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 main() {
  int n, k;
  cin >> n >> k;
  int num[n + 1];
  for (int i = 0; i < n; i++) {
    int a;
    cin >> a;
    num[i] = a;
  }
  sort(num, num + n);
  set<int> largo;
  for (int i = 0; i < n; i++) {
    int l, m;
    l = (abs(num[i] % k));
    m = largo.count(num[i] / k);
    if ((l > 0) || (m == 0)) {
      int a;
      a = num[i];
      largo.insert(a);
    }
  }
  cout << largo.size();
  return 0;
}
