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;

int gcm(int a,int b){
	int x=max(a,b),y=min(a,b);
	if(y==0) return x;
	else return gcm(y, x%y);
}

int main(){
	int a,b,k;
	cin>>a>>b>>k;
	int GCM=gcm(a,b);
	int i;
	for(i=GCM;k!=0;i--){
		if(GCM%i==0) k--;
	}
	cout<<(i+1);
	return 0;
}