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.*;
import java.math.*;

public class Main {
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		// 整数の入力
		long n = sc.nextLong();
		long p = sc.nextLong();
		Map<Long,Long> map = new HashMap<>();

		long i = 2L;

		if(p ==1L){
			System.out.println(1);		
		}else if (n ==1L){
			System.out.println(p);
		}else{
			while(i<=p){
				// System.out.print(i);
				// System.out.print(" ");
				// System.out.println(p);
				if(p%i==0L){
					if(Objects.isNull( map.get(i))){
						map.put(i,1L);
					}else{
						long currentCount = map.get(i);
						map.put(i,currentCount+1L);
					}
					i =2L;
					p = p/i;
				} else{
					i++;
				}
			}
			// System.out.println(map.keySet());
			long result =1L;
			for (long key : map.keySet()) {
				// System.out.println(key + " to " +map.get(key));
				if(map.get(key)>=n){
					result = result * ((long)Math.pow(key,(map.get(key)/n)));
				}
			}
			
			System.out.println(result);
		}
	}

}