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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
using namespace std;
bool compare(int a,int b)
{
      return a>b;
}
int main()
{

      int a,b,c,d[100],j=0;
      cin>>a>>b>>c;
      for(int i=1;i<=min(a,b);i++)
      {
              if(a%i==0&&b%i==0)
              {
                     d[j]=i;
                     j++;
              }
      }
      sort(d,d+j,compare);
      cout<<d[c-1]<<endl;
        return 0;
}