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 (Clang 3.8.0) (judge verdict: Wrong Answer)

#include <stdio.h>
typedef long long ll;

int main()
{
	ll n, p;
	ll i;
	ll cnt;
	ll ans = 1;

	scanf("%lld %lld", &n, &p);

	cnt = 0;
	i = 2;
	while (p > 1 && i * i <= p) {
		if (p % i == 0) {
			p /= i;
			cnt++;

			if (cnt == n) {
				ans *= i;
				cnt = 0;
			}
		}
		else {
			cnt = 0;
			i++;
		}
	}

	ans *= p;

	printf("%lld\n", ans);

	return 0;
}