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, k;
long long a[100005], p;
bool vis[100005];
int main() {
  while (scanf("%d %d", &n, &k) != EOF) {
    int ans = n;
    for (int i = 0; i < n; i++) scanf("%I64d", &a[i]);
    memset(vis, 0, sizeof(vis));
    sort(a, a + n);
    for (int i = 0; i < n; i++) {
      if (vis[i] == 0) {
        p = a[i] * k;
        if (p > a[n - 1]) continue;
        int mi = 1 + i, ma = n - 1;
        while (mi <= ma) {
          int mid = (mi + ma) / 2;
          long long t = a[mid];
          if (a[mid] > p)
            ma = mid - 1;
          else if (a[mid] < p)
            mi = mid + 1;
          else {
            vis[mid] = 1;
            ans--;
            break;
          }
        }
      }
    }
    printf("%d\n", ans);
  }
  return 0;
}
