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: Wrong Answer)

def main():
    n, p = map(int, input().split())
    f = {}
    tmp = 0
    while p % 2 == 0:
        tmp += 1
        p //= 2
    f[2] = tmp
    tmp = 3
    while p > 1:
        if p % tmp == 0:
            p //= tmp
            if tmp in f:
                f[tmp] += 1
            else:
                f[tmp] = 1
        else:
            tmp += 2
    f = sorted(f.items(), key=lambda x: x[1], reverse=True)
    answer = 1
    for ff, cnt in f:
        if cnt < n:
            break
        answer *= ff * (cnt // n)
    print(answer)


if __name__ == '__main__':
    main()