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,b,c,i,j,n[100],k=0;
  scanf("%d%d%d",&a,&b,&c);
  if(a<b){
    j=b;
  }else{
    j=a;
  }
  for(i=1;i<=j;i++){
    if(a%i==0&&b%i==0){
      n[k]=i;
      k++;
    }
  }
  c=k-c;
  printf("%d\n", n[c]);
  return 0;
}