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.Linq;
using System.Collections.Generic;

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]);
        var result = new List<int>();
        
        for (var i = 1; i <= 100; i++)
        {
            if (A % i == 0)
            {
                if (B % i == 0)
                {
                    result.Add(i);
                }
            }
            
            if (A <= i || B <= i)
            {
                break;
            }
        }

        var c = result.Count();
        var d = c - K;
        Console.WriteLine(result[d]);
    }
}