結果
| 問題 |
No.2365 Present of good number
|
| コンテスト | |
| ユーザー |
 ponjuice
|
| 提出日時 | 2023-06-30 22:15:17 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 19 ms / 2,000 ms |
| コード長 | 8,788 bytes |
| コンパイル時間 | 5,446 ms |
| コンパイル使用メモリ | 330,552 KB |
| 実行使用メモリ | 10,112 KB |
| 最終ジャッジ日時 | 2024-07-07 10:04:12 |
| 合計ジャッジ時間 | 6,884 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge5 |
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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;
#include <atcoder/all>
using namespace atcoder;
//高速化
struct ponjuice{ponjuice(){cin.tie(0);ios::sync_with_stdio(0);cout<<fixed<<setprecision(20);}}PonJuice;
//#define endl '\n' //インタラクティブ問題の時は消す
//型
using ll = long long;
using ld = long double;
using mint = modint1000000007;
template<class T>using vc = vector<T>; template<class T>using vvc = vc<vc<T>>; template<class T>using vvvc = vvc<vc<T>>;
using vi = vc<int>; using vvi = vvc<int>; using vvvi = vvvc<int>;
using vl = vc<ll>; using vvl = vvc<ll>; using vvvl = vvvc<ll>;
using pi = pair<int, int>; using pl = pair<ll, ll>;
using ull = unsigned ll;
template<class T>using priq = priority_queue<T>;
template<class T>using priqg = priority_queue<T, vc<T>, greater<T>>;
// for文
#define overload4(a, b, c, d, e, ...) e
#define rep1(n) for(ll i = 0; i < n; i++)
#define rep2(i, n) for(ll i = 0; i < n; i++)
#define rep3(i, a, b) for(ll i = a; i < b; i++)
#define rep4(i, a, b, step) for(ll i = a; i < b; i+= step)
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)
#define per1(n) for(ll i = n-1; i >= 0; i--)
#define per2(i, n) for(ll i = n-1; i >= 0; i--)
#define per3(i, a, b) for(ll i = b-1; i >= a; i--)
#define per4(i, a, b, step) for(ll i = b-1; i >= a; i-= step)
#define per(...) overload4(__VA_ARGS__, per4, per3, per2, per1)(__VA_ARGS__)
#define fore1(a) for(auto&& i : a)
#define fore2(i,a) for(auto&& i : a)
#define fore3(x,y,a) for(auto&& [x, y] : a)
#define fore4(x,y,z,a) for(auto&& [x, y, z] : a)
#define fore(...) overload4(__VA_ARGS__, fore4, fore3, fore2, fore1)(__VA_ARGS__)
//関数
#define mp make_pair
#define mt make_tuple
#define a first
#define b second
#define pb emplace_back
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define si(x) (ll)(x).size()
template<class S, class T>inline bool chmax(S& a, T b){return a < b && ( a = b , true);}
template<class S, class T>inline bool chmin(S& a, T b){return a > b && ( a = b , true);}
template<class T>void uniq(vc<T>&a){sort(all(a));a.erase(unique(all(a)),a.end());}
template<class T>vc<T> operator++(vc<T>&v,signed){auto res = v;fore(e,v)e++;return res;}
template<class T>vc<T> operator--(vc<T>&v,signed){auto res = v;fore(e,v)e--;return res;}
template<class T>vc<T> operator++(vc<T>&v){fore(e,v)e++;return v;}
template<class T>vc<T> operator--(vc<T>&v){fore(e,v)e--;return v;}
//入出力(operator)
template<int T>istream&operator>>(istream&is,static_modint<T>&a){ll v;is>>v;a=v;return is;}
istream&operator>>(istream&is,modint&a){ll v;cin>>v;a=v;return is;}
template<class S,class T>istream&operator>>(istream&is,pair<S,T>&a){is>>a.a>>a.b;return is;}
template<class T>istream&operator>>(istream&is,vc<T>&a){fore(e,a)is>>e;return is;}
template<int T>ostream&operator<<(ostream&os,static_modint<T>a){return os<<a.val();}
ostream&operator<<(ostream&os,modint a){return os<<a.val();}
template<class S,class T>ostream&operator<<(ostream&os,pair<S,T>&a){return os<<a.a<<" "<<a.b;}
template<class T>ostream&operator<<(ostream&os,set<T>&a){fore(it,a){os<<it<<" ";}return os;}
template<class T>ostream&operator<<(ostream&os,multiset<T>&a){fore(it,a){os<<it<<" ";}return os;}
template<class S,class T>ostream&operator<<(ostream&os,map<S,T>&a){fore(x,y,a){os<<x<<" "<<y<<"\n";}return os;}
template<class T>ostream&operator<<(ostream&os,unordered_set<T>&a){fore(it,a){os<<it<<" ";}return os;}
template<class S,class T>ostream&operator<<(ostream&os,unordered_map<S,T>&a){fore(x,y,a){os<<x<<" "<<y<<"\n";}return os;}
template<class T>ostream&operator<<(ostream&os,vc<T>&a){fore(e,a)os<<e<<" ";return os;}
template<class T>ostream&operator<<(ostream&os,vvc<T>&a){fore(e,a)os<<e<<"\n";return os;}
//入出力(関数)
vi readvi(ll n){vi a(n);cin>>a;return a;}
vl readvl(ll n){vl a(n);cin>>a;return a;}
vvi readg(ll n,ll m,bool bidirected=true){vvi g(n);rep(i,m){ll a,b;cin>>a>>b;a--;b--;g[a].pb(b);if(bidirected)g[b].pb(a);}return g;}
vvc<pi>readgc(ll n,ll m,bool bidirected=true){vvc<pi> g(n);rep(i,m){ll a,b,c;cin>>a>>b>>c;a--;b--;g[a].pb(b,c);if(bidirected)g[b].pb(a,c);}return g;}
vvi readt(ll n,bool bidirected=true){return readg(n,n-1,bidirected);}
vvc<pi> readtc(ll n,bool bidirected=true){return readgc(n,n-1,bidirected);}
inline void yes(){cout << "Yes\n";}
inline void no(){cout << "No\n";}
inline void yesno(bool y = true){if(y)yes();else no();}
inline void print(){cout<<endl;}
template<class T>inline void print(T a){cout<<a<<endl;}
template<class T,class... Ts>inline void print(T a,Ts ...b){cout<<a;(cout<<...<<(cout<<' ',b));cout<<endl;}
//定数
constexpr ll mod = 1000000007;
constexpr ll minf=-(1<<29);
constexpr ll inf=(1<<29);
constexpr ll MINF=-(1LL<<60);
constexpr ll INF=(1LL<<60);
constexpr ld EPS = 1e-8;
const ld PI = acosl(-1);
#define equals(a, b) (abs((a) - (b)) < EPS)
const int dx[4] ={-1, 0, 1, 0};
const int dy[4] ={ 0, 1, 0,-1};
const int dx8[8] ={-1,-1,-1, 0, 1, 1, 1, 0};
const int dy8[8] ={-1, 0, 1, 1, 1, 0,-1,-1};
void solve();
int main() {
int t = 1;
// cin >>t;
while(t--)solve();
}
vvc<pi>ss(100'100);
ll md = mod-1;
struct mdint {
ll val;
mdint(int k = 0): val((k % md + md) % md) {}
mdint operator*(const mdint other) {return val * other.val % md;}
mdint& operator+=(const mdint other) {
val = val + other.val >= md? val + other.val - md : val + other.val;
return *this;
}
};
template<class T>
struct Matrix {
int _R , _C;
vector<vector<T>> val;
Matrix(int r, int c, T Val): val(r,vector<T>(c,Val)), _R(r), _C(c) {}
Matrix(int r, int c): Matrix(r, c, 0) {}
vector<T>& operator[](int i) {
return val[i];
}
Matrix operator*(const Matrix& other) {
assert(this->_C == other._R);
Matrix result(this->_R, other._C);
for (int i = 0; i < this->_R; i++) {
for (int j = 0; j < other._C; j++) {
for (int k = 0; k < this->_C; k++) {
result[i][j] += this->val[i][k] * other.val[k][j];
}
}
}
return result;
}
};
Matrix<mdint> pow_mat(Matrix<mdint>a,ll n) {
int si = a[0].size();
Matrix<mdint> res(si,si);
for (int i = 0; i < si; i++) res[i][i] = 1;
while (n > 0) {
if (n & 1) res = res * a;
a = a * a;
n >>= 1;
}
return res;
}
void solve(){
rep(i,2,si(ss)){
if(ss[i].size() == 0){
ll res = 1;
while(res*i < 100100){
res*=i;
for(int j = res; j < 100100; j += res){
if(ss[j].size() && ss[j].back().first == i){
ss[j].back().second++;
}else{
ss[j].emplace_back(i,1);
}
}
}
}
}
ll n,k;
cin >> n >> k;
vc<pi> nw = ss[n];
if(k < 50){
rep(i,k){
vc<pi>res,nx;
rep(j,si(nw)){
rep(k,si(ss[nw[j].first+1])){
res.emplace_back(ss[nw[j].first+1][k]);
res.back().second = res.back().second * nw[j].second % md;
}
}
sort(all(res));
rep(j,si(res)){
if(nx.size() != 0 && nx.back().first == res[j].first){
nx.back().second += res[j].second;
}else{
nx.emplace_back(res[j]);
}
}
rep(j,nx.size()){
nx[j].second %= md;
}
nw.swap(nx);
}
mint ans = 1;
rep(i,si(nw)){
ans *= mint(nw[i].first).pow(nw[i].second);
}
print(ans);
return;
}
k-=50;
rep(i,50){
vc<pi>res,nx;
rep(j,si(nw)){
rep(k,si(ss[nw[j].first+1])){
res.emplace_back(ss[nw[j].first+1][k]);
res.back().second = res.back().second * nw[j].second % md;
}
}
sort(all(res));
rep(j,si(res)){
if(nx.size() != 0 && nx.back().first == res[j].first){
nx.back().second += res[j].second;
}else{
nx.emplace_back(res[j]);
}
}
rep(j,nx.size()){
nx[j].second %= md;
}
nw.swap(nx);
}
Matrix<mdint> dp(2,1,0);
rep(i,si(nw)){
if(nw[i].first == 2){
dp[0][0] = nw[i].second;
}else{
dp[1][0] = nw[i].second;
}
}
Matrix<mdint> mat(2,2,0);
mat[0] = {0,2};
mat[1] = {1,0};
dp = pow_mat(mat,k) * dp;
print(mint(2).pow(dp[0][0].val) * mint(3).pow(dp[1][0].val));
}