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
(要ログイン)
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 #
プレゼンテーションモードにする

#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
vector<int> prime ; //
vector<bool> isprime; //
vector<int> mobius; //
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() ;
}
// 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 ;
}
// 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 ;
}
//
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 ;
}
//
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;
}
//
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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