BZOJ 1951 Sdoi2010 古代猪文

#include <bits/stdc++.h>
#define ll long long
#define inf 1e9+10
using namespace std;
inline ll read(){
	ll x=0;int f=1;char ch=getchar();
	while(!isdigit(ch)) {if(ch==‘-‘) f=-1;ch=getchar();}
	while(isdigit(ch)) {x=x*10+ch-‘0‘;ch=getchar();}
	return x*f;
}
ll p[4]={2,3,4679,35617};
ll fac[4][36000],ans[5],n,g,q[3000010],top;
inline ll fpow(ll x,ll y,ll mod){
	ll res=1;
	while(y){
		if(y&1) res=(res*x)%mod;
		x=(x*x)%mod;
		y>>=1;
	}
	return res;
}
inline ll extend_gcd(ll a,ll b,ll &x,ll &y){
	if(!b){
		x=1;y=0;return a;
	}
	ll d=extend_gcd(b,a%b,y,x);
	y-=(a/b)*x;
	return d;
}
inline ll lucas(int i,ll n,ll m){
	ll res=1;
	while(n&&m){
		ll nn=n%p[i];ll mm=m%p[i];
		if(nn<mm) return 0;
		//cout<<res<<‘ ‘<<p[i]<<‘ ‘<<fac[i][nn]<<‘ ‘<<fac[i][nn-mm]<<‘ ‘<<fac[i][mm]<<endl;
		res=res*fac[i][nn]%p[i]*fpow(fac[i][nn-mm]*fac[i][mm]%p[i],p[i]-2,p[i])%p[i];
		//cout<<i<<‘ ‘<<nn<<‘ ‘<<mm<<‘ ‘<<res<<endl;
		n/=p[i];m/=p[i];
	}
	//cout<<res<<endl;
	return res;
}
int main(){
	//freopen("All.in","r",stdin);
	//freopen("zh.out","w",stdout);
	n=read();g=read();
	if(g==999911659){
		cout<<0<<endl;return 0;
	}
	for(int i=0;i<4;i++) fac[i][0]=1;
	for(int j=0;j<4;j++){
		for(int i=1;i<=p[j];i++){
			fac[j][i]=fac[j][i-1]*i%p[j];
		}
	}
	for(int i=1;i*i<=n;i++){
		if(n%i==0){
			if(i*i==n) q[++top]=i;
			else q[++top]=i,q[++top]=n/i;
		}
	}
	for(int i=1;i<=top;i++){
		for(int j=0;j<4;j++){
			ans[j]+=lucas(j,n,q[i]),ans[j]%=p[j];
		}
    }
    for(int i=0;i<3;i++){
		ll k1,k2,p1=p[i],p2=p[i+1];
		p[i+1]*=p[i];
		extend_gcd(p1,p2,k1,k2);
		k1=(k1%p2)*(ans[i+1]-ans[i]);
		ans[i+1]=(ans[i]+k1*p1)%p[i+1];
	}
	cout<<fpow(g,(ans[3]+p[3])%p[3],999911659);
	return 0;
}