#include <bits/stdc++.h>
using namespace std;
long long a[100001], b[100001], n, m, i, j, k, p, q, l, r;
int main() {
  cin >> n >> m;
  for (i = 1; i <= n; i++) cin >> a[i];
  sort(a + 1, a + n + 1);
  p = n;
  for (i = 1; i <= n; i++) {
    if (b[i] == 0) {
      k = m * a[i];
      l = i + 1;
      r = n + 1;
      while (l < r - 1) {
        q = (l + r) / 2;
        if (a[q] > k)
          r = q;
        else
          l = q;
      }
      if (a[l] == k) {
        p--;
        b[l] = 1;
      }
    }
  }
  cout << p;
  return 0;
}

### Prompt

Generate a CPP solution 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;
long long a[100001], b[100001], n, m, i, j, k, p, q, l, r;
int main() {
  cin >> n >> m;
  for (i = 1; i <= n; i++) cin >> a[i];
  sort(a + 1, a + n + 1);
  p = n;
  for (i = 1; i <= n; i++) {
    if (b[i] == 0) {
      k = m * a[i];
      l = i + 1;
      r = n + 1;
      while (l < r - 1) {
        q = (l + r) / 2;
        if (a[q] > k)
          r = q;
        else
          l = q;
      }
      if (a[l] == k) {
        p--;
        b[l] = 1;
      }
    }
  }
  cout << p;
  return 0;
}

```