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 numpy import sqrt
N,P = map(int,input().split(" "))
lm = pow(P,1/N) + 0.5
if N == 1:
    print(P)
    exit(0)

ans = 1
for i in range(1,int(sqrt(P))+10):
    if P % i == 0:
        if i <= lm and P % pow(i,N) == 0:
            ans = max(i,ans)
        if (P//i) <= lm and P % pow((P//i),N) == 0:
            ans = max(P//i,ans)

print(ans)