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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.util.*;

public class Main {

	public static void main(String[] args) {

		Scanner keyboard = new Scanner(System.in);

		long N = keyboard.nextLong();
		long P = keyboard.nextLong();
		
		HashMap<Long, Integer> prime = new HashMap<Long, Integer>();
		for (int i=2;1L*i*i<=P;i++) {
			while (P % i == 0) {
				int count = prime.containsKey((long)i) ? prime.get((long)i) : 0;
				prime.put((long)i, count + 1);
				P /= i;
			}
		}
		if (P != 1) prime.put(P, 1);
		
		long ans = 1;
        for (Map.Entry<Long, Integer> entry : prime.entrySet()) {
            for (int i=0; i < entry.getValue() / N; i++) {
        		ans *= entry.getKey();
        	} 
        }
		
		System.out.println(ans);
		keyboard.close();
	}
	
}