#include <bits/stdc++.h>
using namespace std;
vector<long long> vec, vec2, vec3, vec4, v, p;
int flag = 0;
long long n, k, m, t, sum, cnt, ans;
vector<pair<vector<int>, int> > graph;
vector<bool> visited;
deque<int> pq, pq2;
map<long long, long long> mp, mpp, mpc;
bool sortBy(pair<long long, long long> &a, pair<long long, long long> &b) {
  return a.second < b.second;
}
const int sss = 1e6 + 1;
const int sss2 = 1e5 + 2;
map<long long, long long> vis, vis2;
void solve() {
  cin >> n >> k;
  vec.resize(n);
  for (long long i = 0; i < n; ++i) cin >> vec[i];
  sort(vec.begin(), vec.end());
  vector<long long> free;
  for (long long i = 0; i < n; ++i) {
    vis[vec[i] * k]++;
  }
  for (long long i = 0; i < n; ++i) {
    if (!vis[vec[i]]) free.push_back(vec[i]);
  }
  for (long long i = 0; i < free.size(); ++i) {
    vis2[free[i]]++;
    vis2[free[i] * k]++;
  }
  for (long long i = 0; i < n; ++i) {
    if (!vis2[vec[i]]) {
      free.push_back(vec[i]);
      vis2[vec[i] * k]++;
    }
  }
  cout << free.size() << '\n';
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  t = 1;
  while (t--) solve();
}

### Prompt

Please formulate 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;
vector<long long> vec, vec2, vec3, vec4, v, p;
int flag = 0;
long long n, k, m, t, sum, cnt, ans;
vector<pair<vector<int>, int> > graph;
vector<bool> visited;
deque<int> pq, pq2;
map<long long, long long> mp, mpp, mpc;
bool sortBy(pair<long long, long long> &a, pair<long long, long long> &b) {
  return a.second < b.second;
}
const int sss = 1e6 + 1;
const int sss2 = 1e5 + 2;
map<long long, long long> vis, vis2;
void solve() {
  cin >> n >> k;
  vec.resize(n);
  for (long long i = 0; i < n; ++i) cin >> vec[i];
  sort(vec.begin(), vec.end());
  vector<long long> free;
  for (long long i = 0; i < n; ++i) {
    vis[vec[i] * k]++;
  }
  for (long long i = 0; i < n; ++i) {
    if (!vis[vec[i]]) free.push_back(vec[i]);
  }
  for (long long i = 0; i < free.size(); ++i) {
    vis2[free[i]]++;
    vis2[free[i] * k]++;
  }
  for (long long i = 0; i < n; ++i) {
    if (!vis2[vec[i]]) {
      free.push_back(vec[i]);
      vis2[vec[i] * k]++;
    }
  }
  cout << free.size() << '\n';
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  t = 1;
  while (t--) solve();
}

```