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, i, tot, now, cc;
long long k;
bool f[100005];
long long a[100005];
int main() {
  scanf("%d%I64d", &n, &k);
  for (i = 0; i < n; i++) scanf("%I64d", &a[i]);
  memset(f, 1, sizeof(f));
  sort(a, a + n);
  int ans = 0;
  for (i = 0; i < n; i++) {
    if (f[i] == 0) continue;
    now = i;
    tot = 1;
    while (1) {
      int cc = lower_bound(a + now + 1, a + n, a[now] * k) - a;
      if (a[cc] == a[now] * k) {
        tot++;
        f[cc] = 0;
      } else
        break;
      now = cc;
    }
    ans += (tot + 1) / 2;
  }
  printf("%d\n", ans);
}
