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 arr[100005];
set<int> st;
int main() {
  int n, k;
  (scanf("%d%d", &n, &k));
  for (int i = 1; i <= n; i++) (scanf("%d", &arr[i]));
  sort(arr + 1, arr + n + 1);
  for (int i = 1; i <= n; i++) {
    if (i == 1)
      st.insert(arr[i]);
    else {
      if (arr[i] % k == 0) {
        if (st.find(arr[i] / k) == st.end()) st.insert(arr[i]);
      } else
        st.insert(arr[i]);
    }
  }
  cout << st.size();
}
