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: Runtime Error)

#include <stdio.h>
int main (void)
{
        int  a, b,c,d,k[100];
        int  i, j=0;
        scanf("%d%d%d" , &a,&b,&c);

        d=a;
        if (a>b) d=b;

        for(i=0; i<=d; i++) {
        if ((a/i==0)&&(b/i==0)) k[j] = i;
        j++;
        }

        printf("%d\n",k[j-c]);
        return 0;
        }