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 <cstdio>
#include <algorithm>

using namespace std;

int main(){
    int a, b, k;
    scanf("%d %d %d",&a, &b, &k);

    int c = min(a, b);
    int count = 0;
    int ans;
    for(int i = c; i >= 1; i--){
        if(a % i == 0 && b % i == 0){
            count++;
            if(count == k){
                ans = i;
                break;
            }
        }
    }
    printf("%d\n",ans);

    return 0;
}