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++ (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream> 
#include <math.h>
#include <algorithm>

using namespace std;



int main() 
{
    int a, b, k, ans, i, counter=0;
    int m[102];

    cin >> a >> b >> k;
    
    for (i=0;i<102;i++) 
    {
        m[i] = 1;
    }

    for (i=100;i>0;i--) 
    {
        if ( (a%i==0) && (b%i==0) )
        {
            counter += 1; 
            m[counter] = i;
            if (counter > k) 
            {
                break;
            }
        }
    }
    cout << m[k];

    return 0;
}