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: Wrong Answer)

# coding: utf-8
# Your code here!
import math
N,P=map(int,input().split())

i=1
ans=1

if N==1:
    print(P)
elif N==2:
    sqrt_P=int(math.sqrt(P))
    for i in range(sqrt_P)[::-1]:
        if P%(i**N)==0:
            print(i)
            break
else:
    while i**N<=P:
        if P%(i**N)==0:
            ans=i
        i+=1
    print(ans)