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: Wrong Answer)

using System;
class Program
{
  static void Main (string[] args)
  {
    string[] input = Console.ReadLine().Split(' ');
    int A = int.Parse(input[0]);
    int B = int.Parse(input[1]);
    int K = int.Parse(input[2]);

    int counter = 0;
    int n = Math.Min(A, B);
    for (int i = 1; i <= n; i++) {
      if ((A%i == 0) && (B%i == 0)) {
		counter++;
        if (counter == K) {
          Console.WriteLine(i);
          return;
        }
      }
    }
  }
}