POJ 2447

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <stdlib.h>
#include <time.h>
#define LL __int64 
using namespace std;

LL e,n,c,p,q,f;
int cnt;
LL prime[10];

LL gcd(LL a,LL b){
	if(b==0) return a;
	return gcd(b,a%b);
}

LL random(LL nc){
	return (LL)((double)rand()/RAND_MAX*nc+0.5);
}

LL multi(LL a,LL b,LL m){
	LL ret=0;
	while(b>0){
		if(b&1)
		ret=(ret+a)%m;
		b>>=1;
		a=(a<<1)%m;
	}
	return ret;
}

LL quick(LL a,LL b,LL m){
	LL ans=1;
	a%=m;
	while(b){
		if(b&1)
		ans=multi(ans,a,m);
		b>>=1;
		a=multi(a,a,m);
	}
	return ans;
}

LL witness(LL a, LL nc){
	LL m=nc-1;
	int j=0;
	while(!(m&1)){
		j++;
		m>>=1;
	}
	LL x=quick(a,m,nc);
	if(x==1||x==nc-1)
	return false;
	while(j--){
		x=multi(x,x,nc);
		if(x==nc-1)
		return false;
	}
	return true;
}

bool miller_rabin(LL nc){
	if(nc<2) return false;
	if(nc==2) return true;
	if(!(nc&1)) return false;
	for(int i=1;i<=10;i++){
		LL a=random(nc-2)+1;
		if(witness(a,nc)) return false;
	}
	return true;
}

LL pollard_rho(LL nc,int inc){
	LL x,y,d,i=1,k=2;
	x=random(nc-1)+1;
	y=x;
	while(1){
		i++;
		x=(multi(x,x,nc)+inc)%nc;
		d=gcd(y-x,nc);
		if(d>1&&d<nc)
		return d;
		if(y==x)
		return nc;
		if(i==k){
			y=x;
			k=(k<<1);
		}
	}
}

bool  find(LL nc,int k){
	if(nc==1)
	return false;
	if(miller_rabin(nc)){
		p=nc;
		return true;
	}
	LL pe=nc;
	while(pe>=nc)
	pe=pollard_rho(pe,k--);
	if(find(pe,k)) return true;;
	if(find(nc/pe,k)) return true;;
}

void exgcd(LL a,LL b,LL &x,LL &y){
	if(b==0){
		x=1; y=0;
		return ;
	}
	exgcd(b,a%b,x,y);
	LL tmp=x;
	x=y;
	y=tmp-a/b*y;
}

int main(){
	LL x,y;
	while(scanf("%I64d%I64d%I64d",&c,&e,&n)!=EOF){
		srand(time(0));
		cnt=0;
		find(n,201);
		q=n/p;
		f=(p-1)*(q-1);
		exgcd(e,f,x,y);
		x=(x%f+f)%f;
		LL ans=quick(c,x,n);
		printf("%I64d\n",ans);
	}
	return 0;
}