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>
#pragma comment(linker, "/STACK:268435456")
using namespace std;
template <class T>
T sqr(T a) {
  return a * a;
}
int a[100010];
map<int, int> b;
int n, k;
int main() {
  cin >> n >> k;
  for (int i = 0; i < n; i++) cin >> a[i];
  sort(a, a + n);
  for (int i = 0; i < n; i++) {
    if (a[i] % k == 0 && b.find(a[i] / k) != b.end()) {
      b[a[i]] = b[a[i] / k] + 1;
      b.erase(a[i] / k);
    } else
      b[a[i]] = 1;
  }
  int result = 0;
  for (map<int, int>::iterator iter = b.begin(); iter != b.end(); iter++)
    result += (iter->second + 1) / 2;
  cout << result;
  return 0;
}
