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: Wrong Answer)

#include<iostream>
#include<iterator>
#include<vector>
using namespace std;
int gcd(int a,int b){
    return b == 0 ?  a : gcd(b,a%b);
}

int main()
{
	int a,b,k;
	cin >> a >> b >> k;
	int count =0;
	for(int i = 1;i<=gcd(a,b);i++){
	    if(a % i == 0 && b % i ==0){
	        count=i;
	    }
	    if(k<=count)
	        break;
	}
	cout << count;
	
}