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: Time Limit Exceeded)

#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <stdlib.h>
#include <math.h>
#include <numeric>

bool isprime(long long p) {
	if (p % 2 == 0) return false;
	for (long long i = 3; i * i <= p; i+=2)
	{
		if (p % i == 0) {
			return false;
		}
	}
	return true;
}

int main() {
	long long n;
	long long p;

	std::cin >> n >> p;

	if (n == 1) {
		std::cout << p << std::endl;
		return 0;
	}

	long long ans = 1;

	int count = 0;

	while (p % 2 == 0) {
		count++;
		p /= 2;
	}

	ans *= pow(2, (count / n));
	count = 0;

	for  (long long i = 3; p != 1; i+=2)
	{
		if (isprime(p)) {
			break;
		}
		if (isprime(i)) {
			while (p % i == 0) {
				count++;
				p /= i;
			}
			ans *= pow(i, (count / n));
			count = 0;
		}
	}

	std::cout << ans << std::endl;
}