#include <bits/stdc++.h>
using namespace std;
int n, k, a[1 << 19], i, r, u;
map<int, int> s;
int main() {
  cin >> n >> k;
  for (i = 0; i < n; i++) cin >> a[i];
  sort(a, a + n);
  for (i = 0; i < n; i++)
    if ((u = a[i]) % k | !s[u / k]) s[u] = ++r;
  cout << r;
}

### 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;
int n, k, a[1 << 19], i, r, u;
map<int, int> s;
int main() {
  cin >> n >> k;
  for (i = 0; i < n; i++) cin >> a[i];
  sort(a, a + n);
  for (i = 0; i < n; i++)
    if ((u = a[i]) % k | !s[u / k]) s[u] = ++r;
  cout << r;
}

```