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(void){
    int A, B, K;
    int counter=1;
    int Kcount=0;
    int max;
    scanf("%d %d %d", &A, &B, &K);
    if (A>=B){
        max = A;
    }
    else{
        max = B;
    }
    counter =max;
    while(counter>0){
        if((A%counter ==0)&&(B%counter==0)){
            Kcount++;
            if(Kcount==K){
                printf("%d", counter);
            }
        }
        counter--;
    }
    return 0;
}