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<string>
#include<algorithm>
#include<vector>
#include<map>
#include<cmath>
#include<string>
#include<bitset>
#include <sstream>
#include<queue>
#include<set>
#define rep(i,n) for(ll i=0;i<(n);++i)
using namespace std;
typedef long long ll;
typedef pair<int,ll>P;

const ll mod = 1e9+7;
const ll INF = ll(1e18)+1;
const ll MAXN = 1e6;

int main()
{
    int a,b,k;
    cin>>a>>b>>k;
    int count=1;
    int ans=0;
    while(count<=k)
    {   
        if(a%count==0 && b%count==0)
        {
            ans=count;
            count++;
        }
    }
    cout<<ans;
}