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 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>

int main(int argc, char const *argv[])
{
    int a = 0, b = 0, k = 0, res = 0, count = 0, div = 0;

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

    if (a % b == 0) {
        for (int i = b; i >= 1; i--) {
            if (count == k) {
                break;
            }
            if ((a % i) == 0 && (b % i) == 0) {
                count++;
                res = i;
            }
        }
        printf("%d\n", res);
    } else if (b % a == 0) {
        for (int i = a; i >= 1; i--) {
            if (count == k) {
                break;
            }
            if ((a % i) == 0 && (b % i) == 0) {
                count++;
                res = i;
            }
        }
        printf("%d\n", res);
    } else {
        for (int i = 1; i <= 100; i++) {
            if (count == k) {
                break;
            }
            if ((a % i) == 0 && (b % i) == 0) {
                count++;
                res = i;
            }
        }
        printf("%d\n", res);
    }
    return 0;
}