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>
#define pb push_back
#define F first
#define S second
#define all(x) x.begin(), x.end()
using namespace std;
typedef long long ll ; 
typedef long double ld ;
typedef pair<ll , ll> pll ;

const ll N = 2e5 + 30 , Mod = 1e9 + 7 ;
const ll SQ = 330 ;

int main () {
    ios::sync_with_stdio(0), cin.tie(0) ;
    ll a, b , k;
    cin >> a>> b >> k;
    ll g = __gcd(a, b) ;
    ll cnt =0 ;
    for (int i = g; i; i --) {
    	if (g % i ==0 ) {
    		cnt ++ ;
    		if (cnt =k) return cout << i, 0;
		}
	}
    
    return (0) ;
}