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++14 (GCC 5.4.1) (judge verdict: Runtime Error)

#include<iostream>
using namespace std;
int main(void)
{
    int a,b,k,i,j;
    cin>>a>>b>>k;
    j=0;
    int y[min(a,b)];
    for(i=0;i< min(a,b);i++)
    {
        if(b%i==0 && a%i==0)
        
            y[j]=i;
            j=j+1;
        
    }
    k=k-1;
    cout<<y[k]<<endl;
    return 0;
}