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 n, m;
int a[100100];
int chk[100100];
int ans;
int main() {
  int i, j;
  scanf("%d%d", &n, &m);
  for (i = 0; i < n; i++) {
    scanf("%d", &a[i]);
  }
  if (m == 1) {
    printf("%d", n);
    return 0;
  }
  std::sort(a, a + n);
  ans = n;
  j = 0;
  for (i = 0; i < n; i++) {
    while (j < i && a[i] / a[j] > m || (a[i] / a[j] == m && a[i] % a[j] != 0))
      j++;
    if (a[i] / a[j] == m && a[i] % a[j] == 0) {
      if (chk[j] == 0) {
        ans--;
        chk[i] = 1;
      }
    }
  }
  printf("%d", ans);
}
