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: Wrong Answer)

#include <iostream>
#include <fstream>
#include <string>
#include <algorithm>
#include <vector>
#include <list>
#include <math.h>
#include <iomanip>
#define rep(i,n) for(int i=1;i<=(n);i++)
using namespace std;


int A,B,K;
int main(){
  cin>>A>>B>>K;

  int c = 0;
  rep(i, min(A,B)){
    if(A%i == 0 && B%i == 0){
      c++;
      cout << "i:" << i << endl;
      if(c == K) cout << i << endl;  
    }
  }
}