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 <iostream>
#include <sstream>
#include <fstream>
#include <string>
#include <vector>
#include <deque>
#include <queue>
#include <stack>
#include <set>
#include <map>
#include <algorithm>
#include <functional>
#include <utility>
#include <bitset>
#include <cmath>
#include <cstdlib>
#include <ctime>
#include <cstdio>
#include <string.h>
#define rep(i,n) for(int i=0;i<n;i++)
#define forn(i,a,b) for(int i=a;i<=b;i++)
#define INF 2147483647
#define LLINF 9223372036854775807
using namespace std;
int main(){
	int a,b,k;
	cin>>a>>b>>k;
	int cnt=0;
	for(int i=min(a,b);i>=1;i--){
		if(a%i==0&&b%i==0)cnt++;
		if(cnt==k){
			cout<<i<<endl;
			break;
		}
	}
	return 0;
}