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 Python (3.4.3) (judge verdict: Accepted)

#!/usr/bin/env python3
import sys

def main():
    N, P = map(int, input().split())
    ans = 1
    if N == 1:
        print(P)
        exit()
    for i in range(2,int(P**(1/N)+1)):
        count = 0
        tmp = P
        while tmp % i == 0:
            count += 1
            tmp = tmp // i
        ans *= i**(count // N)
        P = P // i**count
    print(ans)

if __name__ == '__main__':
    main()