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()
{
 int A;
 int B;
 int K;
 int i;
 int maxnum;
 int count=0;
 scanf("%d %d %d",&A,&B,&K);

 maxnum=A;
 if(A>B) maxnum=B;

 for(i=maxnum;i>=1;i--)
 {
   if( ((A%i)==0)&&((B%i)==0)) count++;
   if(count==K)
   {
    printf("%d\n",i);
    break;
   }
 }

 return 0;
}