#335474 (C++14) No.665 Bernoulli Bernoulli

• 問題: No.665 Bernoulli Bernoulli
• ユーザー: minami
• 提出日時: 2019-04-05 00:18:59
• 言語: C++14 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 440 ms / 2,000 ms
• コード長: 4,040 bytes
• コンパイル時間: 1,705 ms
• コンパイル使用メモリ: 173,240 KB
• 実行使用メモリ: 6,944 KB
• 最終ジャッジ日時: 2024-06-09 04:45:02
• 合計ジャッジ時間: 8,960 ms
• ジャッジサーバーID （参考情報）: judge3 / judge5

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	2 ms; 6,812 KB
testcase_01	AC	2 ms; 6,940 KB
testcase_02	AC	434 ms; 6,944 KB
testcase_03	AC	440 ms; 6,944 KB
testcase_04	AC	414 ms; 6,944 KB
testcase_05	AC	385 ms; 6,944 KB
testcase_06	AC	383 ms; 6,940 KB
testcase_07	AC	366 ms; 6,940 KB
testcase_08	AC	365 ms; 6,944 KB
testcase_09	AC	417 ms; 6,940 KB
testcase_10	AC	372 ms; 6,940 KB
testcase_11	AC	428 ms; 6,940 KB
testcase_12	AC	418 ms; 6,944 KB
testcase_13	AC	436 ms; 6,940 KB
testcase_14	AC	435 ms; 6,940 KB
testcase_15	AC	375 ms; 6,940 KB
testcase_16	AC	397 ms; 6,940 KB
testcase_17	AC	383 ms; 6,944 KB
testcase_18	AC	372 ms; 6,944 KB

ソースコード

#include "bits/stdc++.h"
using namespace std;
#ifdef _DEBUG
#include "dump.hpp"
#else
#define dump(...)
#endif

//#define int long long
#define rep(i,a,b) for(int i=(a);i<(b);i++)
#define rrep(i,a,b) for(int i=(b)-1;i>=(a);i--)
#define all(c) begin(c),end(c)
const int INF = sizeof(int) == sizeof(long long) ? 0x3f3f3f3f3f3f3f3fLL : 0x3f3f3f3f;
const int MOD = 1'000'000'007;
template<class T> bool chmax(T &a, const T &b) { if (a < b) { a = b; return true; } return false; }
template<class T> bool chmin(T &a, const T &b) { if (b < a) { a = b; return true; } return false; }

template<int MOD>
struct ModInt {
	static const int kMod = MOD;
	unsigned x;
	ModInt() :x(0) {}
	ModInt(signed x_) { x_ %= MOD; if (x_ < 0)x_ += MOD; x = x_; }
	ModInt(signed long long x_) { x_ %= MOD; if (x_ < 0)x_ += MOD; x = x_; }
	int get()const { return (int)x; }
	ModInt &operator+=(ModInt m) { if ((x += m.x) >= MOD)x -= MOD; return *this; }
	ModInt &operator-=(ModInt m) { if ((x += MOD - m.x) >= MOD)x -= MOD; return *this; }
	ModInt &operator*=(ModInt m) { x = (unsigned long long)x*m.x%MOD; return *this; }
	ModInt &operator/=(ModInt m) { return *this *= m.inverse(); }
	ModInt operator+(ModInt m)const { return ModInt(*this) += m; }
	ModInt operator-(ModInt m)const { return ModInt(*this) -= m; }
	ModInt operator*(ModInt m)const { return ModInt(*this) *= m; }
	ModInt operator/(ModInt m)const { return ModInt(*this) /= m; }
	ModInt operator-()const { return ModInt(MOD - (signed)x); }
	bool operator==(ModInt m)const { return x == m.x; }
	bool operator!=(ModInt m)const { return x != m.x; }
	ModInt inverse()const {
		signed a = x, b = MOD, u = 1, v = 0;
		while (b) {
			signed t = a / b;
			a -= t * b; swap(a, b);
			u -= t * v; swap(u, v);
		}
		if (u < 0)u += MOD;
		return ModInt(u);
	}
};
template<int MOD>
ostream &operator<<(ostream &os, const ModInt<MOD> &m) { return os << m.x; }
template<int MOD>
istream &operator>>(istream &is, ModInt<MOD> &m) { signed long long s; is >> s; m = ModInt<MOD>(s); return is; };

template<int MOD>
ModInt<MOD> pow(ModInt<MOD> a, unsigned long long k) {
	ModInt<MOD> r = 1;
	while (k) {
		if (k & 1)r *= a;
		a *= a;
		k >>= 1;
	}
	return r;
}

using mint = ModInt<MOD>;

// n < 10^7
// 前計算 O(n)
// 計算 O(1)
// Verified: https://yukicoder.me/submissions/330366
vector<mint> fact, factinv, inv;
void precompute(int n) {
	int m = fact.size();
	if (n < m)return;
	n = min(n, mint::kMod - 1); //  N >= kMod  =>  N! = 0 (mod kMod)
	fact.resize(n + 1);
	factinv.resize(n + 1);
	inv.resize(n + 1);
	if (m == 0) {
		fact[0] = 1;
		m = 1;
	}
	for (int i = m; i <= n; i++)
		fact[i] = fact[i - 1] * i;
	factinv[n] = fact[n].inverse();
	for (int i = n; i >= m; i--)
		factinv[i - 1] = factinv[i] * i; // ((i-1)!)^(-1) = (i!)^(-1) * i
	for (int i = m; i <= n; i++)
		inv[i] = factinv[i] * fact[i - 1];
}

mint C(int n, int k) {
	if (k < 0 || n < k)return 0;
	// Lucas's theorem
	if (n >= mint::kMod)
		return C(n % mint::kMod, k % mint::kMod) * C(n / mint::kMod, k / mint::kMod);
	precompute(n);
	return k > n ? 0 : fact[n] * factinv[n - k] * factinv[k];
}

mint P(int n, int k) {
	if (k < 0 || n < k)return 0;
	precompute(n);
	return k > n ? 0 : fact[n] * factinv[n - k];
}

mint H(int n, int k) {
	if (n == 0 && k == 0)return 1; // H(0,0) = 1 != C(-1,0) = 0
	return C(n + k - 1, k);
}

// ベルヌーイ数 B^-
// O(n^2)
vector<mint> bernoulliNumbers(int n) {
	vector<mint> B(n + 1);
	B[0] = 1;
	precompute(n + 1);
	for (int i = 1; i <= n; i++) {
		for (int k = 0; k <= i - 1; k++)
			B[i] += C(i + 1, k) * B[k];
		B[i] *= -inv[i + 1];
	}
	return B;
}

// 冪乗和
// 1^k + 2^k + ... + n^k
// O(k^2)
mint sumOfPowers(long long n, int k) {
	vector<mint> B = bernoulliNumbers(k);
	mint sum = 0;
	mint p = 1;
	mint s = k & 1 ? -1 : 1;
	for (int i = 1; i < k + 2; i++) {
		p *= n;
		sum += s * C(k + 1, i) * p * B[k + 1 - i];
		s *= -1;
	}
	sum /= k + 1;
	return sum;
}

signed main() {
	cin.tie(0);
	ios::sync_with_stdio(false);
	long long n, k; cin >> n >> k;
	cout << sumOfPowers(n, k) << endl;
	return 0;
}