結果

問題 No.2365 Present of good number
ユーザー cho435
提出日時 2023-06-30 22:56:50
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 25 ms / 2,000 ms
コード長 4,045 bytes
コンパイル時間 3,179 ms
コンパイル使用メモリ 238,644 KB
最終ジャッジ日時 2025-02-15 04:29:01
ジャッジサーバーID
(参考情報)
judge4 / judge3
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;
using ll = long long;
#define rep(i,n) for (int i=0;i<(int)(n);i++)
// https://trap.jp/post/1444/ by tatyam
constexpr uint32_t totient(uint32_t x){
uint32_t ans = x;
for(uint32_t i = 2; i * i <= x; i++) if(x % i == 0){
ans /= i;
ans *= i - 1;
do x /= i; while(x % i == 0);
}
if(x != 1){
ans /= x;
ans *= x - 1;
}
return ans;
}
template<uint32_t P> struct Modint{
static_assert(P < 0x80000000, "P must be smaller than 2^31");
uint32_t a;
Modint<totient(P)> b;
private:
static uint32_t mod(uint64_t x){
if(x < P * 2) return uint32_t(x);
return uint32_t(x % P) + P;
}
static uint32_t mul(uint32_t a, uint32_t b){
return mod(uint64_t(a) * b);
}
static uint32_t pow(uint32_t a, uint32_t b){
uint32_t ans = 1;
while(b){
if(b & 1) ans = mul(ans, a);
a = mul(a, a);
b >>= 1;
}
return ans;
}
public:
Modint(uint64_t x): a(mod(x)), b(x){}
Modint(uint32_t a, Modint<totient(P)> b): a(a), b(b){}
Modint(): a(0), b(0){}
uint32_t val() const {
if(a < P) return a;
return a - P;
}
Modint& operator*=(const Modint& other){
a = mul(a, other.a);
b *= other.b;
return *this;
}
Modint operator*(const Modint& other) const {
return Modint(*this) *= other;
}
Modint& operator+=(const Modint& other){
a += other.a;
if(a >= P * 2) a -= P;
if(a >= P * 2) a -= P;
b += other.b;
return *this;
}
Modint operator+(const Modint& other) const {
return Modint(*this) += other;
}
Modint pow(const Modint& other) const {
return {pow(a, other.b.a), b.pow(other.b)};
};
};
template<> struct Modint<1>{
uint32_t a;
Modint(uint64_t x): a(bool(x)){}
uint32_t val() const {
return 0;
}
Modint& operator*=(const Modint& other){
a &= other.a;
return *this;
}
Modint operator*(const Modint& other) const {
return Modint(*this) *= other;
}
Modint& operator+=(const Modint& other){
a |= other.a;
return *this;
}
Modint operator+(const Modint& other) const {
return Modint(*this) += other;
}
Modint pow(const Modint& other) const {
return {a || !other.a};
}
};
using mint = Modint<1000000007>;
map<int,mint> div(ll x){
map<int,mint> rt;
ll cx=x;
for(int i=2;i*i<=cx;i++){
if(x%i==0){
int ct=0;
while(x%i==0){
ct++;
x/=i;
}
if(!rt.count(i)){
rt.insert({i,0});
}
rt.at(i)+=ct;
}
if(x==1) break;
}
if(x!=1){
rt.insert({x,1});
}
return rt;
}
map<int,mint> f(map<int,mint> &nw){
map<int,mint> rt;
for(auto [x,n]:nw){
auto mp=div(x+1);
for(auto [nx,nn]:mp){
if(!rt.count(nx)){
rt.insert({nx,0});
}
rt.at(nx)+=nn*n;
}
}
return rt;
}
vector<vector<mint>> mmul(vector<vector<mint>> a,vector<vector<mint>> b){
vector<vector<mint>> c={{0,0},{0,0}};
rep(i,2){
rep(k,2){
rep(j,2){
c.at(i).at(j)+=a.at(i).at(k)*b.at(k).at(j);
}
}
}
return c;
}
int main(){
int n;
ll k;
cin>>n>>k;
map<int,mint> nw=div(n);
for(ll i=0;i<k;i++){
if(nw.size()<=2){
vector<mint> v={mint(0),mint(0)};
{
int flg=0;
for(auto [x,n]:nw){
if(x==2) v.at(0)=n;
else if(x==3) v.at(1)=n;
else{
flg=1;
}
}
if(flg){
nw=f(nw);
continue;
}
}
vector<vector<vector<mint>>> mat(60);
mat.at(0)={{0,2},{1,0}};
rep(i,59){
mat.at(i+1)=mmul(mat.at(i),mat.at(i));
}
ll lp=k-i;
vector<vector<mint>> vv={{1,0},{0,1}};
rep(i,60){
if((lp>>i)&1){
vv=mmul(vv,mat.at(i));
}
}
map<int,mint> tmp={{2,0},{3,0}};
rep(i,2){
rep(j,2){
tmp.at(i+2)+=vv.at(i).at(j)*v.at(j);
}
}
nw=tmp;
i+=lp;
break;
}
nw=f(nw);
}
mint ans=1;
for(auto [x,n]:nw){
ans*=(mint(x).pow(n));
}
cout<<ans.val()<<endl;
}
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