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 sys
input = sys.stdin.buffer.readline

def main():
    N,P = map(int,input().split())
    
    is_prime = [True for i in range(int(P**(1/2))+1)]
    is_prime[0] = is_prime[1] = False
    
    for i in range(2,int(P**(1/2)+1)):
        if not is_prime[i]:
            continue
        j = 2*i
        while j<=int(P**(1/2)):
            is_prime[j] = False
            j += i

    ans = 1
    for i in range(1,int(P**(1/2)+1)):
        count = 0
        if is_prime[i]:
            while P%i == 0:
                count += 1
                P//=i
            z = pow(i,count//N)
            ans *= z
    
    z = pow(P,1//N)
    print(ans*z)
    
if __name__ == "__main__":
    main()