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;
            #define rep(i,b) for(i=0;i<b;++i)
            #define repp(i,a,b) for(i=a;i<b;++i)
            #define endl "\n"
            #define pi 3.14159265358979323846
            #define LLONG_MAX 99999999999999
            typedef long long int lli;
            int main(){
                lli i,j,t,k,n,m,f,g,q;
                lli a,b,c;
                cin>>a>>b>>c;
                t=0;
                repp(i,1,min(a,b)+1){
                    if(a%i==0&&b%i==0){
                        t++;
                        if(t==c){
                            cout<<i<<endl;
                            return 0;
                        }
                    }
                }

                return 0;

            }