#include <bits/stdc++.h>
using namespace std;
map<unsigned long long, unsigned long long> num;
const int m = 1e5 + 7;
unsigned long long n, k, v[m], mx, cont;
int main() {
  cin >> n >> k;
  for (int i = 0; i < n; ++i) cin >> v[i];
  sort(v, v + n);
  for (int i = n - 1; i >= 0; --i)
    if (num.find(v[i] * k) == num.end()) num[v[i]] = 1;
  cout << num.size() << endl;
  return 0;
}

### Prompt

Create a solution in cpp for 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;
map<unsigned long long, unsigned long long> num;
const int m = 1e5 + 7;
unsigned long long n, k, v[m], mx, cont;
int main() {
  cin >> n >> k;
  for (int i = 0; i < n; ++i) cin >> v[i];
  sort(v, v + n);
  for (int i = n - 1; i >= 0; --i)
    if (num.find(v[i] * k) == num.end()) num[v[i]] = 1;
  cout << num.size() << endl;
  return 0;
}

```