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;

class Program
{
 static void Main( string[] args )
 {
   int[] num = new int[3];
   int loopNum = 0;
   int cnt =0;
   var intList = new List<int>();
   
   var str = Console.ReadLine().Split(' ');
   
   for( cnt =0; cnt < 3; cnt++ )
   {
     num[cnt] = int.Parse(str[cnt]);
   }
  
   if( num[0] > num[1] )
   {
    loopNum = num[1];
   }
   else
   {
     loopNum = num[0];
   }
   
   for( cnt =1; cnt <= loopNum; cnt++ )
   {
     if( ( ( num[0] % cnt ) == 0 ) && ( ( num[1] % cnt ) == 0 ) )
     {
       intList.Add(cnt);
     }
   }
   
   intList.Sort((a, b) => b - a);
   
   Console.WriteLine(intList[(num[2]-1)]);
 }
}