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,K,C,p,q,kotae,i;

        scanf("%d%d%d",&A,&B,&K);

        if(A>B) C=A;
        else C=B;

        for(i=C; i>0; i--){
           p=A%i;
           q=B%i;
                if((p==0) && (q==0)) K--;
                if(K==0) kotae = i;

}
        printf("%d\n",kotae);
        return 0;
}