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 a[100005];
int bs(int t, int p) {
  int lo = 0, hi = p - 1;
  while (lo <= hi) {
    int mid = (lo + hi) / 2;
    if (a[mid] == t)
      return mid;
    else {
      if (a[mid] > t) {
        hi = mid - 1;
      } else {
        lo = mid + 1;
      }
    }
  }
  return -1;
}
int main() {
  int n, k;
  cin >> n >> k;
  for (int i = 0; i < n; i++) cin >> a[i];
  sort(a, a + n);
  int x = 0, y = 0;
  int dp[100005];
  for (int i = 0; i < n; i++) {
    int r;
    if (a[i] % k != 0)
      r = -1;
    else
      r = bs(a[i] / k, i);
    if (r == -1) {
      x++;
      dp[i] = 0;
    } else {
      if (dp[r] == 0) {
        y++;
        dp[i] = 1;
      } else {
        x++;
        dp[i] = 0;
      }
    }
  }
  cout << max(x, y);
}
