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: Wrong Answer)

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

namespace ConsoleApp60 {
    class Program {
        static void Main(string[] args) {
            var st = Console.ReadLine().Split().Select(int.Parse).ToArray();
            int A = st[0];
            int B = st[1];
            int K = st[2];


            Console.WriteLine(Gcd(A, B) * Math.Max((K - 1), 1));
            
        }

        static int Gcd(int a, int b) {
            if (a < b) {
                return Gcd(b, a);
            }

            while(b != 0) {
                int remain = a % b;
                a = b;
                b = remain;
            }
            return a;

        }
    }
}