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 <cstdio>
#include <cmath>
using namespace std;
#define ll long long int

int main(int argc, const char * argv[]) {
	ll N,P;
	cin >> N >> P;
	if(N==1){
		cout << P << endl;
		return 0;
	}
//	int max = (int)sqrt(P)+1;
	ll max = P/2;
	ll ret = 1;
	for (ll divider = 2; divider <= max && P!=1; ++divider) {
		ll count=0;
		while(P % divider == 0){
//			cerr << divider;
			count++;
			P /= divider;
		}
		if(count > 0){
//			cerr << divider << "**" << count << endl;
		}
		while(count>=N){
//			cerr << divider << endl;
			ret *= divider;
			count -= N;
		}
	}
	cout << ret << endl;
}