#include <bits/stdc++.h>
using namespace std;
int MAX = 1000000;
int MIN = -1000000;
int INF = 1000000000;
int x4[4] = {0, 1, 0, -1};
int y4[4] = {1, 0, -1, 0};
int x8[8] = {0, 1, 1, 1, 0, -1, -1, -1};
int y8[8] = {1, 1, 0, -1, -1, -1, 0, 1};
int i, j, k;
vector<int> v;
map<int, bool> isi;
bool used[100010];
int n, x;
int main() {
  int ans = 0;
  cin >> n >> k;
  memset((used), (false), sizeof(used));
  ;
  for (i = (0); i < (n); i++) {
    cin >> x;
    v.push_back(x);
  }
  sort(v.begin(), v.end());
  for (i = (0); i < (n); i++) {
    if (v[i] % k > 0) {
      isi[v[i]] = true;
      ans++;
      used[i] = true;
    }
  }
  int temp;
  for (i = (0); i < (n); i++) {
    if (used[i] == true) continue;
    temp = v[i] / k;
    if (isi[temp] == false) {
      isi[v[i]] = true;
      ans++;
    }
  }
  cout << ans << endl;
  {
    fflush(stdin);
    getchar();
  };
  return 0;
}

### Prompt

Your task is to create 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;
int MAX = 1000000;
int MIN = -1000000;
int INF = 1000000000;
int x4[4] = {0, 1, 0, -1};
int y4[4] = {1, 0, -1, 0};
int x8[8] = {0, 1, 1, 1, 0, -1, -1, -1};
int y8[8] = {1, 1, 0, -1, -1, -1, 0, 1};
int i, j, k;
vector<int> v;
map<int, bool> isi;
bool used[100010];
int n, x;
int main() {
  int ans = 0;
  cin >> n >> k;
  memset((used), (false), sizeof(used));
  ;
  for (i = (0); i < (n); i++) {
    cin >> x;
    v.push_back(x);
  }
  sort(v.begin(), v.end());
  for (i = (0); i < (n); i++) {
    if (v[i] % k > 0) {
      isi[v[i]] = true;
      ans++;
      used[i] = true;
    }
  }
  int temp;
  for (i = (0); i < (n); i++) {
    if (used[i] == true) continue;
    temp = v[i] / k;
    if (isi[temp] == false) {
      isi[v[i]] = true;
      ans++;
    }
  }
  cout << ans << endl;
  {
    fflush(stdin);
    getchar();
  };
  return 0;
}

```