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)

import math
import collections
# 試し割法

N, P = map(int, input().split())


def trial_division(n):
    # 素因数を格納するリスト
    factor = []
    # 2から√n以下の数字で割っていく
    tmp = int(math.sqrt(n)) + 1
    for num in range(2, tmp):
        while n % num == 0:
            n //= num
            factor.append(num)
    # リストが空ならそれは素数
    if not factor:
        return [n]
    else:
        factor.append(n)
        return factor


lst = trial_division(P)
c_lst = collections.Counter(lst)

ans = 1
for k, v in c_lst.items():
    if v >= N:
        ans *= k
print(ans)