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)

def find(n,p):
    dic=dict()
    i=2
    while i*i<=p:
        while p%i==0:
            if i not in dic.keys():
                dic[i]=1
            else:
                dic[i]+=1
            p=p/i
        i+=1
    ans=1
    for o in dic.keys():
        while dic[o]>=n:
            ans*=o
            dic[o]-=n
    return ans
s=input().split()
n=int(s[0])
p=int(s[1])
print(find(n,p))