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



Sample input:
3 24


Sample output:
2

Submission status: Wrong Answer

Solution code:
# -*- coding: utf-8 -*-

from sys import stdin
import math

primetable = 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n,x = [int(x) for x in stdin.readline().split()]

_max = math.sqrt(x)
memo = {1: []}
for i, p in enumerate(primetable):
    if p > _max:
        primetable = primetable[:i]
        break
    memo[p] = [p]

count = {}

def factorize(x):
    if x in memo:
        count[x] = count.get(x, 0) + 1
    for p in primetable:
        if x % p == 0:
            factorize(x / p)

if x == 1:
    print(1)
elif n == 1:
    print(x)
else:
    factorize(x)
    ans = 1
    for d, c in count.items():
        if c >= n:
            cc = c // n
            ans = ans * d * cc
    print(ans)