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<bits/stdc++.h>
 
using namespace std;
long long n,p,maxx=1,dem=0;
 
void input()
{
	cin>>n>>p;
}
 
void output()
{
	cout<<maxx;
}
 
void kt(long long x)
{
	if (x<4) return;
	long long y=x;
	for (long i=2; i*i<=x; i++)
	{
		if (y==1) return;
		dem=0;
		while (y%i==0)
		{
			y=y/i;
			dem++;
		}
		if (dem/n>0) 
		for (int i=1; i<=dem/n; i++) maxx*=i;
	}
}
 
void fin()
{
	if (n==1) 
	{
		maxx=p;
		return;
	}
	kt(p);
}
 
main()
{
//	freopen("TEST.INP","r",stdin);
//	freopen("TEST.OUT","w",stdout);
	input();
	fin();
	output();
	return 0;
}