結果

問題 No.665 Bernoulli Bernoulli
ユーザー paruki
提出日時 2018-03-09 23:24:32
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 343 ms / 2,000 ms
コード長 3,242 bytes
コンパイル時間 1,841 ms
コンパイル使用メモリ 172,584 KB
実行使用メモリ 5,248 KB
最終ジャッジ日時 2024-10-10 19:39:40
合計ジャッジ時間 7,834 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge3
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 4
other AC * 15
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

#define _USE_MATH_DEFINES
#include "bits/stdc++.h"
using namespace std;
#define FOR(i,j,k) for(int (i)=(j);(i)<(int)(k);++(i))
#define rep(i,j) FOR(i,0,j)
#define each(x,y) for(auto &(x):(y))
#define mp make_pair
#define MT make_tuple
#define all(x) (x).begin(),(x).end()
#define debug(x) cout<<#x<<": "<<(x)<<endl
#define smax(x,y) (x)=max((x),(y))
#define smin(x,y) (x)=min((x),(y))
#define MEM(x,y) memset((x),(y),sizeof (x))
#define sz(x) (int)(x).size()
#define RT return
#define vv(a,b,c,d) vector<vector<a> >(b,vector<a>(c,d))
#define vvv(a,b,c,d,e) vector<vector<vector<a> > >(b,vv(a,c,d,e))
using ll = long long;
using pii = pair<int, int>;
using vi = vector<int>;
using vll = vector<ll>;
template<int MOD>
class ModInt {
public:
    ModInt() :value(0) {}
    ModInt(long long val) :value((int)(val<0 ? MOD + val%MOD : val%MOD)) { }
    ModInt& operator+=(ModInt that) {
        value = value + that.value;
        if (value >= MOD)value -= MOD;
        return *this;
    }
    ModInt& operator-=(ModInt that) {
        value -= that.value;
        if (value<0)value += MOD;
        return *this;
    }
    ModInt& operator*=(ModInt that) {
        value = (int)((long long)value * that.value % MOD);
        return *this;
    }
    ModInt &operator/=(ModInt that) {
        return *this *= that.inverse();
    }
    ModInt operator+(ModInt that) const {
        return ModInt(*this) += that;
    }
    ModInt operator-(ModInt that) const {
        return ModInt(*this) -= that;
    }
    ModInt operator*(ModInt that) const {
        return ModInt(*this) *= that;
    }
    ModInt operator/(ModInt that) const {
        return ModInt(*this) /= that;
    }
    ModInt pow(long long k) const {
        if (value == 0)return 0;
        ModInt n = *this, res = 1;
        while (k) {
            if (k & 1)res *= n;
            n *= n;
            k >>= 1;
        }
        return res;
    }
    ModInt inverse() const {
        long long a = value, b = MOD, u = 1, v = 0;
        while (b) {
            long long t = a / b;
            a -= t * b;
            swap(a, b);
            u -= t * v;
            swap(u, v);
        }
        return ModInt(u);
    }
    int toi() const { return value; }
private:
    int value;
};
typedef ModInt<1000000007> mint;
ostream& operator<<(ostream& os, const mint& x) {
    os << x.toi();
    return os;
}
mint nCr(int n, int r, const vector<mint> &fact, const vector<mint> &rev) {
    if (n < r)return 0;
    return fact[n] * rev[r] * rev[n - r];
}
mint B[10004];
int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout << fixed << setprecision(20);
    ll n;
    int k;
    cin >> n >> k;
    vector<mint> fact(20000), rev(20000);
    fact[0] = 1;
    rep(i, 20000 - 1)fact[i + 1] = fact[i] * (i + 1);
    rep(i, 20000)rev[i] = fact[i].inverse();
    B[0] = 1;
    for (int i = 1; i <= k; ++i) {
        mint x = 0;
        for (int j = 0; j < i; ++j) {
            x += nCr(i + 1, j, fact, rev)*B[j];
        }
        x *= -1;
        x /= (i + 1);
        B[i] = x;
    }
    mint ans = 0;
    for (int j = 0; j <= k; ++j) {
        ans += nCr(k + 1, j, fact, rev) * B[j] * mint(n).pow(k+1-j) * mint(-1).pow(j);
    }
    ans /= k + 1;
    cout << ans << endl;
}
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