#include <bits/stdc++.h>
using namespace std;
void hehe() {
  int n, k;
  cin >> n >> k;
  vector<int> arr(n);
  for (int i = 0; i < n; i++) {
    cin >> arr[i];
  }
  sort(arr.begin(), arr.end());
  map<int, int> hash;
  int ans = 0;
  for (int i = 0; i < n; i++) {
    if (!hash[arr[i]]) {
      if (arr[i] % k == 0) {
        if (!hash[arr[i] / k]) {
          ans++;
          hash[arr[i]]++;
        }
      } else {
        ans++;
        hash[arr[i]]++;
      }
    }
  }
  cout << ans;
}
int main() {
  int t = 1;
  while (t--) {
    hehe();
  }
  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;
void hehe() {
  int n, k;
  cin >> n >> k;
  vector<int> arr(n);
  for (int i = 0; i < n; i++) {
    cin >> arr[i];
  }
  sort(arr.begin(), arr.end());
  map<int, int> hash;
  int ans = 0;
  for (int i = 0; i < n; i++) {
    if (!hash[arr[i]]) {
      if (arr[i] % k == 0) {
        if (!hash[arr[i] / k]) {
          ans++;
          hash[arr[i]]++;
        }
      } else {
        ans++;
        hash[arr[i]]++;
      }
    }
  }
  cout << ans;
}
int main() {
  int t = 1;
  while (t--) {
    hehe();
  }
  return 0;
}

```