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>
#define rep(i,n) for (int i = 0; i < (n); ++i)
using namespace std;
using ll = long long;
using P = pair<int,int>;

int gcd(int a, int b){
   if (a%b == 0){
       return(b);
   }
   else{
       return(gcd(b, a%b));
   }
}

int lcm(int a, int b){
   return a * b / gcd(a, b);
}

int main(){
	int a,b,k;
	cin >> a >> b >> k;
	int cnt = 0;
	int ans = 1;
	for(int i = lcm(a,b);i >= 1;i--){
		if(a%i == 0 && b%i == 0){
			cnt++;
		}
		if(cnt == k){
			cout << i << endl;
			return 0;
		}
	}
}