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.ArrayList;
import java.util.Scanner;

public class Main {
	public static void main(String args[]) {
		Scanner scn = new Scanner(System.in);
		long N = scn.nextLong();
		long P = scn.nextLong();
		ArrayList<Pair> A = new ArrayList<Pair>();
		for(int i = 2;i <= Math.sqrt(P);i++) {
			int num = 0;
			while(P%i == 0) {
				num++;
				P/=i;
			}
			A.add(new Pair(i,num));
		}
		A.add(new Pair(P,1));

		long ans = 1;
		for(int i = 0;i < A.size();i++) {
			long buf;
			Pair p = A.get(i);
			buf = (p.getNum()/N) * p.getx();
			if(buf!=0)ans *= buf;
		}
		System.out.println(ans);
	}
}

class Pair{
	long x;
	long num;
	Pair(long x,long num){
		this.x = x;
		this.num = num;
	}

	long getNum() {
		return num;
	}

	long getx() {
		return x;
	}
}