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: Runtime Error)

import java.util.Scanner;
import java.util.TreeMap;

public class Main {
    public static void main(String args[]) {
    	
    	Scanner sc = new Scanner(System.in);
    	int N = sc.nextInt();
    	long P = sc.nextLong();
    	TreeMap<Long, Integer> treeMap = new TreeMap<Long, Integer>();
    	int answer = 1;
    	long limit = P/N;
    	long i = 2;
    	long y = P;
    	while(y != 1 && i <= limit) {
    	    if(y % i == 0) {
    	    	if(treeMap.containsKey(i)) {
    	            int currentNum = treeMap.get(i);
    	            if(currentNum == N-1) {
    	        	    treeMap.put(i, currentNum-N-1);
    	        	    answer *= i;
    	            }
    	            else {
    	        	    treeMap.put(i, currentNum+1);
    	            }
    	    	} else {
    	    		treeMap.put(i, 1);
    	    	}
    	        y /= i;
    	    }
    	    else {
    	        i++;
    	    }
    	}
    	
	    System.out.println(answer);
    }
}