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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

import sys
input = sys.stdin.readline
def prime_factorize(n):
    res = []
    for i in range(2, int(n**0.5)+1):
        if n % i != 0:continue
        ex = 0
        while n % i == 0:
            ex += 1
            n = n//i
        res.append((i, ex))
    if n != 1:res.append((n, 1))
    return res
def main():
    N, P = map(int, input().split())
    res = prime_factorize(P)
    ans = 1
    for x, ex in res:
        if ex >= N:ans *= x
    print(ans)
if __name__ == "__main__":
    main()