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;

class Plogram
{
    static void Main()
    {

        var num = Console.ReadLine().Split();
        int A = int.Parse(num[0]);
        int B = int.Parse(num[1]);
        int K = int.Parse(num[2]);
        int count = 0;

        for(int i = A; i > 0; i--)
        {
            if(A % i == 0 && B % i == 0)
            {
                count++;
            }
            if(count == K)
            {
                Console.WriteLine(i);
                break;
            }
        }
    }
}