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) {
		Scanner sc = new Scanner(System.in);
		
		long N = sc.nextLong();
		long P = sc.nextLong();
		long baseP = P;
		
		if (N == 1) {
			System.out.println(P);
			return;
		}
		
		int pSqrt = (int)Math.sqrt(P) + 1;
		int[] map = new int[pSqrt];
		for (int i = 2; i < pSqrt; i++) {
			while(P % i == 0) {
				map[i]++;
				P /= i;
			}
		}
		
		long max = 1;
		for (int i = 2; i < map.length; i++) {
			if (map[i] >= N) {
				max *= i;
			}
			
			if (max * N > baseP) {
				max /= i;
				break;
			}
		}
		
		System.out.println(max);
	}
}