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 (3.8.2) (judge verdict: Wrong Answer)

def resolve():
    '''
    code here
    '''
    import collections
    import copy

    N, P = [int(item) for item in input().split()]
    P_org = copy.deepcopy(P)

    fact_list = [1]

    cnt = 2
    while P > 1 and cnt**2 <= P:
        if P % cnt == 0:
            fact_list.append(cnt)
            P //= cnt
        else:
            cnt += 1

    if N == 1:
        res = P_org
    else:
        cnt_num = collections.Counter(fact_list[1:])
        res_list = []
        for i, v in cnt_num.items():
            if v//N > 0:
                res_list.append(i**(v//N))
        
        res = 1
        for item in res_list:
            res *= item
    # print(cnt_num)
    print(res)

if __name__ == "__main__":
    resolve()