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.ArrayDeque;
import java.util.Queue;
import java.util.Scanner;

public class Main {
	static Scanner sc = new Scanner(System.in);
	static long N = sc.nextLong();
	static long P = sc.nextLong();
	static class Pair {
		public long x;
		public long y;
		public Pair(long x, long y) {
			this.x = x;
			this.y = y;
		}
	}
	public static void main(String[] args) {
		long ans = 1;
		Queue<Pair> que = new ArrayDeque<>();
		for (long i = 2; i*i <= P; i++) {
			if (P%i != 0) continue;
			long count = 0;
			while (P % i == 0) {
				count++;
				P /= i;
			}
//			System.out.println(count);
			Pair pair = new Pair(i, count);
			que.add(pair);
		}
//		if (P != 1) {
//			que.add(new Pair(P, 1));
//		}
		while (!que.isEmpty()) {
			Pair pair2 = que.poll();
			for (int i = 0; i < pair2.y/N; i++) {
				ans *= pair2.x;
			}
		}
		System.out.println(ans);
	}
}