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.Linq;
using System.Collections;
using System.Collections.Generic;
using static System.Console;
using System.Text;
using System.Threading.Tasks;
using System.IO;
using System.Diagnostics;
class Program
{
    public static Scanner cin;
    static void Main()
    {
        
        cin = new Scanner();
        int[] abk = cin.arrayInt(3);
        int a = abk[0];
        int b = abk[1];
        int k = abk[2];
        int count = 0;
        for(int c = Math.Min(a, b); c >0 ; c++)
        {
            if (a % c == 0 && b % c == 0) count++;
            if (count == k) break;
        }
        WriteLine(k);
        ReadLine();

    }
}





class Scanner
{
    string[] s;
    int i;

    char[] cs = new char[] { ' ' };

    public Scanner()
    {
        s = new string[0];
        i = 0;
    }

    public string input()
    {
        if (i < s.Length) return s[i++];
        string st = Console.ReadLine();
        while (st == "") st = Console.ReadLine();
        s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
        if (s.Length == 0) return input();
        i = 0;
        return s[i++];
    }

    public int inputInt()
    {
        return int.Parse(input());
    }
    public int[] arrayInt(int N, int add = 0)
    {
        int[] Array = new int[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = inputInt() + add;
        }
        return Array;
    }

    public long inputLong()
    {
        return long.Parse(input());
    }

    public long[] arrayLong(int N, long add = 0)
    {
        long[] Array = new long[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = inputLong() + add;
        }
        return Array;
    }

    public double inputDouble()
    {
        return double.Parse(input());
    }


    public double[] arrayDouble(int N, double add = 0)
    {
        double[] Array = new double[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = inputDouble() + add;
        }
        return Array;
    }
}