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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.*;
import java.io.*;
 
import static java.lang.System.in;
 
public class Main {
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        long n = sc.nextLong();
        long P = sc.nextLong();
        if(n==1){
            System.out.println(P);
            System.exit(0);
        }
        long upper = (long) Math.sqrt(P)+1;
        long ans=1;
        for(long i=2;i<=upper&&i<=P;i++){
            if(P%i!=0) continue;
            long cnt=0;
            while(P%i==0){
                cnt++;
                P = P/i;
            }
            long now = cnt/n;
            ans*=(long) Math.pow(i,now);
        }
        PrintWriter out = new PrintWriter(System.out);
        out.println(ans);
        out.flush();
    }
}