#include <bits/stdc++.h>
using namespace std;
int main() {
  int a, b, d, e, f, g, h, k, x, arr[100100], y, z, cnt = 0, n, m, sum = 0, pos,
                                                    tmp;
  string s;
  char c;
  vector<int> v;
  map<int, int> chk;
  cin >> n >> k;
  for (int i = 0; i < n; i++) cin >> arr[i];
  sort(arr, arr + n);
  for (int i = n - 1; i >= 0; i--) {
    if (chk[arr[i]] != 1) {
      if ((arr[i] % k) == 0) chk[arr[i] / k] = 1;
      cnt++;
    }
  }
  cout << cnt << endl;
  return 0;
}

### Prompt

In cpp, your task is to solve 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;
int main() {
  int a, b, d, e, f, g, h, k, x, arr[100100], y, z, cnt = 0, n, m, sum = 0, pos,
                                                    tmp;
  string s;
  char c;
  vector<int> v;
  map<int, int> chk;
  cin >> n >> k;
  for (int i = 0; i < n; i++) cin >> arr[i];
  sort(arr, arr + n);
  for (int i = n - 1; i >= 0; i--) {
    if (chk[arr[i]] != 1) {
      if ((arr[i] % k) == 0) chk[arr[i] / k] = 1;
      cnt++;
    }
  }
  cout << cnt << endl;
  return 0;
}

```