#include <bits/stdc++.h>
using namespace std;
const double PI = acos(-1.0);
const int N = 1e5 + 1;
const long long inf = 2e9;
const long long OO = 1e18;
const long long MOD = 1e9 + 7;
int mx, ans;
int main() {
  int n, k, a;
  cin >> n >> k;
  set<int> ans;
  vector<int> v(n);
  for (int i = 0; i < n; i++) cin >> v[i];
  sort(v.begin(), v.end());
  for (auto x : v)
    if (x % k != 0 || ans.find(x / k) == ans.end()) ans.insert(x);
  cout << (int)ans.size();
  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;
const double PI = acos(-1.0);
const int N = 1e5 + 1;
const long long inf = 2e9;
const long long OO = 1e18;
const long long MOD = 1e9 + 7;
int mx, ans;
int main() {
  int n, k, a;
  cin >> n >> k;
  set<int> ans;
  vector<int> v(n);
  for (int i = 0; i < n; i++) cin >> v[i];
  sort(v.begin(), v.end());
  for (auto x : v)
    if (x % k != 0 || ans.find(x / k) == ans.end()) ans.insert(x);
  cout << (int)ans.size();
  return 0;
}

```