Problem:
Score : 200 points

Problem Statement

You are given positive integers A and B.

Find the K-th largest positive integer that divides both A and B.

The input guarantees that there exists such a number.

Constraints

All values in input are integers.

1 \leq A, B \leq 100

The K-th largest positive integer that divides both A and B exists.

K \geq 1

Input

Input is given from Standard Input in the following format:

A B K

Output

Print the K-th largest positive integer that divides both A and B.

Sample Input 1

8 12 2

Sample Output 1

2

Three positive integers divides both 8 and 12: 1, 2 and 4.
Among them, the second largest is 2.

Sample Input 2

100 50 4

Sample Output 2

5

Sample Input 3

1 1 1

Sample Output 3

1

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;
public class Test
{
    public static void Main()
    {
        var input = Console.ReadLine().Split(' ').Select(v => int.Parse(v)).ToArray();
        Console.WriteLine(Div(Gcd(input[0], input[1]),input[2]));
        Console.ReadKey();
    }
    public static int Gcd(int a, int b)
    {
        if (a < b)
            return Gcd(b, a);
        while (b != 0)
        {
            var remainder = a % b;
            a = b;
            b = remainder;
        }
        return a;
    }
    public static int Div(int a, int b)
    {
        for (int i = 105;true;i--)
        {
            if (a % i == 0)
            {
                b--;
            }
            if(b==0)
                return i;
        }
    }
}