結果
問題 | No.2365 Present of good number |
ユーザー |
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提出日時 | 2023-07-09 03:19:22 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 2 ms / 2,000 ms |
コード長 | 3,807 bytes |
コンパイル時間 | 2,226 ms |
コンパイル使用メモリ | 213,196 KB |
最終ジャッジ日時 | 2025-02-15 09:16:50 |
ジャッジサーバーID (参考情報) |
judge2 / judge4 |
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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;using ll = long long;const ll modc = 1e9+6;class mint {ll x;public:mint(ll x=0) : x((x%modc+modc)%modc) {}mint operator-() const {return mint(-x);}mint& operator+=(const mint& a) {if ((x += a.x) >= modc) x -= modc;return *this;}mint& operator-=(const mint& a) {if ((x += modc-a.x) >= modc) x -= modc;return *this;}mint& operator*=(const mint& a) {(x *= a.x) %= modc;return *this;}mint operator+(const mint& a) const {mint res(*this);return res+=a;}mint operator-(const mint& a) const {mint res(*this);return res-=a;}mint operator*(const mint& a) const {mint res(*this);return res*=a;}mint pow(ll t) const {if (!t) return 1;mint a = pow(t>>1);a *= a;if (t&1) a *= *this;return a;}mint inv() const {return pow(modc-2);}mint& operator/=(const mint& a) {return (*this) *= a.inv();}mint operator/(const mint& a) const {mint res(*this);return res/=a;}bool operator == (const mint& a) const{return x == a.x;}friend ostream& operator<<(ostream& os, const mint& m){os << m.x;return os;}friend istream& operator>>(istream& ip, mint&m) {ip >> m.x;return ip;}ll val(){return x;}};vector<vector<mint>> dot(vector<vector<mint>> &a, vector<vector<mint>> &b){int M = a.size();vector<vector<mint>> c(M, vector<mint>(M));for (int i=0; i<M; i++){for (int k=0; k<M; k++){for (int j=0; j<M; j++) c[i][j] += (a[i][k] * b[k][j]);}}return c;}vector<vector<mint>> pow(vector<vector<mint>> A, ll N){int M = A.size();vector<vector<mint>> B(M, vector<mint>(M));for (int i=0; i<M; i++) B[i][i] = 1;while(N){if (N % 2 == 1) B = dot(B, A);N >>= 1;A = dot(A, A);}return B;}map<ll, ll> prime_factor(ll n){ll m = n;map<ll, ll> prime;if (n % 2 == 0){while(n % 2 == 0){prime[2]++;n /= 2;}}for (ll i = 3; i*i <= m; i+=2){if (n % i == 0){while(n % i == 0){prime[i]++;n /= i;}}}if (n != 1){prime[n]++;}return prime;}ll mod_exp(ll b, ll e, ll m){if (e > 0 && b == 0) return 0;ll ans = 1;b %= m;while (e > 0){if ((e & 1LL)) ans = (ans * b) % m;e = e >> 1LL;b = (b*b) % m;}return ans;}const ll modc2 = 1e9+7;int main(){ll N, K;cin >> N >> K;map<ll, ll> mp = prime_factor(N), pr;for (int i=0; i<min(K, 60LL); i++){map<ll, ll> mp2;for (auto [p, e] : mp){pr = prime_factor(p+1);for (auto [p1, e1] : pr){mp2[p1] += (e1 * e) % modc;mp2[p1] %= modc;}}swap(mp, mp2);}if (K <= 60){ll ans=1;for (auto [p, e] : mp){ans *= mod_exp(p, e, modc2);ans %= modc2;}cout << ans << endl;return 0;}K -= 60;for (auto [x, y] : mp) assert(x == 2 || x == 3);vector<vector<mint>> m = {{0, 2}, {1, 0}};m = pow(m, K);mint two, thr;ll ans=1;two = m[0][0] * mp[2] + m[0][1] * mp[3];thr = m[1][0] * mp[2] + m[1][1] * mp[3];ans *= mod_exp(2, two.val(), modc2);ans %= modc2;ans *= mod_exp(3, thr.val(), modc2);ans %= modc2;cout << ans << endl;return 0;}