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 tmp,x,y,i=0,k,count=1,ans=0,arr[3];
    for(i=0;i<3;i++){
        scanf("%d",&arr[i]);
    }
    x = arr[0];
    y = arr[1];
    k = arr[2];
    while (x % y != 0) {
        tmp = y;
        y = x % y;
        x = tmp;
    }
        for(i=y-1; i >0; i--)
        {
            if (y%i == 0)
            {
                ans = i;
                count++;
                if(count==k){
                    printf("%d",ans);
                    break;
                }
            }
        }
    
    
    
    return 0;
}