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;
    scanf("%d %d %d", &A, &B, &K);
    int i, tmp;
    if(A>B){
        tmp = A;
        A = B;
        B = tmp;
    }
    int n[A];
    for(i=0;i<A;i++){
        if((A%(i+1)==0)&&(B%(i+1)==0)){
            n[i] = 1;
        }
        else{
            n[i] = 0;
        }
    }
    int count=0, ans=1;
    for(i=0;i<A;i++){
        if(n[A-1-i] == 1){
            count += 1;
        }
        if(count == K){
            ans = A-i;
            break;
        }
    }
    printf("%d\n", ans);
}