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 main() {
  long l, r, n, i, size1 = 0, w = 1, j, mid;
  long long k;
  long long m[100005];
  int f[100005] = {0}, h[100005] = {0};
  scanf("%ld %I64d", &n, &k);
  for (i = 0; i < n; i++) {
    scanf("%I64d", &m[i]);
  }
  size1 = n;
  sort(&m[0], &m[n]);
  if (k == 1) {
    printf("%ld\n", n);
  } else {
    for (i = 0; i < n; i++) {
      l = 0;
      r = n - 1;
      while (l <= r) {
        mid = (l + r) / 2;
        if (m[mid] > m[i] * k) {
          r = mid - 1;
        } else if (m[mid] < m[i] * k) {
          l = mid + 1;
        } else if (m[mid] == m[i] * k) {
          if (f[i]) {
            size1--;
            f[mid] = f[i];
            h[f[i]]++;
          } else {
            size1 -= 2;
            f[i] = w;
            f[mid] = w;
            h[f[i]] += 2;
            w++;
          }
          break;
        }
      }
    }
    for (i = 1; i < n && h[i] != 0; i++) {
      if (h[i] % 2 == 0) {
        size1 += h[i] / 2;
      } else {
        size1 += (h[i] / 2 + 1);
      }
    }
    printf("%ld\n", size1);
  }
}
