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<math.h>

long long k[1000001] = {};

int main()
{
    long long n, p, i, ori_p;
    scanf("%lld %lld", &n, &p);

    if (n == 1)
    {
        printf("%lld\n", p);
        return 0;
    }
    ori_p = p;
    for (i = 2; i <= (long long)sqrt(ori_p); i++)
        while (p % i == 0)
        {
            k[i]++;
            p /= i;
        }

    long long sum = 1;
    for (i = 2; i <= (long long)sqrt(ori_p); i++)
        if (k[i] >= n)
            sum *= (long long)pow(i, (k[i] / n));
    printf("%lld\n", sum);
    return 0;
}