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 <vector>
#include <string>
#include <algorithm>
#include <cmath>
#include <iomanip>
#include <string>
 
using namespace std;
 
int main() {
	long long N, P;
	cin >> N >> P;
	long long temp;
	bool flg;
	for (long long i = pow(P,1/double(N))+1; i > 0; i--) {
		temp = P;
		flg = true;
		if (i == 1) {
			cout << i;
			break;
		}
		for (long long j = 0; j < N; j++) {
			if (temp%i == 0) {
				temp = temp / i;
			}
			else {
				flg = false;
				break;
			}
		}
		if (flg) {
			cout << i;
			break;
		}
		
	}
	return 0;
}