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<map>
using namespace std;

typedef long long ll;

ll N, P;

map<ll, ll> prime_factor(ll n) {
	map<ll, ll> res;
	for (ll i = 2; i*i <= n; i++) {
		while (n%i == 0) {
			res[i]++;
			n /= i;
		}
	}
	if (n != 1)res[n] = 1;
	return res;
}

int main() {
	cin >> N >> P;

	map<ll, ll> res;
	res = prime_factor(P);

	ll sum = 1;
	for (map<ll,ll>::iterator i = res.begin(); i != res.end(); i++) {
		if (i->second >= N) {
			sum *= i->first*(i->second / N);
		}
	}

	cout << sum << endl;
}