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++ (GCC 9.2.1) (judge verdict: Accepted)

#include <iostream>
using namespace std;

int main() {
    int a, b, k;
    cin >> a >> b >> k;
    int min;
    if (a > b) min = b;
    else min = a;
    if (min == 1) {
        cout << 1 << endl;
        return 0;
    }
    int c[100001] ;
    int cnt = 0;
    for (int i = min; i > 0; i--) {
        if (a % i == 0 && b % i == 0) cnt++;
        if (cnt == k) {
            cout << i << endl;
            return 0;
        }
    }

    // for (int i = 0; i < cnt; i++) cout << c[i] << endl;
    
    // cout << c[k-1] << endl;
    // return 0;
}