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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <cstdio>
#include <cmath>
using namespace std;
long long n,p,ans=1,tot;
int main()
{
	cin>>n>>p;
	if (n==1) 
	{
		printf("%lld",p);
		return 0;
	}
	for (long long i=sqrt(n);i>1;--i)
		if (n%i==0)
			for (long long i=2;i<=p&&p>=n;++i,tot=0)
			{
				while (p%i==0) p/=i,tot++;
				for (;tot/n;tot-=n) ans*=i;
			}
	printf("%lld",ans);
}