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: Wrong Answer)

#include<stdio.h>
   int main(void)
   {
           int a,b,c,i,j,x,y,k,n=0;
   
          scanf("%d%d%d",&a,&b,&k);
   
           if(b>a){
                  c=b;
                  b=a;
                  a=c;
          }
          printf("%d,%d\n",a,b);
  
          for(i=b;i>0;i--){
                  if((b%i==0)&&(a%i==0)){
                          n=n+1;
                          if(n==k) y=i;
                  }
          }
  
          printf("%d\n",y);
  
          return 0;
  }