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 N = 1e5 + 5;
int n, ans, k, a[N];
map<long long, int> f;
int main() {
  scanf("%d%d", &n, &k);
  if (k == 1) return printf("%u\n", n), 0;
  for (int i = 1; i <= n; i++) {
    scanf("%d", a + i);
    f[a[i]]++;
  }
  sort(a + 1, a + n + 1);
  for (int i = 1; i <= n; i++) {
    if (a[i] % k == 0) f[a[i]] += f[a[i] / k];
    if (!f[a[i] * 1LL * k]) ans += (f[a[i]] + 1) / 2;
  }
  printf("%d\n", ans);
  scanf("\n");
}
