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

public class Main{
	static Map<Long,Long> map= new TreeMap<>();
  public static void main(String[] args){
	  Scanner sc = new Scanner(System.in);
	  long n=sc.nextLong(),p=sc.nextLong();
	  primeEnum(p);
	  long res=1;
	  for (long key : map.keySet()){
	    	if(map.get(key)>=n) {
	    		res*=key;
	    	}
	  }
	  System.out.println(res);

  }
	public static Map<Long,Long> primeEnum(long n) {
		for(long i=2;i<=Math.sqrt(n);i++) {
			if(n%i!=0)continue;
			long e=0;
			while(n%i==0) {
				e++;
				n/=i;
			}
			if(map.containsKey(i)) {
				map.put(i, e+map.get(i));
			}else {
				map.put(i, e);
			}
		}
		if(n!=1) {
			if(map.containsKey(n)) {
				map.put(n, 1+map.get(n));
			}else {
				map.put(n, 1L);
			}
		}
		return map;
	}
}