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.Collections.Generic;
class Program
{
    static void Main(string[] args)
    {
        //入力の受け取り
        string[] input = Console.ReadLine().Split(' ');
        int num1 = int.Parse(input[0]);
        int num2 = int.Parse(input[1]);
        int numK = int.Parse(input[2]);

        //num1を割れる数
        List<int> num1List = new List<int>();
        for(int ii = 1; ii <= num1; ii++)
        {
            if(num1 % ii == 0)
            {
                num1List.Add(ii);
            }
        }

        //num2を割れる数
        List<int> num2List = new List<int>();
        for(int jj = 1; jj <= num2; jj++)
        {
            if(num2 % jj == 0)
            {
                num2List.Add(jj);
            }
        }

        //共通する数を得る
        List<int> numCommon = new List<int>();
        foreach(int kk in num1List)
        {
            for(int ll = 0; ll < num2List.Count; ll++)
            {
                if(kk == num2List[ll])
                {
                    numCommon.Add(kk);
                }
            }
        }

        numCommon.Reverse();
        Console.WriteLine(numCommon[numK - 1]);

    }
}