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>
//#define int long long

using namespace std;
using LL = long long;
using P = pair<int, int>;

#define FOR(i, a, n) for(int i = (int)(a); i < (int)(n); ++i)
#define REP(i, n) FOR(i, 0, n)

#define pb(a) push_back(a)
#define all(x) (x).begin(),(x).end()

const int INF = (int)1e9;
const LL INFL = (LL)1e18;
const int MOD = 1e9 + 7;

signed main(){
    cin.tie(0);
    ios::sync_with_stdio(false);

    int a, b, k;
    cin >> a >> b >> k;

    vector<int> ans;
    REP(i, 100) if(a % (i+1) == 0 && b % (i+1) == 0) ans.pb(i+1);
    cout << ans[ans.size() - k] << endl;
}