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 Max(int a,int b){
    if(a>b) return a;
    return b;
}


int main(void){
    int A,B,K,count=0;
    scanf("%d %d %d",&A,&B,&K);

    for(int i=Max(A,B);i>=0;i--){
        if(A%i==0&&B%i==0){
            count++;
            if(count==K){
                printf("%d",i);
                break;
            }
        }
        
    }

    return 0;
}