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 <bits/stdc++.h>
using namespace std;
using lli = long long int;
using ulli = unsigned long long int;
#define debug(x) cerr << #x << " : " << x << endl

namespace atcoder {
	void judge_outer(bool judge_exp, string ok = "Yes", string ng = "No") {
		if (judge_exp) {
			cout << ok << endl;
		}
		else {
			cout << ng << endl;
		}
	}

	template<typename T>
	T ncr(T left, T right) {
		right = min(left - right, right);
		T ans = 1;
		for (T i = 1; i <= right; i++) {
			ans = ans * (left - right + i) / i;
		}
		return ans;
	}

	const int LIMIT = 1000000007;
	const int tenfive = 100000;
}

using namespace atcoder;

int main() {
	lli N, P;
	cin >> N >> P;
	if (N == 1) {
		cout << P << endl;
		return 0;
	}
	
	int ans = 1;
	for (lli i = 1; pow(i,N) <= P; i++) {
		if (P % (lli)pow(i, N) == 0) {
			ans = i;
		}
	}
	cout << ans << endl;
	return 0;
}