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 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 39 |
ソースコード
#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()?" ":"");}returnos;}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();}