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: Runtime Error)

using System;
class paiza
{
  static public void Main(string[] args)
  {
    int A = int.Parse(args[0]);
    int B = int.Parse(args[1]);
    int K = int.Parse(args[2]);
    int min = 0;
    if(A < B)
      min = A;
    else
      min = B;
    int current_K = 0;
    int i = 0;
    for(i = 1;i < min;i++)
    {
      if(A % i == 0 && B % i == 0)
      {
        current_K++; 
        //Console.WriteLine("Current K = " + current_K + " i = " + i);
        if(current_K == K)
          break;
      }
    }
    Console.WriteLine(i);
  }
}