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;
using System.Linq;
using System.Text;

namespace atcorder_BeginnerContest_120
{
    class Program
    {

        static void Main(string[] args)
        {
            int[] dataArr = Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);
            int a = dataArr[0];
            int b = dataArr[1];
            int k = dataArr[2];

            int retCnt = 0;
            if (a < b)
            {
                retCnt = a;
            }
            else
            {
                retCnt = b;
            }

            int endCnt = 0;
            while (true)
            {
                if ((0 == a % retCnt) && (0 == b % retCnt))
                {
                    endCnt++;
                }
                if (endCnt == k)
                {
                    break;
                }
                retCnt--;
            }

            Console.WriteLine(retCnt);

        }
    }
}