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<bits/stdc++.h>
using namespace std;
long long n,p;
map<long long,long long> f;
map<long long,long long>::iterator it;
void get() {
	long long temp=p;
	for(long long i=2;i<=p;i++) {
		if(temp==1) break;
		if(temp%i==0) {
			while(temp%i==0) {
				temp/=i;
				f[i]++;
			}
		}
	} 
}
int main() {
	cin>>n>>p;
	get();
	long long cnt=1;
	for(it=f.begin();it!=f.end();it++) {
		if(it->second>=n) cnt*=it->first;
	}
	cout<<cnt;
	return 0;
}