#336737 (C++14) No.665 Bernoulli Bernoulli

• 問題: No.665 Bernoulli Bernoulli
• ユーザー: minami
• 提出日時: 2019-04-10 14:33:13
• 言語: C++14 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 8 ms / 2,000 ms
• コード長: 2,894 bytes
• コンパイル時間: 1,523 ms
• コンパイル使用メモリ: 169,924 KB
• 実行使用メモリ: 4,380 KB
• 最終ジャッジ日時: 2023-09-21 11:14:13
• 合計ジャッジ時間: 2,767 ms
• ジャッジサーバーID （参考情報）: judge15 / judge14

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	2 ms; 4,376 KB
testcase_01	AC	2 ms; 4,380 KB
testcase_02	AC	2 ms; 4,376 KB
testcase_03	AC	7 ms; 4,376 KB
testcase_04	AC	7 ms; 4,376 KB
testcase_05	AC	8 ms; 4,376 KB
testcase_06	AC	7 ms; 4,376 KB
testcase_07	AC	7 ms; 4,380 KB
testcase_08	AC	7 ms; 4,380 KB
testcase_09	AC	7 ms; 4,380 KB
testcase_10	AC	7 ms; 4,376 KB
testcase_11	AC	8 ms; 4,380 KB
testcase_12	AC	7 ms; 4,380 KB
testcase_13	AC	8 ms; 4,380 KB
testcase_14	AC	8 ms; 4,380 KB
testcase_15	AC	7 ms; 4,376 KB
testcase_16	AC	7 ms; 4,376 KB
testcase_17	AC	7 ms; 4,380 KB
testcase_18	AC	7 ms; 4,376 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>;



template<typename X>
X lagrangeInterpolate(const vector<X> &y, X t) {
	int n = y.size();
	X a = 1;
	for (int i = 0; i < n; i++) {
		if (t == i)return y[i];
		a *= t - i;
	}
	X b = 1;
	for (int i = 1; i < n; i++)
		b *= -i;
	X ret = 0;
	for (int i = 0; i < n; i++) {
		ret += y[i] * a / (t - i) / b;
		b = b / -(n - (i + 1)) * (i + 1);
	}
	return ret;
}

mint sumOfPowers(long long n, int k) {
	vector<mint> y;
	mint t = 0;
	for (int x = 0; x <= k + 1; x++) {
		t += pow(mint(x), k);
		y.push_back(t);
	}
	return lagrangeInterpolate(y, mint(n));
}

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