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,t,i,r,r1,r2;

    scanf("%d %d %d",&a,&b,&k);

    if((1<=a)&&(a<=100)&&(1<=b)&&(b<=100)&&(1<=k)){
       if(a<b){
         t = a;
         a = b;
         b = t;
       }
       i = b;
       while(k!=0){
            r1 = a%i;
            r2 = b%i;
            if(r1 == r2) {r = i;i--;k = k-1;}
            else i--;
       }
    printf("%d",r);
    }
    return 0;
}