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<bits/stdc++.h>
using namespace std;
#define int long long
#define double long double
#define REP(i,m,n) for(int i=m;i<n;i++)
#define rep(i,n) for(int i=0;i<n;i++)
#define sort(vec) sort(vec.begin(),vec.end())
#define reverse(vec) reverse(vec.begin(),vec.end())
int gcd(int x,int y){
    if(x%y==0)return y;
    return gcd(y,x%y);
}
int a,b,k;
int cnt=0;
signed main(){
    cin>>a>>b>>k;
    int sks=gcd(a,b);
    for(int i=sks;i>0;i--){
        if(sks%i==0)cnt++;
        if(cnt==k){
            cout<<i<<endl;
            return 0;
        }
    }
}