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 <iostream>
#include <string>
#include <vector>
#include <map>
#include <algorithm>
#include <cmath>
#include <sstream>
#include <iomanip>
#include <set>
using namespace std;
typedef long long int ll;

#define rep(i, n) for(int i = 0; i < (int)(n); i++)
#define YES cout << "YES" << endl
#define Yes cout << "Yes" << endl
#define yes cout << "yes" << endl
#define NO cout << "NO" << endl
#define No cout << "No" << endl
#define no cout << "no" << endl

const int INF = 1001001001;
const int mod = 1000000007;
#define PI 3.14159265359;

void P(int x) {cout << x << endl;}
void P(long x) {cout << x << endl;}
void P(double x) {cout << x << endl;}
void P(ll x) {cout << x << endl;}
void P(string x) {cout << x << endl;}
void P(char x) {cout << x << endl;}

ll gcd(ll a, ll b) { return b?gcd(b,a%b):a;}
ll lcm(ll a, ll b) { return a/gcd(a,b)*b;}

int main() {
  int a, b, k;
  cin >> a >> b >> k;
  int count = 0;
  for (int i = 100; i > 0; i--) {
    if (a % i == 0 && b % i == 0) {
      count++;
      if (count == k) {
        P(i);
        return 0;
      }
    }

  }
  return 0;

}