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: Accepted)

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

const int maxn=1000005;
long long c[maxn];
long long p[maxn], m;
void divide(long long n)
{
    m = 0;
    for(int i = 2; i <= sqrt(n)*10; i++)
	{
        if(n % i == 0)
		{
            p[++m] = i, c[m] = 0;
            while(n % i == 0)
			{
                n /= i, c[m]++;
            }
        }
    }
    if(n > 1)
	{
        p[++m]=n, c[m] = 1;
    }
}

long long ans=1;

long long val,mmm;

long long qm(long long a,long long b)
{
	long long qwe=1;
	while(b)
	{
		if(b&1)
		qwe=qwe*a;
		a=a*a;
		b>>=1;
	}
	return qwe;
}

int main()
{
	scanf("%lld%lld",&mmm,&val);
	divide(val);
	for(int i=1;i<=m;i++)
	{
	    long long k=c[i]/mmm;
		if(k!=0)
		{
		   long long rbq=qm(p[i],k);
		   ans *= rbq;
		}
	}
	printf("%lld",ans);
}