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>

int separate(unsigned long long n, int s);

int main(void) {

    unsigned long long num;
    int s;
    int a;

    scanf("%d %llu", &s, &num);
    a = separate(num, s);

    printf("%d\n", a);

    return 0;
}

int separate(unsigned long long n, int s) {

    unsigned long long i;
    int c;
    int a = 1;

    for ( i = 2; i <= n; i++ ) {
        for ( c = 0; !(n % i); c++ ) {
            n /= i;
        }
        if ( c/s ) {
            a *= i * ( c/s );
        }
    }

    return a;

}