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 C# (Mono 4.6.2.0) (judge verdict: Runtime Error)

using System;
using System.Collections.Generic;
 
class Program {
	static void Main(string[] args) {
		string input = Console.ReadLine();
		string[] inputs = input.Split(' ');
		
		int max = int.Parse(inputs[0]);
		int count = 1;
		
		long product = long.Parse(inputs[1]);
		long divisor = 2;
		var factors = new List<long>();
		
		while (true) {
		    if (product <= 1) {
		        divisor = 1;
		    }
		    
		    if (count >= max) {
		        factors.Add(product);
		        break;
		    }
		    
		    if (product % divisor == 0) {
		        factors.Add(divisor);
		        product /= divisor;
		        count++;
		    } else {
		        divisor++;
		    }
		    
		}
		
		if (factors.Count == 1) {
		    Console.WriteLine(factors[0]);
		} else {
        	long temp = 0;
		    long remainder = factors[0];
		    
		    for (int i = 0; i < (factors.Count - 1); i++) {
        		divisor = factors[i + 1];
        		
        		while (true) {
            		if (divisor == 0) {
            		    break;
            		} else {
            		    temp = divisor;
            		    divisor = remainder % divisor;
            		    remainder = temp;
            		}
        		}
		    }
		    
		    Console.WriteLine(remainder);
		}
	}
}