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.math.BigInteger;
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 int[] sosu =
	public static void main(String[] args) {
		long ans = 1;
		int ii = 0;
		long i = 2;
		out: while (i <= P) {
			long p = P;
			for (long j = 0; j < N; j++) {
				if (p%i != 0) {
					p = P;
					while (true) {
						i++;
						if (BigInteger.valueOf(i).isProbablePrime(1)) {
							break;
						}
					}
//					i = sosu[ii];
					continue out;
				}
				p /= i;
			}
			ans *= i;
			P = p;
		}
		System.out.println(ans);
	}
}