結果

問題 No.665 Bernoulli Bernoulli
ユーザー rniyarniya
提出日時 2020-09-22 12:29:12
言語 C++14
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 4 ms / 2,000 ms
コード長 5,821 bytes
コンパイル時間 2,012 ms
コンパイル使用メモリ 171,364 KB
実行使用メモリ 6,944 KB
最終ジャッジ日時 2024-06-25 23:59:04
合計ジャッジ時間 2,768 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge2
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テストケース

テストケース表示
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 2 ms
6,940 KB
testcase_03 AC 3 ms
6,940 KB
testcase_04 AC 3 ms
6,944 KB
testcase_05 AC 3 ms
6,944 KB
testcase_06 AC 3 ms
6,944 KB
testcase_07 AC 2 ms
6,944 KB
testcase_08 AC 3 ms
6,944 KB
testcase_09 AC 4 ms
6,940 KB
testcase_10 AC 3 ms
6,944 KB
testcase_11 AC 3 ms
6,940 KB
testcase_12 AC 3 ms
6,944 KB
testcase_13 AC 3 ms
6,940 KB
testcase_14 AC 3 ms
6,940 KB
testcase_15 AC 3 ms
6,940 KB
testcase_16 AC 3 ms
6,940 KB
testcase_17 AC 3 ms
6,940 KB
testcase_18 AC 3 ms
6,944 KB
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 # 

#include <bits/stdc++.h>
using namespace std;
#define LOCAL
#pragma region Macros
typedef long long ll;
#define ALL(x) (x).begin(),(x).end()
const long long MOD=1000000007;
// const long long MOD=998244353;
const int INF=1e9;
const long long IINF=1e18;
const int dx[4]={1,0,-1,0},dy[4]={0,1,0,-1};
const char dir[4]={'D','R','U','L'};

template<typename T>
istream &operator>>(istream &is,vector<T> &v){
    for (T &x:v) is >> x;
    return is;
}
template<typename T>
ostream &operator<<(ostream &os,const vector<T> &v){
    for (int i=0;i<v.size();++i){
        os << v[i] << (i+1==v.size()?"": " ");
    }
    return os;
}
template<typename T,typename U>
ostream &operator<<(ostream &os,const pair<T,U> &p){
    os << '(' << p.first << ',' << p.second << ')';
    return os;
}
template<typename T,typename U>
ostream &operator<<(ostream &os,const map<T,U> &m){
    os << '{';
    for (auto itr=m.begin();itr!=m.end();++itr){
        os << '(' << itr->first << ',' << itr->second << ')';
        if (++itr!=m.end()) os << ',';
        --itr;
    }
    os << '}';
    return os;
}
template<typename T>
ostream &operator<<(ostream &os,const set<T> &s){
    os << '{';
    for (auto itr=s.begin();itr!=s.end();++itr){
        os << *itr;
        if (++itr!=s.end()) os << ',';
        --itr;
    }
    os << '}';
    return os;
}

void debug_out(){cerr << '\n';}
template<class Head,class... Tail>
void debug_out(Head&& head,Tail&&... tail){
    cerr << head;
    if (sizeof...(Tail)>0) cerr << ", ";
    debug_out(move(tail)...);
}
#ifdef LOCAL
#define debug(...) cerr << " ";\
cerr << #__VA_ARGS__ << " :[" << __LINE__ << ":" << __FUNCTION__ << "]" << '\n';\
cerr << " ";\
debug_out(__VA_ARGS__)
#else
#define debug(...) 42
#endif

template<typename T> T gcd(T x,T y){return y!=0?gcd(y,x%y):x;}
template<typename T> T lcm(T x,T y){return x/gcd(x,y)*y;}

template<class T1,class T2> inline bool chmin(T1 &a,T2 b){
    if (a>b){a=b; return true;} return false;
}
template<class T1,class T2> inline bool chmax(T1 &a,T2 b){
    if (a<b){a=b; return true;} return false;
}
#pragma endregion

template<uint32_t mod> class modint{
    using i64=int64_t;
    using u32=uint32_t;
    using u64=uint64_t;
public:
    u32 v;
    constexpr modint(const i64 x=0) noexcept :v(x<0?mod-1-(-(x+1)%mod):x%mod){}
    constexpr u32 &value() noexcept {return v;}
    constexpr const u32 &value() const noexcept {return v;}
    constexpr modint operator+(const modint &rhs) const noexcept {return modint(*this)+=rhs;}
    constexpr modint operator-(const modint &rhs) const noexcept {return modint(*this)-=rhs;}
    constexpr modint operator*(const modint &rhs) const noexcept {return modint(*this)*=rhs;}
    constexpr modint operator/(const modint &rhs) const noexcept {return modint(*this)/=rhs;}
    constexpr modint &operator+=(const modint &rhs) noexcept {
        v+=rhs.v;
        if (v>=mod) v-=mod;
        return *this;
    }
    constexpr modint &operator-=(const modint &rhs) noexcept {
        if (v<rhs.v) v+=mod;
        v-=rhs.v;
        return *this;
    }
    constexpr modint &operator*=(const modint &rhs) noexcept {
        v=(u64)v*rhs.v%mod;
        return *this;
    }
    constexpr modint &operator/=(const modint &rhs) noexcept {
        return *this*=rhs.pow(mod-2);
    }
    constexpr modint pow(u64 exp) const noexcept {
        modint self(*this),res(1);
        while (exp>0){
            if (exp&1) res*=self;
            self*=self; exp>>=1;
        }
        return res;
    }
    template<class T> friend constexpr modint operator+(T x,modint y) noexcept {return modint(x)+y;}
    template<class T> friend constexpr modint operator-(T x,modint y) noexcept {return modint(x)-y;}
    template<class T> friend constexpr modint operator*(T x,modint y) noexcept {return modint(x)*y;}
    template<class T> friend constexpr modint operator/(T x,modint y) noexcept {return modint(x)/y;}
    constexpr modint &operator++() noexcept {return ++v,*this;}
    constexpr modint &operator--() noexcept {return --v,*this;}
    constexpr modint operator++(int) noexcept {modint t=*this; return ++v,t;}
    constexpr modint operator--(int) noexcept {modint t=*this; return --v,t;}
    constexpr bool operator==(const modint &rhs) const noexcept {return v==rhs.v;}
    constexpr bool operator!=(const modint &rhs) const noexcept {return v!=rhs.v;}
    constexpr bool operator!() const noexcept {return !v;}
    friend istream &operator>>(istream &s,modint &rhs) noexcept {
        i64 v; rhs=modint{(s>>v,v)}; return s;
    }
    friend ostream &operator<<(ostream &s,const modint &rhs) noexcept {
        return s<<rhs.v;
    }
};

template<typename M>
M lagrange_interpolation(vector<M> x,vector<M> y,M T){
    int n=x.size()-1;
    M res=0;
    for (int i=0;i<=n;++i){
        M c=1;
        for (int j=0;j<=n;++j){
            if (i==j) continue;
            (c*=T-x[j])/=x[i]-x[j];
        }
        res+=c*y[i];
    }
    return res;
}

template<typename M>
M lagrange_interpolation_arithmetic(vector<M> &y,M T){
    int n=y.size()-1;
    if (T.v<=n) return y[T.v];
    vector<M> left(n+1,1),right(n+1,1),fac(n+1,1),finv(n+1,1);
    for (int i=0;i<n;++i) left[i+1]=left[i]*(T-i);
    for (int i=n-1;i>=0;--i) right[i]=right[i+1]*(T-(i+1));
    for (int i=1;i<=n;++i) fac[i]=fac[i-1]*i;
    finv[n]=(M)1/fac[n];
    for (int i=n;i>0;--i) finv[i-1]=finv[i]*i;
    M res=0;
    for (int i=0;i<=n;++i){
        M add=y[i]*left[i]*right[i]*finv[i]*finv[n-i];
        if ((n-i)&1) res-=add;
        else res+=add;
    }
    return res;
}

using mint=modint<1000000007>;

int main(){
    cin.tie(0);
    ios::sync_with_stdio(false);
    long long n; int k; cin >> n >> k;
    vector<mint> A(k+2,0);
    for (int i=1;i<=k+1;++i) A[i]=A[i-1]+((mint)i).pow(k);
    cout << lagrange_interpolation_arithmetic(A,(mint)n) << '\n';
}
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