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.HashMap;
import java.util.Map;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		long n = sc.nextLong();
		long p = sc.nextLong();
		if(n==1) {
			System.out.println(p);
			return;
		}
		Map<Long,Long> sosuMap = new HashMap<Long,Long>();
		for(long i =2;i <= p;i++) {
			if(p % i == 0) {
				long sosuCount = 0;
				while(p % i == 0) {
					sosuCount++;
					p /= i;
					sosuMap.put((long) i, sosuCount);
				}
			}
		}

		long answer = 1;
		for(Map.Entry<Long, Long> entry:sosuMap.entrySet()) {
			if(entry.getValue() >= n) {
				answer *=Math.pow((double)entry.getKey(),(double)(entry.getValue() / n));

			}

		}

		System.out.println(answer);
	}

}