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>
int h[100005];
int cmp(const void *a, const void *b) { return *(int *)a < *(int *)b ? 1 : -1; }
int main() {
  int n, k, i, j, s;
  while (scanf("%d%d", &n, &k) != EOF) {
    for (i = 0; i < n; i++) {
      scanf("%d", &h[i]);
    }
    qsort(h, n, sizeof(int), cmp);
    for (i = 0, s = 0; i < n; i++) {
      if (h[i] % k == 0) {
        for (j = i + 1; j < n; j++) {
          if (h[i] / k == h[j]) {
            h[j] = -1;
            s++;
            break;
          }
        }
      }
    }
    printf("%d\n", n - s);
  }
  return 0;
}
