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)

int func(int a,int b,int c){
  int min = a>b?b:a;
  int array[99];
  int count = 0;
  for(int i = 1 ; i < min ; i ++){
    if ((a % i == 0) && (b % i == 0)){
      array[count] = i;
      count ++;
    }


  }
  return ("%d",array[count - c]);

}
int main(){
    int a,b,c;
    scanf("%d%d%d",&a,&b,&c);
    printf("%d\n",func(a,b,c));
    return 0;
}