#include <bits/stdc++.h>
using namespace std;
long long gcd(long long a, long long b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
long long lcm(long long a, long long b) { return a * (b / (gcd(a, b))); }
inline int toInt(string s) {
  int v;
  istringstream sin(s);
  sin >> v;
  return v;
}
inline long long toLL(string s) {
  long long v;
  istringstream sin(s);
  sin >> v;
  return v;
}
template <class T>
inline string toString(T x) {
  ostringstream sout;
  sout << x;
  return sout.str();
}
using namespace std;
long long N, K;
set<long long> s;
int main() {
  std::ios_base::sync_with_stdio(false);
  cin >> N >> K;
  if (K == 1) {
    cout << N;
    cout << "\n";
    return 0;
  }
  vector<long long> v;
  v.resize(N);
  for (int i = 0; i < (int)N; i++) {
    cin >> v[i];
    s.insert(v[i]);
  }
  sort(((v).begin()), ((v).end()));
  for (int k = 0; k < ((int)((v).size())); k++) {
    if (s.find(v[k]) == s.end()) continue;
    if (s.find((long long)(v[k] * K)) != s.end())
      s.erase((long long)(v[k] * K));
  }
  cout << ((int)((s).size()));
}

### Prompt

Construct a CPP code solution to the problem outlined:

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;
long long gcd(long long a, long long b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
long long lcm(long long a, long long b) { return a * (b / (gcd(a, b))); }
inline int toInt(string s) {
  int v;
  istringstream sin(s);
  sin >> v;
  return v;
}
inline long long toLL(string s) {
  long long v;
  istringstream sin(s);
  sin >> v;
  return v;
}
template <class T>
inline string toString(T x) {
  ostringstream sout;
  sout << x;
  return sout.str();
}
using namespace std;
long long N, K;
set<long long> s;
int main() {
  std::ios_base::sync_with_stdio(false);
  cin >> N >> K;
  if (K == 1) {
    cout << N;
    cout << "\n";
    return 0;
  }
  vector<long long> v;
  v.resize(N);
  for (int i = 0; i < (int)N; i++) {
    cin >> v[i];
    s.insert(v[i]);
  }
  sort(((v).begin()), ((v).end()));
  for (int k = 0; k < ((int)((v).size())); k++) {
    if (s.find(v[k]) == s.end()) continue;
    if (s.find((long long)(v[k] * K)) != s.end())
      s.erase((long long)(v[k] * K));
  }
  cout << ((int)((s).size()));
}

```