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<iomanip>
#include<vector>
#include<algorithm>
#include<set>
#include<map>
#include<stack>
#include<queue>
using namespace std;
typedef long long ll;
typedef long double ld;
#define MOD 1000000007LL
#define INF 1000000000LL
#define EPS 1e-10
#define FOR(i,n,m) for(int i=n;i<(int)m;i++)
#define REP(i,n) FOR(i,0,n)
#define DUMP(a) REP(d,a.size()){cout<<a[d];if(d!=a.size()-1)cout<<" ";else cout<<endl;}
#define ALL(v) v.begin(),v.end()
#define UNIQUE(v)  sort(ALL(v));v.erase(unique(ALL(v)),v.end());
#define pb push_back

int main() {
	cin.tie(0);
	ios::sync_with_stdio(false);
	int a, b, k;
	cin >> a >> b >> k;
	int c = 0;
	for(int i = 100; i > 0; i--) {
		if(a % i == 0 && b % i == 0) {
			c++;
		}
		if(c == k) {
			cout << i << endl;
			return 0;
		}
	}
	return 0;
}
/* --------------------------------------- */