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.*;


public class Main {
    public static void main(String args[]){
            Scanner sc = new Scanner(System.in);
           
            long a = sc.nextLong();
            long n = sc.nextLong();
            long[] yakusu = new long[2000000];
            long pro = 1;
            if (a == 1) {
                System.out.println(n);
            } else {
                for (int i = 2; i <= Math.sqrt(n); i++) {
                    while (n >= i && n % i == 0) {
                        yakusu[i] = yakusu[i] + 1;
                         n = n / i;
                    }
                }   
                for (int i = 2; i < yakusu.length; i++) {
                    while (yakusu[i] >= a) {
                        pro = pro * i;
                        yakusu[i] = yakusu[i] -a;
                    }
                }
                System.out.println(pro);
            }


            sc.close();
        }
    
}