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: Runtime Error)

def main():
    N, P = map(int, input().split())
    if N == 1:
        print(P)
        return
    primes = []
    i = 2
    while i**N <= P:
        isprime = True
        for p in primes:
            if i % p == 0:
                isprime = False
                break
        if isprime:
            primes.append(i)
        i += 1

    F = {}
    i = 0
    while P > 1 and i < len(primes):
        factor = primes[i]
        while P % factor == 0:
            if factor not in F:
                F[factor] = 0
            F[factor] += 1
            P //= factor
        i += 1
    retval = 1
    for p in F:
        if F[p] >= N:
            retval *= p
    print(retval)


if __name__ == "__main__":
    main()