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)

#include <stdio.h>
#define Min(a, b) a < b ? a : b
void initArray(int a[], int len);
int main(void)
{
    int a, b, k;
    scanf("%d%d%d", &a, &b, &k);
    int min = Min(a, b);
    int divisors[min];
    initArray(divisors, min);
    int count_divisors = 0;
    int first = 1, last = min;
    while(first <= last)
    {
        if (a % first + b % first == 0)
        {
            divisors[count_divisors] = first;
            count_divisors++;
        }
        first++;
    }
    printf("%d\n", divisors[count_divisors - k]);
    return 0;
}

void initArray(int a[], int len)
{
    for (int i = 0; i < len; i++)
    {
        a[i] = 0;
    }
}