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.Scanner;
public class Main {

	public static void main(String[] args) {

		Scanner sc = new Scanner(System.in);

		long N = sc.nextLong();

		long P = sc.nextLong();


		long ans = 1L;

		if(N==1) {

			System.out.println(P);

		}else {

			long i = 2L;

			boolean flag = false;

			while(true) {

				if(P==1) break;

				flag = false;


				for(int j=2;j<=i/2;j++) {

					if(i%j==0) {

						flag = true;

						break;

					}

					if(i%(i-j+1)==0) {

						flag = true;

						break;
					}
				}




				if(flag==false) {

					long count = 0;

					while(flag==false&&P%i==0) {

						P /= i;

						count++;

						//System.out.println(i);

					}



					if(count/N!=0) {

						ans *= (count/N)*i;



					}
					//System.out.println("i"+i);

				}

				i++;


			}

			System.out.println(ans);
		}
	}

}