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 {
	Scanner sc = new Scanner(System.in);
	void doIt() {
		long n = sc.nextLong();
		long p = sc.nextLong();
		long max = (long)Math.pow(p, 1.0 / n);
		System.out.println(getAns(n, p, max));
	}
	long getAns(long n, long p, long max) {
		for(long i = max; i >= 1; i--) {
			if(p % Math.pow(i, n) == 0)return i;
		}
		return 1;
	}
	public static void main(String[] args) {
		new Main().doIt();
	}
}