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 <cmath>
#include <iostream>
using namespace std;

//-------------------------------
int get_fact_nums(int a, int b, int K){
    
    int min;
    int count = 0;
    int mod_at_k = 0;
    
    if(a>=b){
        min = b;
    }else{
        min = a;
    };

    for(int i=1; i<=min; i++){
        int mod_a = a % i;
        int mod_b = b % i;
        if(mod_a==0 && mod_b==0){
            mod_at_k = i;
            count++;
        };

        if(count==K){ break; };
    };

    return mod_at_k;
};





int main() {
    int A, B, K;
    int out;

    cin >> A >> B >> K;
    out = get_fact_nums(A, B, K);
    cout << out << endl;
}