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 double PI = acos(-1);
const double eps = 1e-9;
int main() {
  long long i, j, k, l, p, q, r, x, y, z, n, m, c(0), t, h, mn = pow(2, 62) - 1,
                                                            mx = 0;
  scanf("%lld", &n), scanf("%lld", &k);
  map<long long, bool> mp;
  long long a[n + 1];
  for (i = 1; i <= n; i++) scanf("%lld", &a[i]);
  sort(a + 1, a + n + 1);
  for (i = 1; i <= n; i++)
    if (!mp.count(a[i])) ++c, mp[a[i] * k] = 1;
  printf("%lld\n", c);
}
