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 (GCC 5.4.1) (judge verdict: Accepted)

#include<stdio.h>
#include<math.h>
long long int f(long long int n)
{
	if (n < 2)
		return 1;
	long long int i;
	for (i = 2; i <= sqrt(n); i++)
		if (n % i == 0)
			return i;
	return n;
}
int main()
{
	long long int n, p;
	scanf("%lld %lld", &n, &p);
	long long int ans = 1;
	long long int count, x;
	while (p > 1)
	{
		x = f(p);
		count = 0;
		while (p % x == 0)
		{
			count++;
			p /= x;
		}
		while (count >= n)
		{
			ans *= x;
			count -= n;
		}
	}
	printf("%lld\n", ans);
	return 0;
}