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>
#include <ext/pb_ds/assoc_container.hpp> // Common file
#include <ext/pb_ds/tree_policy.hpp> // Including tree_order_statistics_node_update

using namespace std;
using namespace __gnu_pbds;

//find_by_order gives kth-largest element
//order_of_key gives the number of items in the set that are strictly smaller!!

// OT.find_by_order(k-1)
// 
typedef tree<int, null_type, less<int>, rb_tree_tag, tree_order_statistics_node_update> ordered_set;

#define db(x) cerr << #x << "=" << x << endl
#define db2(x, y) cerr << #x << "=" << x << "," << #y << "=" << y << endl
#define db3(x, y, z) cerr << #x << "=" << x << "," << #y << "=" << y << "," << #z << "=" << z << endl
#define db4(x, y, z, w) cerr << #x << "=" << x << "," << #y << "=" << y << "," << #z << "=" << z << "," << #w << "=" << w << endl
#define ll long long
#define pb push_back
#define eb emplace_back
#define all(x) (x).begin(), (x).end()
#define mp make_pair
#define X first
#define Y second
#define sz(x) (int)((x).size())
#define pii pair<int,int>
#define MOD (ll)(998244353)
#define rep(i, n)    for(int i = 0; i < (n); ++i)
#define repA(i, a, n)  for(int i = a; i <= (n); ++i)
#define repD(i, a, n)  for(int i = a; i >= (n); --i)
#define trav(a, x) for(auto& a : x)
typedef vector<int> vi;
#define inf (ll)(1e18)
#define double long double
#define int long long

//////////////////////
const int N = 2005;


int32_t main() {

    ios::sync_with_stdio(false);
    cin.tie(0); 
    cout.tie(0);

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

    repA(i,1,a) {
        if(!(a%k) and !(b%k)) {
            if(k==1) {
                cout << i << '\n';
                return 0;
            }
            k--;
        }
    }
}