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>
using namespace std;

long long gcd(long long a,long long b){
    //if(b == 0) return a;
    //return gcd(b,a%b);
    return b ? gcd(b,a%b) : a;
}

int main() {
    //input
    int a, b, k;
    cin >> a;
    cin >> b;
    cin >> k;
    //
    long long g = gcd(a,b);
    int count = 1;
    int res = 1;
    for(int i=2;i<g;i++){
        if(g%i == 0){
            count++;
            if(count == k){
                res = i;
                break;
            }
        }
    }
    cout << res;

    return 0;
}