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)

def primeFactor(n):
    res = {}
    i = 2
    while i*i <= n:
        while n % i == 0:
            key = str(i)
            res.update({key : 1+int(res.get(key,0))})
            n=n//i
        i=i+1    
    if n!=1:
        key = str(n)
        res.update({key : 1+int(res.get(key,0))})
    return res

N, P = map(int, input().split())
max = 1
for divisor, count in primeFactor(P).items():
    while count >= N:
        max *= int(divisor)
        count -= N
print(max)