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.io.*;
import java.math.*;
import java.util.*;
public class Main { 
 
	public static void main(String[] args) { 
		Scanner input = new Scanner(System.in);
		long N = input.nextLong();
		long P = input.nextLong(); //Product
		long maxGCD = 1;
		for (long prime = 2; prime <= Math.sqrt(P); prime++) {
			long numCurPrime = 0;
			while (P%prime==0) {
				P/=prime;
				numCurPrime++;
				if (numCurPrime%N==0) {
					maxGCD*=prime;
					numCurPrime=0; //Effectively floor division using simulation counters
				}
			}
		}
		System.out.println(maxGCD);
	}
}