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}.
#include <bits/stdc++.h>
using namespace std;
int n;
int k;
long long a[100005];
long long b[100005];
long long c[100005];
long long procurando;
long long atual;
int main() {
  cin >> n >> k;
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
  }
  sort(a + 1, a + n + 1);
  for (int i = 1; i <= n; i++) {
    b[i] = a[n] + 1;
  }
  int qtd = 0;
  int de = 1;
  int ate = n - 1;
  int h = 0;
  int i = 1;
  int g = 0;
  while (i <= n) {
    atual = a[i];
    if ((atual % k != 0)) {
      g = 1;
    } else {
      procurando = atual / k;
    }
    while (de < ate) {
      if (g == 1) {
        break;
      }
      int meio = (de + ate) / 2;
      if (procurando > b[meio]) {
        de = meio + 1;
      } else if (procurando < b[meio]) {
        ate = meio - 1;
      } else {
        ate = meio;
      }
    }
    if (b[ate] != procurando || g == 1) {
      h++;
      qtd++;
      b[h] = a[i];
      g = 0;
    }
    de = 1;
    ate = n;
    i++;
  }
  cout << qtd << endl;
}
