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: Accepted)

#include<iostream>
#include<math.h>
#include<cmath>
#include<iomanip>
#include<string.h>
#include<stdio.h>
#include<algorithm>
using namespace std;
int main()
{
    ios::sync_with_stdio(false);
    cin.tie(0);
    int a,b,c,d;
    cin>>a>>b>>d;
    int y[100]={0};
    c=a%b;
    while(c!=0){
    	int t=b;
		b=a%b;
    	a=t;
    	c=a%b;
	}
	int j=0;
	for(int i=b;i>=1;i--){
		if(b%i==0){
			y[j]=i;
			j++;
		}
	}
	cout<<y[d-1]<<endl;
    return 0;
}