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: Time Limit Exceeded)

def main():
    n, p = map(int, input().split())
    if n == 1:
        print(p)
    else:
        ans = 1
        for i in range(0, 10**6+1):
            if p % (2**(i+1)) != 0:
                ans *= 2**(i//n)
                p //= 2**i
                break
        for i in range(3, 10**6+1, 2):
            if i**n > p:
                break
            for j in range(0, 10**6+1):
                if p % (i**(j+1)) != 0:
                    ans *= i**(j//n)
                    p //= i**j
                    break
        print(ans)

if __name__ == "__main__":
    main()