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 <bits/stdc++.h>
using namespace std;

struct Compare
{
    bool operator()(int a, int b)
    {
        return a>b;
    }
};

int main()
{
	int a,b,c;
  	cin>>a>>b>>c;
  	set<int,Compare> common_divisors;
  	int minimum=min(a,b);
  	for(int i=1 ; (i*i)<=minimum ; ++i)
    {
    	if(a%i==0 && b%i==0)
        {
            common_divisors.insert(i);
            int divisor_a=a/i;
            int divisor_b=b/i;
            if(a%divisor_a==0 && b%divisor_a==0)
            common_divisors.insert(divisor_a);
            if(b%divisor_b==0 && a%divisor_b==0)
            common_divisors.insert(divisor_b);
        }
    }
  	if(max(a,b)%minimum==0)
    common_divisors.insert(minimum);
    vector<int> divisors(common_divisors.begin(),common_divisors.end());
  	cout<<divisors[c-1]<<endl;
	return 0;
}