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)

from math import sqrt

def fact(n):
    insu = []
    for i in range(2,int(sqrt(n))+1):
        if n % i == 0:
            while n % i == 0:
                n //= i
                insu.append(i)
        if n == 1:
            break
    if n > 1:
        insu.append(n)
    return insu

def main():
    N,P = map(int,input().split())
    insu = fact(P)
    insu_set,insu_list,pt = set(),[],0
    for i in range(len(insu)):
        if insu[i] not in insu_set:
            insu_set.add(insu[i])
            insu_list.append([insu[i],1])
            pt += 1
        else:
            insu_list[pt-1][1] += 1
    for i in range(len(insu_list)):
        insu_list[i][1] //= N

    ans = 1
    for a,b in insu_list:
        ans *= a**b
    print(ans)

if __name__ =="__main__":
    main()