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: Time Limit Exceeded)

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

int main(void)
{
    long long int N;
    long long int P;
    long long int num = 1;
    int i,j;
    int max = 0;
    
    if(scanf("%lld %lld", &N, &P) == 1){};
    
    if(N == 1){
        printf("%lld\n",P);
        return 0;
    }
    
    long long int a = pow(P, 1.0/N) + 1;
    
    long long int P_tmp;
    
    P_tmp = P;
    
    for(j=1; j<=a; j++){
        for(i=0; i<N; i++){
            if(P_tmp%j == 0){
                P_tmp /= j;
            }
            else{
                P_tmp = 0;
                break;
            }
            
            if(i == N-1){
                max = j;
            }
            
        }
        
        P_tmp = P;
    }
    
    printf("%d\n", max);
    return 0;
    
}