POJ 2429

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <stdlib.h>
#include <time.h>
#define LL __int64
#define C 201
using namespace std;
const int Max=100000;
int atop;
LL ans[100];
bool se[Max];

bool cmp(LL a,LL b){
	if(a<b) return true;
	return false;
}

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

LL random(LL n){
	return (LL)((double)rand()/RAND_MAX*n+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 Pollard_rho(LL n,int c){
	LL x,y,d,i=1,k=2;
	x=random(n-1)+1;
	y=x;
	while(true){
		i++;
		x=(multi(x,x,n)+c)%n;
		d=gcd(y-x,n);
		if(d>1&&d<n) return d;
		if(y==x) return n;
		if(i==k){
			y=x;
			k=k<<1;
		}
	}
}

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

bool Miller_Rabin(LL n){
	if(n<2) return false;
	if(n==2) return true;
	if(!(n&1)) return false;
	for(int i=1;i<=12;i++){
		LL a=random(n-2)+1;
		if(Witness(a,n)) return false;
	}
	return true;
}

void find(LL n, int k){
	if(n==1) return ;
	if(Miller_Rabin(n)){
		ans[atop++]=n;
		return ;
	}
	LL p=n;
	while(p>=n)
	p=Pollard_rho(p,k--);
	find(p,k);
	find(n/p,k);
}

LL getrt(int g){
	LL ret=1;
	for(int i=0;i<atop;i++){
		if(g&(1<<i)){
			ret*=ans[i];
		}
	}
	return ret;
}

int main(){
	LL gcd,lcm;
	srand(time(0));
	while(scanf("%I64d%I64d",&gcd,&lcm)!=EOF){
		lcm/=gcd; atop=0;
		memset(se,false,sizeof(se));
		find(lcm,C);
		sort(ans,ans+atop,cmp);
		int m=atop;
		atop=1;
		ans[0]=ans[0];
		for(int i=1;i<m;i++){
			if(ans[i]==ans[i-1]){
				ans[atop-1]*=ans[i];
			}
			else if(ans[i]!=ans[i-1]){
				ans[atop++]=ans[i];
			}
		}
	//	cout<<atop<<endl;
		int all=(1<<atop)-1;
		LL at=-1;
		LL sum=(1LL<<63)-1;
	//	cout<<sum<<endl;
		LL ret;
		for(int i=0;i<=all;i++){
			if(se[i]) continue;
			se[i]=se[all^i]=true;
			ret=getrt(i);
		//	cout<<ret<<endl;
			if(sum>ret+lcm/ret){
			//	cout<<ret<<endl;
				at=ret;
				sum=ret+lcm/ret;
			}
		}
		LL a=gcd*at,b=gcd*(lcm/at);
		printf("%I64d %I64d\n",a<b?a:b,a>b?a:b);
	}
	return 0;
}