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;
using System.Threading.Tasks;

namespace atcoder_B120問題
{
    class Program
    {
        static void Main(string[] args)
        {
            string[] input = Console.ReadLine().Split(' ');
            int A = Convert.ToInt32(input[0]);
            int B = Convert.ToInt32(input[1]);
            int K = Convert.ToInt32(input[2]);
            int C = Math.Min(A, B);
            int D = Math.Max(A, B);
            int count = 0;
            for (int i = C; i > 0; --i)
            {
                if (C % i == 0 && D % i == 0)
                {
                    //K番目に大きい数と比較するため、1番目、2番目・・・とcountを加算
                    count++;
                    if (K == count)
                    {
                        Console.WriteLine(i);
                    }
                }
            }
        }
    }
}