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 gcd(int a,int b){int r,tmp;if(a < b){tmp = a;a = b;b = tmp;}r = a % b;while(r != 0){a = b;b = r;r = a % b;}return b;}


int main()
{
    int a,b,k,r,cnt = 0,ans = 0,i;
    scanf("%d %d %d",&a,&b,&k);
    r = gcd(a,b);
    i = r;
    while (cnt < k)
    {
        if(r % i == 0)
        {
            cnt++;
            ans = i;
        }
        i--;
    }
    
    printf("%d",ans);
}