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)

// A Dynamic Programming based 
// C# program to find minimum 
// number operations to 
// convert str1 to str2 
using System;
using System.Collections.Generic;
using System.Linq;
class GFG
{
    static int k = 0;
    static List<int> ans = new List<int>();
    public static void Main()
    {
        var input = Console.ReadLine().Split(' ');
        var a = int.Parse(input[0]);
        var b = int.Parse(input[1]);
        k = int.Parse(input[2]);
        int count = 0;
        for(int i=1;i<=Math.Min(a,b);i++)
        {
            if((a%i==0)&&(b%i)==0)
            {
                ans.Add(i);
            }

            if (count == k)
                break;
        }

        
        Console.Write(ans[ans.Count-k]);
          
    }

    static int GCD(int a, int b)
    {
        if (a == 0)
            return b;
        
        return GCD(b % a, a);
    }



}