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 <cstdio>
#include <iostream>
#include <vector>
#include <set>
#include <cstring>
#include <string>
#include <map>
#include <cmath>
#include <ctime>
#include <algorithm>
#include <bitset>
#include <queue>
#include <sstream>
using namespace std;
#define mp make_pair
#define pb push_back
#define re return
#define fi first
#define se second
typedef vector<int> vi;
typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef vector<pii> vpii;
typedef vector<string> vs;
typedef vector<vi> vvi;
long long n,p,sum=1;
int mx=1;
long long cnt[1000100]; 
int main() {
    //freopen("input.txt","r",stdin);
	//freopen("output.txt","w",stdout);
	cin>>n>>p;
	if(n==1){
		cout<<p<<endl;
		return 0;
	}
	for(int i=2;i*i<=p;i++){
		while(p%i==0){
			p/=i;
			cnt[i]++;
			mx=i;
		}
	}
	for(int i=2;i<=mx;i++){
		if(cnt[i]>=n){
			int t=cnt[i]/n;
			for(int j=0;j<t;j++){
				sum*=i;
			}
		}
	}
	cout<<sum<<endl;
    return 0;
}