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 arr[100000 + 5];
bool flag[100000 + 5];
int main() {
  long long n, k;
  scanf("%I64d %I64d", &n, &k);
  for (int i = 0; i < n; i++) {
    scanf("%I64d", &arr[i]);
  }
  sort(arr, arr + n);
  int cnt = 0;
  for (int i = 0; i < n; i++) {
    if (flag[i]) continue;
    long long high = k * arr[i];
    int indx = lower_bound(arr, arr + n, high) - arr;
    long long ans = arr[indx];
    if (high == ans) {
      flag[indx] = true;
    }
    cnt++;
  }
  printf("%d\n", cnt);
  return 0;
}
