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: Accepted)

// 10min
#include <stdio.h>
#include <stdlib.h>
#include <string.h>

int main(void) {
    char buffer[20];
    int  A, B, K;

    if (fgets(buffer, 20, stdin) != NULL) {
        A = atoi(strtok(buffer, " "));
        B = atoi(strtok(NULL, " "));
        K = atoi(strtok(NULL, " "));
    } else {
        return 1;
    }
    int max_num   = 0;
    if (A <= B) {
        max_num = A;
    } else {
        max_num = B;
    }

    int lcm_num = 0, lcm_value = 0;
    for (int i = max_num; 1 <= i; i--) {
        if (lcm_num != K) {
            if (A % i == 0 && B % i == 0) {
                lcm_num  += 1;
                lcm_value = i;
            }
        } else {
            break;
        }
    }
    printf("%d", lcm_value);
    return 0;
}