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| #include<bits/stdc++.h>
using namespace std;
typedef long long LL;
inline int Get_Int() {
int num=0,bj=1;
char x=getchar();
while(!isdigit(x)) {if(x=='-')bj=-1;x=getchar();}
while(isdigit(x)) {num=num*10+x-'0';x=getchar();}
return num*bj;
}
const int TIMES=10;
LL Quick_Mul(LL a,LL b,LL p) {
LL tmp=(a*b-(LL)((long double)a/p*b+1e-8)*p);
if(tmp<0)return tmp+p;
else return tmp;
}
LL Quick_Pow(LL a,LL b,LL p) {
LL sum=1;
for(a%=p; b; b>>=1,a=Quick_Mul(a,a,p))if(b&1)sum=Quick_Mul(sum,a,p);
return sum;
}
mt19937 g(rand());
bool Witness(LL a,LL n) {
LL u=n-1,t=0;
while(u%2==0)t++,u>>=1;
LL x=Quick_Pow(a,u,n);
if(x==1)return false;
for(int i=1; i<=t; i++,x=Quick_Mul(x,x,n))
if(x!=n-1&&x!=1&&Quick_Mul(x,x,n)==1)return true;
return x!=1;
}
bool Miller_Rabin(LL n) {
if(n==2)return true;
if(n<2||!(n&1))return false;
for(int i=1; i<=TIMES; i++)
if(Witness(g()%(n-1)+1,n))return false;
return true;
}
LL Pollar_Rho(LL n) {
if(!(n&1))return 2;
while(true) {
LL a=g()%(n-1)+1,b=a,c=g()%(n-1)+1;
if(c==2)c=3;
while(true) {
a=(Quick_Mul(a,a,n)+c)%n;
b=(Quick_Mul(b,b,n)+c)%n;
b=(Quick_Mul(b,b,n)+c)%n;
if(a==b)break;
LL d=__gcd(abs(b-a),n);
if(d>1)return d;
}
}
}
vector<int> fac;
void Find_Fac(LL n) {
if(Miller_Rabin(n)) {fac.push_back(n);return;}
LL p=Pollar_Rho(n);
Find_Fac(p);
Find_Fac(n/p);
}
LL gcd,lcm;
int main() {
while(~scanf("%lld%lld",&gcd,&lcm)) {
if(gcd==lcm) {printf("%lld %lld\n",gcd,lcm);continue;}
LL n=lcm/gcd;
fac.clear();
Find_Fac(n);
sort(fac.begin(),fac.end());
fac.erase(unique(fac.begin(),fac.end()),fac.end());
int all=1<<(fac.size());
LL ans=LLONG_MAX/2,ansa=0,ansb=0;
for(int S=0; S<all; S++) {
LL a=1;
for(int i=0; i<fac.size(); i++)if(S&(1<<i)) {
LL tmp=n,sum=1;
while(tmp%fac[i]==0)tmp/=fac[i],sum*=fac[i];
a*=sum;
}
LL b=n/a;
if((a+b)*gcd<ans) {
ans=(a+b)*gcd;
ansa=min(gcd*a,gcd*b);
ansb=max(gcd*a,gcd*b);
}
}
printf("%lld %lld\n",ansa,ansb);
}
return 0;
}
|
