Problem:
Score : 300 points

Problem Statement

There are N integers a_1, a_2, ..., a_N not less than 1.
The values of a_1, a_2, ..., a_N are not known, but it is known that a_1 \times a_2 \times ... \times a_N = P.

Find the maximum possible greatest common divisor of a_1, a_2, ..., a_N.

Constraints

1 \leq N \leq 10^{12}

1 \leq P \leq 10^{12}

Input

Input is given from Standard Input in the following format:

N P

Output

Print the answer.

Sample Input 1

3 24

Sample Output 1

2

The greatest common divisor would be 2 when, for example, a_1=2, a_2=6 and a_3=2.

Sample Input 2

5 1

Sample Output 2

1

As a_i are positive integers, the only possible case is a_1 = a_2 = a_3 = a_4 = a_5 = 1.

Sample Input 3

1 111

Sample Output 3

111

Sample Input 4

4 972439611840

Sample Output 4

206

Solution in C++14 (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include <iostream>
#include <cmath>
#include <string>
#include <vector>
#include <algorithm>
#include <numeric>
#define ll long long
using namespace std;
int main(){
ll N,P,tmp,boset,ans=1;
cin>>N>>P;

if(N==1){
  printf("%lld\n",P);
  return 0;
}

boset=1;
for(ll i=1;;i++){
  boset*=2;
  tmp=1;
  for(ll j=0;j<N;j++){
    tmp*=boset;
  }
  if(tmp>P)
  break;
}
if(P%2==0){
for(ll i=boset;i>0;i--){
  tmp=1;
  for(ll j=0;j<N;j++){
    tmp*=i;
    if(P%tmp!=0)
    break;
  }
if(P%tmp==0){
ans=i;
break;
}
}
}
else{
  for(ll i=boset-1;i>0;i--){
    tmp=1;
    for(ll j=0;j<N;j++){
      tmp*=i;
      if(P%tmp!=0)
      break;
    }
  if(P%tmp==0){
  ans=i;
  break;
  }
  i--;
  }
}

printf("%lld\n",ans);
}