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 <bits/stdc++.h>
using namespace std;

struct Fast {Fast() {std::cin.tie(0); ios::sync_with_stdio(false);}} fast;
using ll = long long;
using vi = vector<int>;
using vvi = vector<vi>;
using pii = pair<int, int>;
using vll = vector<long long>;
using pll = pair<ll, ll>;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define all(x) (x).begin(),(x).end()
#define pb push_back
#define mp make_pair
#define F first
#define S second
#define MOD 1000000007


int main() {
    int A, B, K; cin >> A >> B >> K;
    int ans, num = 0;
    rep(i,100){
        if(A % (i+1) == 0 && B % (i+1) == 0) num++;
        if(num == K){
            ans = i+1;
            break;
        }
    }
    cout << ans << endl;
}