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 long long mod = 1000000007, mod2 = 2e9, Pi = 3.141592653589793238;
long long gcd(long long a, long long b) { return b == 0 ? a : gcd(b, a % b); }
long long lcm(long long a, long long b) { return (a * b) / gcd(a, b); }
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  unsigned long long co = 0, x, t, k;
  cin >> t >> k;
  map<unsigned long long, bool> man;
  unsigned long long arr[t];
  for (int i = 0; i < t; i++) cin >> arr[i];
  ;
  sort(arr, arr + t);
  for (int i = (0); i < (t); i++) {
    x = arr[i];
    if (man[x]) continue;
    co++;
    man[(x * k)] = 1;
  }
  cout << co;
}
