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.Diagnostics;
using System.Text;
using System.Linq;

class Program
{
    static void Main()
    {
        int[] inp = Console.ReadLine().Split().Select(int.Parse).ToArray();
        int a = inp[0];
        int b = inp[1];
        int k = inp[2];
        int c = 0;
        for (int i = Math.Min(a, b); ; i--)
        {
            if (a % i == 0 && b % i == 0)
                c++;
            if (c == k)
            {
                Console.WriteLine(i);
                return;
            }
        }
    }
}