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;

namespace B_K_th_Common_Divisor
{
    class Program
    {
        static void Main(string[] args)
        {
            var ABK = Console.ReadLine().Split().Select(int.Parse).ToArray();
            var A = ABK[0];
            var B = ABK[1];
            var K = ABK[2];

            for (int i = Math.Max(A, B), cnt = 0; i >= 1; i--)
            {
                if (A % i == 0 && B % i == 0)
                {
                    cnt++;
                    if (cnt == K)
                    {
                        Console.WriteLine(i);
                        continue;
                    }
                }
            }

        }
    }
}