結果

問題 No.2365 Present of good number
ユーザー asaringo
提出日時 2023-06-30 22:27:22
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 51 ms / 2,000 ms
コード長 9,031 bytes
コンパイル時間 2,446 ms
コンパイル使用メモリ 214,396 KB
最終ジャッジ日時 2025-02-15 04:11:42
ジャッジサーバーID
（参考情報） 		judge3 / judge2
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 * 2
other AC * 39
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 fast_io ios::sync_with_stdio(false); cin.tie(nullptr);
#pragma GCC optimize("Ofast,no-stack-protector,unroll-loops,fast-math")
typedef long long ll ;
typedef long double ld ;
#define chmin(a,b) a = min(a,b)
#define chmax(a,b) a = max(a,b)
#define bit_count(x) __builtin_popcountll(x)
#define leading_zero_count(x) __builtin_clz(x)
#define trailing_zero_count(x) __builtin_ctz(x)
#define gcd(a,b) __gcd(a,b)
#define lcm(a,b) a / gcd(a,b) * b
#define rep(i,n) for(int i = 0 ; i < n ; i++)
#define rrep(i,a,b) for(int i = a ; i < b ; i++)
#define repi(it,S) for(auto it = S.begin() ; it != S.end() ; it++)
#define pt(a) cout << a << endl
#define debug(a) cout << #a << " " << a << endl
#define all(a) a.begin(), a.end()
#define endl "\n"
#define v1(n,a) vector<ll>(n,a)
#define v2(n,m,a) vector<vector<ll>>(n,v1(m,a))
#define v3(n,m,k,a) vector<vector<vector<ll>>>(n,v2(m,k,a))
#define v4(n,m,k,l,a) vector<vector<vector<vector<ll>>>>(n,v3(m,k,l,a))
template<typename T,typename U>istream &operator>>(istream&is,pair<T,U>&p){is>>p.first>>p.second;return is;}
template<typename T,typename U>ostream &operator<<(ostream&os,const pair<T,U>&p){os<<p.first<<" "<<p.second;return os;}
template<typename T>istream &operator>>(istream&is,vector<T>&v){for(T &in:v){is>>in;}return is;}
template<typename T>ostream &operator<<(ostream&os,const vector<T>&v){for(auto it=v.begin();it!=v.end();){os<<*it<<((++it)!=v.end()?" ":"");}return os;}
template<typename T>istream &operator>>(istream&is,vector<vector<T>>&v){for(T &in:v){is>>in;}return is;}
template<typename T>ostream &operator<<(ostream&os,const vector<vector<T>>&v){for(auto it=v.begin();it!=v.end();){os<<*it<<((++it)!=v.end()?"\n":"");}return os;}
template<typename T>ostream &operator<<(ostream&os,const set<T>&v){for(auto it=v.begin();it!=v.end();){os<<*it<<((++it)!=v.end()?" ":"");}return os;}

const int mod = 1000000007;

template< int mod >
struct ModInt {
    int x;

    ModInt() : x(0) {}

    ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

    ModInt &operator+=(const ModInt &p) {
        if((x += p.x) >= mod) x -= mod;
        return *this;
    }

    ModInt &operator-=(const ModInt &p) {
        if((x += mod - p.x) >= mod) x -= mod;
        return *this;
    }

    ModInt &operator*=(const ModInt &p) {
        x = (int) (1LL * x * p.x % mod);
        return *this;
    }

    ModInt &operator/=(const ModInt &p) {
        *this *= p.inverse();
        return *this;
    }

    ModInt operator-() const { return ModInt(-x); }

    ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }

    ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }

    ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }

    ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }

    bool operator==(const ModInt &p) const { return x == p.x; }

    bool operator!=(const ModInt &p) const { return x != p.x; }

    ModInt inverse() const {
        int a = x, b = mod, u = 1, v = 0, t;
        while(b > 0) {
            t = a / b;
            swap(a -= t * b, b);
            swap(u -= t * v, v);
        }
        return ModInt(u);
    }

    ModInt pow(int64_t n) const {
        ModInt ret(1), mul(x);
        while(n > 0) {
            if(n & 1) ret *= mul;
            mul *= mul;
            n >>= 1;
        }
        return ret;
    }

    friend ostream &operator<<(ostream &os, const ModInt &p) {
        return os << p.x;
    }

    friend istream &operator>>(istream &is, ModInt &a) {
        int64_t t;
        is >> t;
        a = ModInt< mod >(t);
        return (is);
    }

    static int get_mod() { return mod; }
};

using modint = ModInt< mod >;

struct Eratosthenes{

    private :
        int n ;
        vector<int> factor ; // factor[i]: i を割ることのできる素数
        vector<int> prime ; // 素数
        vector<bool> isprime; // 素数判定
        vector<int> mobius; // メビウス関数

        void build(){
            for(int i = 2 ; i < n ; ++i){
                if(factor[i] != -1) continue ;
                prime.push_back(i) ;
                isprime[i] = true ;
                for(int j = i ; j < n ; j += i) {
                    factor[j] = i ;
                    if((j / i) % i == 0) mobius[j] = 0;
                    else mobius[j] = -mobius[j];
                }

            }
        }

        void init_(int n_){
            n = max(n_,303030) ;
            factor.resize(n,-1) ;
            isprime.resize(n,false) ;
            mobius.resize(n,1);
            build() ;
        }
        
        // 素因数分解 20 -> { (5,1), (2,2) }
        vector<pair<int,ll>> prime_factorization_(int k){
            vector<pair<int,ll>> res ;
            while(k != 1){
                int ex = 0 ;
                int d = factor[k] ;
                while(k % d == 0){
                    k /= d ;
                    ex++ ;
                }
                res.push_back(pair<int,ll>(d,ex)) ;
            }
            return res ;
        }

        // 素因数分解の素因数のみ 20 -> { 5, 2 }
        vector<int> prime_factor_(int k){
            vector<int> res ;
            while(k != 1){
                int ex = 0 ;
                int d = factor[k] ;
                while(k % d == 0){
                    k /= d ;
                    ex++ ;
                }
                res.push_back(d) ;
            }
            return res ;
        }

        // オイラーのファイ関数
        int get_euler_phi_(int k) {
            int euler = k ;
            while(k != 1){
                int d = factor[k] ;
                while(k % d == 0) k /= d ;
                euler -= euler / d ;
            }
            return euler ;
        }

        // 高速ゼータ変換
        template<typename T> vector<T> zeta_transform_(vector<T> f){
            int n = f.size();
            for(int i = 2 ; i < n ; i++){
                if(!isprime[i]) continue;
                for(int j = (n - 1) / i ; j > 0 ; --j){
                    f[j] += f[j * i];
                }
            }
            return f;
        }

        // 高速メビウス変換
        template<typename T> vector<T> mobius_transform_(vector<T> F){
            int n = F.size();
            for(int i = 2 ; i < n ; ++i){
                if(!isprime[i]) continue;
                for(int j = 1 ; j * i < n ; ++j){
                    F[j] -= F[j * i];
                }
            }
            return F;
        }

        template<typename T> vector<T> gcd_convolution_(vector<T> f, vector<T> g){
            int n = max((int)f.size(), (int)g.size());
            vector<T> F = zeta_transform_(f);
            vector<T> G = zeta_transform_(g);
            vector<T> H(n);
            for(int i = 1 ; i < min((int)F.size(), (int)G.size()) ; ++i) H[i] = F[i] * G[i];
            return mobius_transform_(H);
        }

    public :
        Eratosthenes(){}
        Eratosthenes(int n_){ init_(n_); }
        void init(int n_) { init_(n_); }
        vector<pair<int,ll>> prime_factorization(int k) { return prime_factorization_(k); }
        vector<int> prime_factor(int k) { return prime_factor_(k); }
        int get_euler_phi(int k) { return get_euler_phi_(k); }
        int get_mobius(int k) { return mobius[k]; }
        vector<int> get_prime() { return prime ; }
        bool is_prime(int i) { return isprime[i] ; }
        template<typename T> vector<T> zeta_transform(vector<T> f) { return zeta_transform_(f); }
        template<typename T> vector<T> mobius_transform(vector<T> F) { return mobius_transform_(F); }
        template<typename T> vector<T> gcd_convolution(vector<T> f, vector<T> g) { return gcd_convolution_(f, g); }
};

ll powmod(ll x, ll n, ll mod){
    ll res = 1;
    while(n > 0){
        if(n & 1) (res *= x) %= mod;
        (x *= x) %= mod;
        n >>= 1;
    }
    return res;
}

void solve(){
    ll n, k, N;
    cin >> n >> k;
    Eratosthenes ets(1010101);
    vector<ll> P(101010,0);
    P[n] = 1;
    int cnt = 0;
    while(cnt < k && cnt < 100){
        vector<ll> Q(101010,0);
        rep(i,101010){
            if(P[i] == 0) continue;
            auto V = ets.prime_factorization(i);
            for(auto[x,ex] : V) {
                (Q[x+1] += ex * P[i] % (mod - 1)) %= mod - 1;
            }
        }
        P = Q;
        cnt++;
    }
    k -= cnt;
    if(k == 0){
        modint res = 1;
        rep(i,101010){
            if(P[i] == 0) continue;
            res *= powmod(i,P[i],mod);
        }
        pt(res);
        return;
    }
    ll c = k / 2;
    ll two = powmod(2,c,mod-1);
    ll thr = powmod(2,c,mod-1);
    (two *= P[4]) %= mod - 1;
    (thr *= P[3]) %= mod - 1;
    if(k % 2 == 1){
        swap(two,thr);
        (thr *= 2) %= mod - 1;
    }
    modint res = powmod(4,two,mod) * powmod(3,thr,mod);
    cout << res << endl;
}

int main(){
    fast_io
    // int t;
    // cin >> t;
    // rep(i,t) solve();
    solve();
}
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