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;



    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]);

            int Max = 0;
            int res = 0;

            while (Max <= K) {

                for (int i = 1; i < 100; ++i) {

                    int amariA = A % i;
                    int amariB = B % i;

                    if (amariA + amariB == 0) {
                        ++Max;
                    res = i;

                    }


                }
            }

            Console.WriteLine(res);

        }
    }