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;
class MainClass
{
    static void Main()
    {
        string[] input = Console.ReadLine().Split(' ');

        int a = int.Parse(input[0]);
        int b = int.Parse(input[1]);
        int k = int.Parse(input[2]);

        int i = 1;
        int cnt = 0;
        int N = 0;

        for( var j = 1; j <= a && j <= b;j++ )
        {
            if (a % j == 0 && b % j == 0)
            {
                N++;
            }
        }

        int m = N - k + 1;


        while (i <= a && i <= b )
        {
            if(a%i==0 && b%i ==0 )
            {
                cnt++;
                if (cnt == m)
                {
                    Console.WriteLine(i);
                    break;
                }
                
            }
            i++;
        }
    }
}