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<cstdio>
#include<cmath>
#include<cstring>
#include<algorithm>
#include <numeric>
using namespace std;

int main()
{	
	long long int N;
	long long int P;
	scanf("%lld %lld", &N, &P);

	long long int soin[1000000][2];
	for(long long int i=0;i<1000000;i++){
		soin[i][0]=0;
		soin[i][1]=0;
	}
	long long int p=2;
	long long int counter=0;
	while(p<=1000000){
		if(P%p==0)
		{	
			P=P/p;
			soin[counter][0]=p;
			soin[counter][1]++;
		}
		else
		{
			if(soin[counter][0]!=0){counter++;}
			p++;
		}
	}
	long long int ans=1;
	for(long long int i=0;i<1000000;i++){
		if(soin[i][0]!=0)
		{
			if((soin[i][1])/N!=0)
			{
				for(long long int j=0;j<(soin[i][1])/N;j++)
				{
					ans=ans*soin[i][0];
				}
			}
		}
	}
	printf("%lld", ans);
}