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>

int main(void)
{
        int a, b, c, n[100]={}, k, i, j=0;

        scanf("%d%d%d", &a, &b, &k);
        if(a<b) c=b;
        else c=a;
        for(i=c;i>0;i--)
                if((a%i==0)&&(b%i==0)) {
                        n[j] = i;
                        j++;
        }
        printf("%d\n",n[k-1]);
        return 0;
}