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: Wrong Answer)

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <stdbool.h>
#include <math.h>
typedef long long ll;
int main(void){
    ll n,p,ans=1;
    scanf("%lld%lld",&n,&p);
    for (ll i=1; i*i<=p; i++){
        if (p%i==0){
            if ((ll)p%(ll)(pow(i,n))==0){
                ans=i;
            }
            if ((ll)p%(ll)(pow(p/i,n))==0){
                ans=i;
            }
        }
    }
    

    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    printf("%lld\n",ans);
	return 0 ;
}