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<iostream>
#include<vector>
#include<algorithm>
#include<math.h>
using namespace std;
typedef long long int llint;
int main() {
	llint n;
	llint p;
	cin >> n >> p;
	llint pp = p;
	llint tmp = pow(p, (double)1 / n);
	if (p % 2 == 0) {
		if (tmp % 2 == 1) {
			tmp--;
		}
	}
	else {
		if (tmp % 2 == 0) {
			tmp--;
		}
	}
	for (llint i = tmp;0 < i;i -= 2) {
		if (p%i == 0) {
			for (llint j = 0;j < n;j++) {
				if (p%i != 0) {
					break;
				}
				p /= i;
				if (j == n - 1) {
					cout << i << endl;
					return 0;
				}
			}
		}
		p = pp;
	}
	return 0;
}