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 v[112345], n, k;
set<int> s[112345];
int buscab(int x) {
  int ini = 1, fim = n, meio;
  while (ini <= fim) {
    meio = (ini + fim) / 2;
    if (v[meio] == x) {
      return -1;
    } else if (v[meio] < x) {
      ini = meio + 1;
    } else {
      fim = meio - 1;
    }
  }
  return 1;
}
int main() {
  cin >> n >> k;
  for (int i = 1; i <= n; i++) {
    cin >> v[i];
  }
  sort(v + 1, v + n + 1);
  set<int> ajuda;
  int resp = 0;
  for (int i = 1; i <= n; i++) {
    if (v[i] % k != 0) {
      ajuda.insert(v[i]);
    } else {
      if (ajuda.find(v[i] / k) == ajuda.end()) {
        ajuda.insert(v[i]);
      }
    }
  }
  resp = ajuda.size();
  printf("%d\n", resp);
}
