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,k,tmp,x,i,f[100];
   scanf("%d %d %d",&a,&b,&k);
   if (1>a) return 1;
   else if (b>100) return 1;
   else if (k<1) return 1;

   if(a<b){
        tmp=a;
        a=b;
        b=tmp;
   }
   for(i=1;i<=b;i++){
        if(a%i==0&&b%i==0){
           x++;
           f[x]=i;
        }
   }

   printf("%d\n",f[x-k+1]);
   return 0;
}