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: Wrong Answer)

import java.util.*;

public class Main {
    public static void main(String[] args) {
        @SuppressWarnings("resource")
        Scanner sc = new Scanner(System.in);
        long N = sc.nextLong();
        long P = sc.nextLong();
        int ans = 1;
        Map<Integer, Integer> map = new HashMap<Integer, Integer>();
        for (int i = 2; i <= P; i++) {
            if (P % i == 0) {
                P /= i;
                try {
                    map.put(i, map.get(i) + 1);
                } catch (NullPointerException e) {
                    map.put(i, 1);
                }
                if (map.get(i) >= N) {
                    ans *= i;
                    map.put(i, 0);
                    //System.out.println(i);
                }
                i = 1;
                if (P == 1) break;
            }
        }
        for (int i = 2; i <= P; i++) {

        }
        System.out.println(ans);
    }
}