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 cmp(const void *a, const void *b) { return ((int *)b)[0] - ((int *)a)[0]; }
int a[100001][2];
int main() {
  int n, k;
  int sum = 0;
  scanf("%d%d", &n, &k);
  for (int i = 0; i < n; i++) scanf("%d", &a[i][0]);
  qsort(a, n, sizeof(int) * 2, cmp);
  for (int i = 0; i < n; i++) {
    if (a[i][0] % k != 0 && a[i][1] != 1) {
      sum++;
      continue;
    }
    if (a[i][1]) continue;
    if (!a[i][1]) {
      sum++;
      int low = i + 1;
      int high = n - 1;
      int find = a[i][0] / k;
      while (low <= high) {
        int mid = (low + high) / 2;
        if (a[mid][0] == find) {
          a[mid][1] = 1;
          break;
        }
        if (a[mid][0] > find)
          low = mid + 1;
        else
          high = mid - 1;
      }
    }
  }
  printf("%d", sum);
  return 0;
}
