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;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  set<long long> s1, s2;
  long long n, k;
  cin >> n >> k;
  std::vector<long long> a(n);
  for (long long int i = 0; i < n; i++) cin >> a[i];
  sort((a).begin(), (a).end());
  for (long long int i = 0; i < n; i++) {
    long long x;
    x = a[i];
    long long vl1 = 0, vl2 = 0, vl3 = 0, vl4 = 0;
    if ((x % k) == 0) {
      long long z = x / k;
      if (s1.find(z) != s1.end()) vl1 = 1;
      if (s2.find(z) != s2.end()) vl3 = 1;
    }
    long long zz = (x * k);
    if (s1.find(zz) != s1.end()) vl2 = 1;
    if (s2.find(zz) != s2.end()) vl4 = 1;
    if (!vl1 && !vl2) {
      s1.insert(x);
      continue;
    }
    if (!vl3 && !vl4) {
      s2.insert(x);
      continue;
    }
  }
  cout << max(s1.size(), s2.size());
}
