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
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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 # 

#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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