#include <bits/stdc++.h>
using namespace std;
long long arr[100010];
bool b[100010] = {0};
bool bins(long long x, int low, int high) {
  if (low > high)
    return false;
  else {
    int mid = (high + low) / 2;
    if (arr[mid] == x)
      if (b[mid])
        return false;
      else
        return true;
    else if (arr[mid] > x)
      return bins(x, low, mid - 1);
    else
      return bins(x, mid + 1, high);
  }
}
int main() {
  int n, k;
  cin >> n >> k;
  for (int i = 0; i < n; i++) cin >> arr[i];
  sort(arr + 0, arr + n);
  int ans = 0;
  for (int i = 0; i < n; i++) {
    if (arr[i] % k == 0) {
      if (!bins(arr[i] / k, 0, i - 1))
        ans++;
      else
        b[i] = true;
    } else
      ans++;
  }
  cout << ans << endl;
  return 0;
}

### Prompt

Please formulate 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 arr[100010];
bool b[100010] = {0};
bool bins(long long x, int low, int high) {
  if (low > high)
    return false;
  else {
    int mid = (high + low) / 2;
    if (arr[mid] == x)
      if (b[mid])
        return false;
      else
        return true;
    else if (arr[mid] > x)
      return bins(x, low, mid - 1);
    else
      return bins(x, mid + 1, high);
  }
}
int main() {
  int n, k;
  cin >> n >> k;
  for (int i = 0; i < n; i++) cin >> arr[i];
  sort(arr + 0, arr + n);
  int ans = 0;
  for (int i = 0; i < n; i++) {
    if (arr[i] % k == 0) {
      if (!bins(arr[i] / k, 0, i - 1))
        ans++;
      else
        b[i] = true;
    } else
      ans++;
  }
  cout << ans << endl;
  return 0;
}

```