結果

問題 No.665 Bernoulli Bernoulli
ユーザー rniyarniya
提出日時 2020-09-17 23:40:52
言語 C++14
(gcc 13.2.0 + boost 1.83.0)
結果
AC  
実行時間 3 ms / 2,000 ms
コード長 6,142 bytes
コンパイル時間 1,935 ms
コンパイル使用メモリ 168,420 KB
実行使用メモリ 4,384 KB
最終ジャッジ日時 2023-09-04 08:04:26
合計ジャッジ時間 2,726 ms
ジャッジサーバーID
（参考情報） 		judge11 / judge14
このコードへのチャレンジ
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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
4,380 KB
testcase_01 AC 2 ms
4,380 KB
testcase_02 AC 2 ms
4,380 KB
testcase_03 AC 3 ms
4,376 KB
testcase_04 AC 3 ms
4,380 KB
testcase_05 AC 3 ms
4,380 KB
testcase_06 AC 3 ms
4,380 KB
testcase_07 AC 2 ms
4,380 KB
testcase_08 AC 3 ms
4,380 KB
testcase_09 AC 3 ms
4,376 KB
testcase_10 AC 3 ms
4,380 KB
testcase_11 AC 3 ms
4,384 KB
testcase_12 AC 3 ms
4,380 KB
testcase_13 AC 2 ms
4,380 KB
testcase_14 AC 3 ms
4,376 KB
testcase_15 AC 2 ms
4,376 KB
testcase_16 AC 3 ms
4,380 KB
testcase_17 AC 2 ms
4,380 KB
testcase_18 AC 2 ms
4,376 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<uint_fast64_t Modulus> class modint{
    using u64=uint_fast64_t;
public:
    u64 a;
    constexpr modint(const u64 x=0) noexcept:a(x%Modulus){}
    constexpr u64 &value() noexcept{return a;}
    constexpr const u64 &value() const noexcept{return a;}
    constexpr modint &operator+=(const modint &rhs) noexcept{
        a+=rhs.a;
        if (a>=Modulus) a-=Modulus;
        return *this;
    }
    constexpr modint operator+(const modint &rhs) const noexcept{
        return modint(*this)+=rhs;
    }
    constexpr modint &operator++() noexcept{
        return ++a,*this;
    }
    constexpr modint operator++(int) noexcept{
        modint t=*this; return ++a,t;
    }
    constexpr modint &operator-=(const modint &rhs) noexcept{
        if (a<rhs.a) a+=Modulus;
        a-=rhs.a;
        return *this;
    }
    constexpr modint operator-(const modint &rhs) const noexcept{
        return modint(*this)-=rhs;
    }
    constexpr modint &operator--() noexcept{
        return --a,*this;
    }
    constexpr modint operator--(int) noexcept{
        modint t=*this; return --a,t;
    }
    constexpr modint &operator*=(const modint &rhs) noexcept{
        a=a*rhs.a%Modulus;
        return *this;
    }
    constexpr modint operator*(const modint &rhs) const noexcept{
        return modint(*this)*=rhs;
    }
    constexpr modint &operator/=(modint rhs) noexcept{
        u64 exp=Modulus-2;
        while(exp){
            if (exp&1) *this*=rhs;
            rhs*=rhs; exp>>=1;
        }
        return *this;
    }
    constexpr modint operator/(const modint &rhs) const noexcept{
        return modint(*this)/=rhs;
    }
    constexpr modint operator-() const noexcept{
        return modint(Modulus-a);
    }
    constexpr bool operator==(const modint &rhs) const noexcept{
        return a==rhs.a;
    }
    constexpr bool operator!=(const modint &rhs) const noexcept{
        return a!=rhs.a;
    }
    constexpr bool operator!() const noexcept{return !a;}
    friend constexpr modint pow(modint rhs,long long exp) noexcept{
        modint res{1};
        while(exp){
            if (exp&1) res*=rhs;
            rhs*=rhs; 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;
    }
    friend ostream &operator<<(ostream &s,const modint &rhs) noexcept{
        return s << rhs.a;
    }
    friend istream &operator>>(istream &s,modint &rhs) noexcept{
        u64 a; rhs=modint{(s >> a,a)}; return s;
    }
};

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.a<=n) return y[T.a];
    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]+pow((mint)i,k);
    cout << lagrange_interpolation_arithmetic(A,(mint)n) << '\n';
}
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