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 (GCC 5.4.1) (judge verdict: Accepted)

#include<stdio.h>
#include <stdlib.h>
#include<math.h>

int main(){
  long int n,p;
  long int i,m,k,t;
  scanf("%ld %ld",&n,&p);
  m=1;
  
  t=(long int)pow(p,(double)1/n);
  
  if(pow(2,n)>p)
    
    m=1;
 else if(n==1)
    m=p;
  
  else if(pow(t,n)==p)
    m=t;
          
  
          
  else {
  for(i=2;(long int)pow(i,n)<=p;i++){
    
    if(p%(long int)pow(i,n)==0){
      for(k=2;k<10000;k++){
        if(p%(long int)pow(i,n*k)!=0)
          break;
      }
    
      p=p/(long int)pow(i,n*(k-1));
      m=m*pow(i,(k-1));
    }
  }
  }
  
  printf("%ld",m);
  
}