#include <bits/stdc++.h>
using namespace std;
const double EPS = 1e-9;
const int oo = (int)1e9;
const double PI = 2 * acos(0.0);
const double eps = 1e-7;
const int MAXN = 1e5 + 10;
int dx[] = {1, 0, -1, 0, -1, -1, 1, 1};
int dy[] = {0, 1, 0, -1, 1, -1, 1, -1};
int main() {
  int n, k, a[100009];
  cin >> n >> k;
  for (int i = 0; i < n; i++) cin >> a[i];
  sort(a, a + n);
  set<long long> s;
  for (int i = n - 1; i >= 0; i--)
    if (s.find((long long)k * a[i]) == s.end()) s.insert(a[i]);
  cout << ((int)((s).size())) << endl;
}

### Prompt

Please create a solution in CPP to the following problem:

A k-multiple free set is a set of integers where there is no pair of integers where one is equal to another integer multiplied by k. That is, there are no two integers x and y (x < y) from the set, such that y = x·k.

You're given a set of n distinct positive integers. Your task is to find the size of it's largest k-multiple free subset.

Input

The first line of the input contains two integers n and k (1 ≤ n ≤ 105, 1 ≤ k ≤ 109). The next line contains a list of n distinct positive integers a1, a2, ..., an (1 ≤ ai ≤ 109).

All the numbers in the lines are separated by single spaces.

Output

On the only line of the output print the size of the largest k-multiple free subset of {a1, a2, ..., an}.

Examples

Input

6 2
2 3 6 5 4 10


Output

3

Note

In the sample input one of the possible maximum 2-multiple free subsets is {4, 5, 6}.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const double EPS = 1e-9;
const int oo = (int)1e9;
const double PI = 2 * acos(0.0);
const double eps = 1e-7;
const int MAXN = 1e5 + 10;
int dx[] = {1, 0, -1, 0, -1, -1, 1, 1};
int dy[] = {0, 1, 0, -1, 1, -1, 1, -1};
int main() {
  int n, k, a[100009];
  cin >> n >> k;
  for (int i = 0; i < n; i++) cin >> a[i];
  sort(a, a + n);
  set<long long> s;
  for (int i = n - 1; i >= 0; i--)
    if (s.find((long long)k * a[i]) == s.end()) s.insert(a[i]);
  cout << ((int)((s).size())) << endl;
}

```