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;
long long int a[999999];
int b[999999];
int main() {
  int n, m;
  memset(a, 0, sizeof(a));
  memset(b, 0, sizeof(b));
  scanf("%d%d", &n, &m);
  for (int i = 0; i < n; i++) {
    scanf("%lld", &a[i]);
  }
  sort(a, a + n);
  int sum = n;
  for (int i = 0; i < n; i++) {
    if (b[i] == 0) {
      long long mark;
      mark = a[i] * m;
      if (a[n - 1] < mark) continue;
      int l = i + 1, r = n - 1, mid;
      while (l <= r) {
        mid = (l + r) / 2;
        if (a[mid] > mark)
          r = mid - 1;
        else if (a[mid] < mark)
          l = mid + 1;
        else {
          b[mid] = 1;
          sum--;
          break;
        }
      }
    }
  }
  printf("%d\n", sum);
}
