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;
long long a[1001001], used[1001001], n, br, k, p;
void read() {
  int i;
  scanf("%I64d%I64d", &n, &k);
  for (i = 1; i <= n; i++) scanf("%I64d", &a[i]);
}
int check(long long x) {
  int l = 1, r = p, mid;
  while (l <= r) {
    mid = (l + r) / 2;
    if (used[mid] == x) return 1;
    if (used[mid] > x)
      r = mid - 1;
    else
      l = mid + 1;
  }
  return 0;
}
void update(int x) {
  p++;
  used[p] = x;
}
void solve() {
  int i;
  sort(a + 1, a + (n + 1));
  for (i = 1; i <= n; i++)
    if (!check(a[i])) {
      br++;
      if (a[i] * k <= a[n]) update(a[i] * k);
    }
}
void print() { printf("%I64d\n", br); }
int main() {
  read();
  solve();
  print();
}
