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 v[112345];
bool valid[112345];
int main() {
  int n, k, ans = 0;
  scanf("%d %d", &n, &k);
  for (int i = 0; i < n; ++i) scanf("%I64d", v + i);
  if (k == 1) {
    printf("%d\n", n);
    return 0;
  }
  sort(v, v + n);
  for (int i = 0, p; i < n; ++i) {
    if (valid[i]) continue;
    p = (int)(lower_bound(v + i, v + n, v[i] * (long long int)k) - v);
    if (p != i && p < n && v[i] * (long long int)k == v[p]) valid[p] = 1;
    ++ans;
  }
  printf("%d\n", ans);
}
