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: Time Limit Exceeded)

import java.util.*;

public class Main {
	Scanner sc = new Scanner(System.in);
	void doIt() {
		long n = sc.nextLong();
		long p = sc.nextLong();
		System.out.println(getAns(n, p));
	}
	long getAns(long n, long p) {
		long ans = 1;
		for(long i = 2; i <= p; i++) {
			if(p % i != 0)continue;
			long num = (long)Math.pow(i, n);
			while(p % num == 0) {
				ans *= i;
				p /= num;
				//System.out.println(p + " " + ans + " " + i);
				if(p == 0)return ans;
			}
		}
		return ans;
	}
	public static void main(String[] args) {
		new Main().doIt();
	}
}