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"
using namespace std;
#define rep(i, n) for(int i = 0; i < n; i++)
#define REPR(i, n) for(int i = n; i >= 0; i--)
#define FOR(i, m, n) for(int i = m; i < n; i++)
#define ALL(x) (x).begin(), (x).end()
#define SZ(x) ((int)(x).size)
#define MOD 1000000007
const long long mod = 1e9+7;
typedef vector<long long> Vl;
typedef vector<int> VI;  // VI a(n);
typedef vector<string> VS;   
typedef vector<VI> VVI;   // VVI a(n,vector<int>(m)) n * m 
typedef vector<Vl> VVl;
typedef pair<int, int> PII;
typedef long long ll;
// cout << << endl;
// cin >> ;

int main(){
    ll a,b,d=0,n,m,ans=0;
    string s,s2;
    cin >> a >> b >> n;
    VI c(100);
    for(int i=1; i<=100;i++){
        if(a%i==0&&b%i==0){
            c[ans]=i;
            ans++;
        }
    }
    cout << c[ans-n] <<endl;
    return 0;
}