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;
const int MAXN = (int)1e5;
const int MAXVAL = (int)1e9;
map<int, int> indx, cnt;
int arr[MAXN + 5];
int n, k;
void add(int v) {
  if ((long long)v * k > MAXVAL || indx.count(v * k) == 0)
    indx[v] = cnt.size();
  else
    indx[v] = indx[v * k];
  cnt[indx[v]]++;
}
int main() {
  int c, c2;
  scanf("%d%d", &n, &k);
  for (c = 0; c < n; c++) scanf("%d", &arr[c]);
  sort(arr, arr + n);
  for (c = n - 1; c >= 0; c--) add(arr[c]);
  int ret = 0;
  for (__typeof((cnt).begin()) it = (cnt).begin(); it != (cnt).end(); it++)
    ret += (it->second + 1) >> 1;
  printf("%d\n", ret);
  return 0;
}
