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 main(){
    int A,B,K ;
    int i,cnt,small;
    int a[101]={};
    int ans=0;
    cnt=0;
    
    scanf("%d %d %d",&A,&B,&K);
    if(A>B) small=B;
    else small=A;
    for(i=1;i<=small;i++){
        if(A%i==0 && B%i==0){
            cnt++;
            a[cnt]=i;
            // if(cnt==K) ans = i;
        }
    }
    //printf("%d\n",cnt);
    //for(i=0;i<=small;i++){
    //    printf("%d\n",a[i]);
    //}
    printf("%d\n",a[cnt-K+1]);

}