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)

from collections import defaultdict
n, p = map(int, input().split())


def fctr_d(n):
    c = 0
    r = int(n**0.5)
    f = defaultdict(int)
    for i in range(2, r+2):
        while n % i == 0:
            c += 1
            n = n//i
        if c != 0:
            f[i] += c
            c = 0
    if n != 1:
        f[n] += 1
    return f


d = fctr_d(p)
ans = 1
for key, v in d.items():
    if v >= n:
        a = v // n
        ans *= a*key
print(ans)