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.Linq;
using System.Text;
using System.Threading.Tasks;

namespace Atcoder
{
    class AtCodeeeeeeeeeeeeeeeeeeeer
    {
        static void Main(string[] args)
        {
            int[] s = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
            int A = s[0];
            int B = s[1];
            int K = s[2];
            int ans = 0;
            List<int> ls = Func(A, B);
            ls.Sort();
            ls.Reverse();
            Console.WriteLine(ls[K-1]);

            
        }
        static List<int> Func(int a,int b)
        {
            List<int> ls = new List<int>();
            for (int i = 1; i <= a||i<=b; i++)
            {
                if (b%i==0&&a%i==0)
                {
                    ls.Add(i);
                }
            }
            return ls;
        }
    }
}