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: Accepted)

import math,sys

n,p=map(int,sys.stdin.readline().split())
limit = int(p ** (1/n))+1
if limit==1:
    print(1)
elif n==1:
    print(p)
else:
    cnt,ans=0,1

    while p % 2 == 0:
        p /= 2
        cnt += 1
    ans *= pow(2, cnt//n)
    
    for div in range(3, limit, 2):
        cnt = 0
        while p % div == 0:
            cnt += 1
            p /= div
        if cnt >= n:
            ans *= pow(div, cnt // n)
    print(ans)