#include <bits/stdc++.h>
using namespace std;
const double pi = acos(-1.0);
const int inf = 10000000;
int arr[100005];
map<int, int> mm;
int main() {
  int n, k;
  cin >> n >> k;
  for (int i = 0; i < (n); i++) {
    cin >> arr[i];
    mm[arr[i]] = 1;
  }
  sort(arr, arr + n);
  int ans = 0;
  for (int i = n - 1; i >= 0; i--) {
    if (mm[arr[i]] == 0) continue;
    if (arr[i] % k != 0) {
      ans++;
      continue;
    }
    if (mm.find(arr[i] / k) != mm.end()) mm[arr[i] / k] = 0;
    ans++;
  }
  cout << ans << endl;
  return 0;
}

### 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 pi = acos(-1.0);
const int inf = 10000000;
int arr[100005];
map<int, int> mm;
int main() {
  int n, k;
  cin >> n >> k;
  for (int i = 0; i < (n); i++) {
    cin >> arr[i];
    mm[arr[i]] = 1;
  }
  sort(arr, arr + n);
  int ans = 0;
  for (int i = n - 1; i >= 0; i--) {
    if (mm[arr[i]] == 0) continue;
    if (arr[i] % k != 0) {
      ans++;
      continue;
    }
    if (mm.find(arr[i] / k) != mm.end()) mm[arr[i] / k] = 0;
    ans++;
  }
  cout << ans << endl;
  return 0;
}

```