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: Accepted)

import java.util.*;

public class Main {
	long N, P;
	List<Long> coords;
	long limit;
	long result = 1;

	Main() {
		Scanner in = new Scanner(System.in);
		N = in.nextLong();
		P = in.nextLong();
		in.close();
		calcLimit();
	}

	void calcLimit() {
		long times = N;
		limit = P;
		while (times >= 2) {
			limit = (long) Math.sqrt((double) limit);
			times /= 2;
		}
	}

	void calc() {
		for (long v = limit; v > 0; --v) {
			if (Math.pow(v, N) > P) {
				continue;
			}
			if (P % (long)Math.pow(v, N) == 0) {
				result = v;
				break;
			}
		}
	}

	public static void main(String[] args) {
		Main ins = new Main();
		ins.calc();
		System.out.println(ins.result);
	}

}