		return res;
	}
	F& operator*=(const T& g) {
		for (auto& e : *this) e *= g;
		return *this;
	}
	F& operator/=(const T& g) {
		assert(g != T(0));
		*this *= g.inv();
		return *this;
	}
	F& operator+=(const F& g) {
		int n = this->size(), m = g.size();
		for (int i = 0; i < std::min(n, m); ++i) (*this)[i] += g[i];
		return *this;
	}
	F& operator-=(const F& g) {
		int n = this->size(), m = g.size();
		for (int i = 0; i < std::min(n, m); ++i)(*this)[i] -= g[i];
		return *this;
	}
	F& operator<<=(const int d) {
		int n = this->size();
		if (d >= n) *this = F(n);
		this->insert(this->begin(), d, 0);
		this->resize(n);
		return *this;
	}
	F& operator>>=(const int d) {
		int n = this->size();
		this->erase(this->begin(), this->begin() + min(n, d));
		this->resize(n);
		return *this;
	}

	// O(n log n)
	F inv(int d = -1) const {
		int n = this->size();
		assert(n != 0 && (*this)[0] != 0);
		if (d == -1) d = n;
		assert(d >= 0);
		F res{ (*this)[0].inv() };
		for (int m = 1; m < d; m *= 2) {
			F f(this->begin(), this->begin() + std::min(n, 2 * m));
			F g(res);
			f.resize(2 * m), atcoder::internal::butterfly(f);
			g.resize(2 * m), atcoder::internal::butterfly(g);
			for (int i = 0; i < 2 * m; ++i) f[i] *= g[i];
			atcoder::internal::butterfly_inv(f);
			f.erase(f.begin(), f.begin() + m);
			f.resize(2 * m), atcoder::internal::butterfly(f);
			for (int i = 0; i < 2 * m; ++i) f[i] *= g[i];
			atcoder::internal::butterfly_inv(f);
			T iz = T(2 * m).inv(); iz *= -iz;
			for (int i = 0; i < m; ++i) f[i] *= iz;
			res.insert(res.end(), f.begin(), f.begin() + m);
		}
		res.resize(d);
		return res;
	}

	F& add_inplace(const F& g, int d = -1) {
		int n = this->size();
		if (d == -1) d = n;
		assert(d >= 0);
		this->resize(d);
		for (int i = 0; i < std::min(d, (int)g.size()); ++i)
			(*this)[i] += g[i];
		return *this;
	}
	F& add_resize_inplace(const F& g) { return add_inplace(g, std::max((int)this->size(), (int)g.size())); }
	F add(const F& g, int d = -1) const { return F(*this).add_inplace(g, d); }
	F add_resize(const F& g) const { return F(*this).add_resize_inplace(g); }

	F& sub_inplace(const F& g, int d = -1) {
		int n = this->size();
		if (d == -1) d = n;
		assert(d >= 0);
		this->resize(d);
		for (int i = 0; i < std::min(d, (int)g.size()); ++i)
			(*this)[i] -= g[i];
		return *this;
	}
	F& sub_resize_inplace(const F& g) { return sub_inplace(g, std::max((int)this->size(), (int)g.size())); }
	F sub(const F& g, int d = -1) const { return F(*this).sub_inplace(g, d); }
	F sub_resize(const F& g) const { return F(*this).sub_resize_inplace(g); }

	// fast: FMT-friendly modulus only
	// O(n log n)
	F& multiply_inplace(const F& g, int d = -1) {
		int n = this->size();
		if (d == -1) d = n;
		assert(d >= 0);
		*this = convolution(move(*this), g);
		this->resize(d);
		return *this;
	}
	F& multiply_resize_inplace(const F& g) { return multiply_inplace(g, (int)this->size() + (int)g.size() - 1); }
	F multiply(const F& g, const int d = -1) const { return F(*this).multiply_inplace(g, d); }
	F multiply_resize(const F& g) const { return F(*this).multiply_resize_inplace(g); }

	// O(n log n)
	F& divide_inplace(const F& g, int d = -1) {
		int n = this->size();
		if (d == -1) d = n;
		assert(d >= 0);
		*this = convolution(move(*this), g.inv(d));
		this->resize(d);
		return *this;
	}
	// F& divide_resize_inplace(const F& g) { return divide_inplace(g, (int)this->size() + (int)g.size() - 1); }
	F divide(const F& g, const int d = -1) const { return F(*this).divide_inplace(g, d); }
	// F divide_resize(const F& g) const { return F(*this).divide_resize_inplace(g); }
	// // naive
	// // O(n^2)
	// F &multiply_inplace(const F &g) {
	//   int n = this->size(), m = g.size();
	//   rrep(i, n) {
	//     (*this)[i] *= g[0];
	//     rep2(j, 1, min(i+1, m)) (*this)[i] += (*this)[i-j] * g[j];
	//   }
	//   return *this;
	// }
	// F multiply(const F &g) const { return F(*this).multiply_inplace(g); }
	// // O(n^2)
	// F &divide_inplace(const F &g) {
	//   assert(g[0] != T(0));
	//   T ig0 = g[0].inv();
	//   int n = this->size(), m = g.size();
	//   rep(i, n) {
	//     rep2(j, 1, min(i+1, m)) (*this)[i] -= (*this)[i-j] * g[j];
	//     (*this)[i] *= ig0;
	//   }
	//   return *this;
	// }
	// F divide(const F &g) const { return F(*this).divide_inplace(g); }

	// sparse
	// O(nk)
	F& add_inplace(const SparseFPS& g, int d = -1) {
		int n = this->size();
		if (d == -1) d = n;
		assert(d >= 0);
		this->resize(d);
		for (auto& [i, c] : g) {
			if (i >= d) break;
			(*this)[i] += c;
		}
		return *this;
	}
	F& add_resize_inplace(const SparseFPS& g) {
		int d = this->size();
		if (!g.empty()) d = std::max(d, g.back().first + 1);
		return add_inplace(g, d);
	}
	F add(const SparseFPS& g, int d = -1) const { return F(*this).add_inplace(g, d); }
	F add_resize(const SparseFPS& g) const { return F(*this).add_resize_inplace(g); }

	// sparse sub
	// O(k)
	F& sub_inplace(const SparseFPS& g, int d = -1) {
		int n = this->size();
		if (d == -1) d = n;
		assert(d >= 0);
		this->resize(d);
		for (auto& [i, c] : g) {
			if (i >= d) break;
			(*this)[i] -= c;
		}
		return *this;
	}
	F& sub_resize_inplace(const SparseFPS& g) {
		int d = this->size();
		if (!g.empty()) d = std::max(d, g.back().first + 1);
		return sub_inplace(g, d);
	}
	F sub(const SparseFPS& g, int d = -1) const { return F(*this).sub_inplace(g, d); }
	F sub_resize(const SparseFPS& g) const { return F(*this).sub_resize_inplace(g); }

	F& multiply_inplace(SparseFPS g) {
		int n = this->size();
		auto [d, c] = g.front();
		if (d == 0) g.erase(g.begin());
		else c = 0;

		for (int i = (n - 1); i >= 0; --i) {
			(*this)[i] *= c;
			for (auto& [j, b] : g) {
				if (j > i) break;
				(*this)[i] += (*this)[i - j] * b;
			}
		}
		return *this;
	}
	F& multiply_resize_inplace(SparseFPS g) {
		int d = this->size();
		if (!g.empty()) d += g.back().first;
		this->resize(d);
		return multiply_inplace(std::move(g));
	}
	F multiply(const SparseFPS& g) const { return F(*this).multiply_inplace(g); }
	F multiply_resize(const SparseFPS& g) const { return F(*this).multiply_resize_inplace(g); }
	// O(nk)
	F& divide_inplace(SparseFPS g) {
		int n = this->size();
		auto [d, c] = g.front();
		assert(d == 0 && c != T(0));
		T ic = c.inv();
		g.erase(g.begin());
		for (int i = 0; i < n; ++i) {
			for (auto& [j, b] : g) {
				if (j > i) break;
				(*this)[i] -= (*this)[i - j] * b;
			}
			(*this)[i] *= ic;
		}
		return *this;
	}
	F divide(const SparseFPS& g) const { return F(*this).divide_inplace(g); }

	// divide by x^shift * h(x), where h(0) != 0
	// return the removed shift amount
	// O(nk)
	int divide_shifted_inplace(std::vector<std::pair<int, T>> g) {
		int n = this->size();
		assert(!g.empty());

		int shift = g.front().first;

		// remove x^shift
		*this >>= shift;

		for (auto& [d, c] : g) d -= shift;

		assert(g.front().first == 0);
		assert(g.front().second != T(0));

		divide_inplace(std::move(g));

		return shift;
	}

	F divide_shifted(const std::vector<std::pair<int, T>>& g) const { return F(*this).divide_shifted_inplace(g); }

	// multiply and divide (1 + cz^d)
	// O(n)
	void multiply_inplace(const int d, const T c) {
		int n = this->size();
		if (c == T(1)) for (int i = (n - d - 1); i >= 0; --i) (*this)[i + d] += (*this)[i];
		else if (c == T(-1)) for (int i = (n - d - 1); i >= 0; --i) (*this)[i + d] -= (*this)[i];
		else for (int i = (n - d - 1); i >= 0; --i) (*this)[i + d] += (*this)[i] * c;
	}
	// O(n)
	void divide_inplace(const int d, const T c) {
		int n = this->size();
		if (c == T(1)) for (int i = 0; i < n - d; ++i) (*this)[i + d] -= (*this)[i];
		else if (c == T(-1)) for (int i = 0; i < n - d; ++i) (*this)[i + d] += (*this)[i];
		else for (int i = 0; i < n - d; ++i) (*this)[i + d] -= (*this)[i] * c;
	}

	// O(n)
	T eval(const T& a) const {
		T x(1), res(0);
		for (auto e : *this) res += e * x, x *= a;
		return res;
	}

	// O(n)
	F& integ_inplace() {
		int n = this->size();
		assert(n > 0);
		if (n == 1) return *this = F{ 0 };
		this->insert(this->begin(), 0);
		this->pop_back();
		std::vector<T> inv(n);
		inv[1] = 1;
		int p = T::mod();
		for (int i = 2; i < n; ++i) inv[i] = -inv[p % i] * (p / i);
		for (int i = 2; i < n; ++i) (*this)[i] *= inv[i];
		return *this;
	}
	F integ() const { return F(*this).integ_inplace(); }

	// O(n)
	F& deriv_inplace() {
		int n = this->size();
		assert(n > 0);
		for (int i = 2; i < n; ++i) (*this)[i] *= i;
		this->erase(this->begin());
		this->push_back(0);
		return *this;
	}
	F deriv() const { return F(*this).deriv_inplace(); }

	// O(n log n)
	F& log_inplace(int d = -1) {
		int n = this->size();
		assert(n > 0 && (*this)[0] == 1);
		if (d == -1) d = n;
		assert(d >= 0);
		if (d < n) this->resize(d);
		F f_inv = this->inv();
		this->deriv_inplace();
		this->multiply_inplace(f_inv);
		this->integ_inplace();
		return *this;
	}
	F log(const int d = -1) const { return F(*this).log_inplace(d); }

	// O(n log n)
	// https://arxiv.org/abs/1301.5804 (Figure 1, right)
	F& exp_inplace(int d = -1) {
		int n = this->size();
		assert(n > 0 && (*this)[0] == 0);
		if (d == -1) d = n;
		assert(d >= 0);
		F g{ 1 }, g_fft{ 1, 1 };
		(*this)[0] = 1;
		this->resize(d);
		F h_drv(this->deriv());
		for (int m = 2; m < d; m *= 2) {
			// prepare
			F f_fft(this->begin(), this->begin() + m);
			f_fft.resize(2 * m), atcoder::internal::butterfly(f_fft);

			// Step 2.a'
			// {
			F _g(m);
			for (int i = 0; i < m; ++i) _g[i] = f_fft[i] * g_fft[i];
			atcoder::internal::butterfly_inv(_g);
			_g.erase(_g.begin(), _g.begin() + m / 2);
			_g.resize(m), atcoder::internal::butterfly(_g);
			for (int i = 0; i < m; ++i) _g[i] *= g_fft[i];
			atcoder::internal::butterfly_inv(_g);
			_g.resize(m / 2);
			_g /= T(-m) * m;
			g.insert(g.end(), _g.begin(), _g.begin() + m / 2);
			// }

			// Step 2.b'--d'
			F t(this->begin(), this->begin() + m);
			t.deriv_inplace();
			// {
			  // Step 2.b'
			F r{ h_drv.begin(), h_drv.begin() + m - 1 };
			// Step 2.c'
			r.resize(m); atcoder::internal::butterfly(r);
			for (int i = 0; i < m; ++i) r[i] *= f_fft[i];
			atcoder::internal::butterfly_inv(r);
			r /= -m;
			// Step 2.d'
			t += r;
			t.insert(t.begin(), t.back()); t.pop_back();
			// }

			// Step 2.e'
			if (2 * m < d) {
				t.resize(2 * m); atcoder::internal::butterfly(t);
				g_fft = g; g_fft.resize(2 * m); atcoder::internal::butterfly(g_fft);
				for (int i = 0; i < 2 * m; ++i) t[i] *= g_fft[i];
				atcoder::internal::butterfly_inv(t);
				t.resize(m);
				t /= 2 * m;
			}
			else { // この場合分けをしても数パーセントしか速くならない
				F g1(g.begin() + m / 2, g.end());
				F s1(t.begin() + m / 2, t.end());
				t.resize(m / 2);
				g1.resize(m), atcoder::internal::butterfly(g1);
				t.resize(m), atcoder::internal::butterfly(t);
				s1.resize(m), atcoder::internal::butterfly(s1);
				for (int i = 0; i < m; ++i) s1[i] = g_fft[i] * s1[i] + g1[i] * t[i];
				for (int i = 0; i < m; ++i) t[i] *= g_fft[i];
				atcoder::internal::butterfly_inv(t);
				atcoder::internal::butterfly_inv(s1);
				for (int i = 0; i < m / 2; ++i) t[i + m / 2] += s1[i];
				t /= m;
			}

			// Step 2.f'
			F v(this->begin() + m, this->begin() + std::min<int>(d, 2 * m)); v.resize(m);
			t.insert(t.begin(), m - 1, 0); t.push_back(0);
			t.integ_inplace();
			for (int i = 0; i < m; ++i) v[i] -= t[m + i];

			// Step 2.g'
			v.resize(2 * m); atcoder::internal::butterfly(v);
			for (int i = 0; i < 2 * m; ++i) v[i] *= f_fft[i];
			atcoder::internal::butterfly_inv(v);
			v.resize(m);
			v /= 2 * m;

			// Step 2.h'
			for (int i = 0; i < std::min(d - m, m); ++i)(*this)[m + i] = v[i];
		}
		return *this;
	}
	F exp(const int d = -1) const { return F(*this).exp_inplace(d); }

	// O(n log n)
	F& pow_inplace(const long long k, int d = -1) {
		int n = this->size();
		if (d == -1) d = n;
		assert(d >= 0 && k >= 0);
		if (k == 0) {
			*this = F(d);
			if (d > 0) (*this)[0] = 1;
			return *this;
		}
		int l = 0;
		while (l < n && (*this)[l] == 0) ++l;
		if (l > (d - 1) / k || l == n) return *this = F(d);
		T c = (*this)[l];
		this->erase(this->begin(), this->begin() + l);
		*this /= c;
		this->log_inplace(d - l * k);
		*this *= k;
		this->exp_inplace();
		*this *= c.pow(k);
		this->insert(this->begin(), l * k, 0);
		return *this;
	}
	F pow(const long long k, const int d = -1) const { return F(*this).pow_inplace(k, d); }

	// O(n log n)
	F& shift_inplace(const T c) {
		int n = this->size();
		auto fc = Factorial<T>(n);
		for (int i = 0; i < n; ++i) (*this)[i] *= fc.fac[i];
		reverse(this->begin(), this->end());
		F g(n);
		T cp = 1;
		for (int i = 0; i < n; ++i) g[i] = cp * fc.finv[i], cp *= c;
		this->multiply_inplace(g, n);
		reverse(this->begin(), this->end());
		for (int i = 0; i < n; ++i) (*this)[i] *= fc.finv[i];
		return *this;
	}
	F shift(const T c) const { return F(*this).shift_inplace(c); }

	F operator*(const T& g) const { return F(*this) *= g; }
	F operator/(const T& g) const { return F(*this) /= g; }
	F operator+(const F& g) const { return F(*this) += g; }
	F operator-(const F& g) const { return F(*this) -= g; }
	F operator<<(const int d) const { return F(*this) <<= d; }
	F operator>>(const int d) const { return F(*this) >>= d; }
	F operator*(std::vector<std::pair<int, T>> g) const { return F(*this) *= g; }
	F operator/(std::vector<std::pair<int, T>> g) const { return F(*this) /= g; }
};


} // namespace kwm_t::math::fps

#endif // KWM_T_MATH_FPS_FPS_HPP
int main() {
	std::ios::sync_with_stdio(false);
	std::cin.tie(nullptr);
	int n, m, k; cin >> n >> m >> k;
	m = n * (n - 1) / 2 - m;// 残す数。
	int s = n - 2;
	kwm_t::math::modint::Binom<mint>binom;
	// 残り、last
	using fps = kwm_t::math::fps::FormalPowerSeries<mint>;
	using sfps = vector<pair<int, mint>>;

	vector<vector<fps>>dp(s + 1, vector<fps>(s + 2));
	dp[s][1] = { 1 };
	// K-1層目までを決める

	rep(_, k - 1) {
		vector<vector<fps>>ndp(s + 1, vector<fps>(s + 2));
		rep(i, s + 1)rep(j, s + 2) {
			if (dp[i][j].empty())continue;
			auto tmp = dp[i][j];
			rep2(k, 1, i + 1) {
				sfps s = { {0,-1},{j,1} };
				tmp.multiply_resize_inplace(s);

				auto ctmp = tmp * binom(i, k);
				s = { { k * (k - 1) / 2,1} };
				ctmp.multiply_resize_inplace(s);

				ndp[i - k][k].add_resize_inplace(ctmp);

			}
		}
		dp.swap(ndp);
	}
	// K層
	int lim = n * (n - 1) / 2;
	fps ldp(lim + 1, 0);
	rep(i, s + 1)rep(j, s + 2) {
		auto f = dp[i][j];
		// ldp+= f * (x^j-1) * x^base
		if (f.empty())continue;
		int base = (j + 1) * i + i * (i - 1) / 2;
		sfps s = { {base,-1},{base + j,1} };
		f.multiply_resize_inplace(s);
		ldp.add_resize_inplace(f);
	}
	mint ans = 0;
	rep2(i, m, lim + 1) ans += binom(i, m) * ldp[i];
	cout << ans.val() << endl;
	return 0;
}