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)

////////////////////////////////////////////////////////////////////
// This source code is for Visual Studio
////////////////////////////////////////////////////////////////////
#include <iostream>
#include <string>
#include <vector>
#include <list>
#include <queue>
#include <map>
#include <set>
#include <algorithm>
#include <sstream>
#include <iterator>
#include <stack>
#include <functional>
#include <iomanip>
#include <string>
#include <cstring>
#include <deque>
#include <math.h>
#include <assert.h>

#define	numberof(a)	(sizeof(a) / sizeof(a[0]))
#define	INF32		INT32_MAX
#define	INF64		INT64_MAX
#define Rep(i,n) for(int i = 0; i < (n); ++i )

using namespace std;

typedef vector< vector<int> > MAT;
typedef pair<int, int> PINT;
typedef long long ll;
typedef uint32_t u32;
typedef uint64_t u64;
typedef int32_t s32;
typedef int64_t s64;

//constant
//--------------------------------------------
const double EPS = 1e-10;
const double PI = acos(-1.0);


// main function
int main()
{
	ll A = 0;
	ll B = 0;
	ll K = 0;
	ll ans = 1;

	cin >> A >> B >> K;
	ll tmp = (A >= B) ? B : A;
	ll cnt = 0;
	for (ans = tmp; ans > 1; --ans ) {
		if (A % ans == 0 && B % ans == 0) {
			cnt++;
			if (cnt == K) break;
		}
	}

	cout << ans << endl;

	return 0;
}