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;

int main(){
   int a, b, k;
   cin >> a >> b >> k; 

   vector<int> x(k);

   for (int j=min(a,b);;j--){
           if(a%j==0 && b%j==0){
               x.at(0)=j;
               break;
           }
       }

   for (int i= 1; i < k; i++){
       for (int j=x.at(i-1)-1;;j--){
           if(a%j==0 && b%j==0){
               x.at(i)=j;
               break;
           }
       }
   }
   cout << x.at(k-1) << endl;
}