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 <stdio.h>
#include <iostream>
#include <vector>
#include <string>
#include <set>
#include <map>
#include <queue>
#include <stack>
#include <math.h>
#include <algorithm>
using namespace std;
#define ll long long
const double EPS = 1e-10;

int main (){
  ll a,b,k;
  cin>>a>>b>>k;
  ll ans=min(a,b);
  for(ll i=0;i<k;i++){
    while(a%ans!=0||b%ans!=0)ans--;
    ans--;
  }
  ans++;
  cout<<ans<<endl;
}