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.abc120
{
  class b
  {
    static void Main(string[] args)
    {
      int[] ABK = GetIntArray();
      int N = 1 + (ABK[0] > ABK[1] ? ABK[1] : ABK[0]);
      while (ABK[2] != 0)
      {
        N--;
        if (ABK[0] % N == 0 && ABK[1] % N == 0) ABK[2]--;
      }
      Console.Write(N);
    }
    static int GetInt() => int.Parse(Console.ReadLine());
    static int[] GetIntArray()
    {
      string[] r = Console.ReadLine().Split(' ');
      int[] a = new int[r.Length];
      Parallel.For(0, r.Length, i => a[i] = int.Parse(r[i]));
      return a;
    }
  }
}