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 n, i, j, h, k;
long long a[100005], b[100005];
long long f(long long cc, long long ll, long long rr) {
  long long x;
  x = (ll + rr) / 2;
  if (ll > rr) return -1;
  if (cc == a[x]) return x;
  if (cc > a[x]) {
    return f(cc, x + 1, rr);
  }
  if (cc < a[x]) {
    return f(cc, ll, x - 1);
  }
}
int main() {
  scanf("%I64d%I64d", &n, &k);
  for (i = 1; i <= n; i++) {
    scanf("%I64d", &a[i]);
  }
  sort(a + 1, a + n + 1);
  h = n;
  for (i = 1; i <= n; i++) b[i] = 1;
  if (n == 1) {
    printf("%d", 1);
  } else {
    if (k != 1) {
      for (i = 1; i <= n; i++) {
        if (b[i] > 0) {
          if (f(a[i] * k, 1, n) != -1) {
            h = h - 1;
            b[f(a[i] * k, 1, n)] = -1;
          }
        }
      }
      printf("%I64d\n", h);
    } else {
      printf("%I64d", n);
    }
  }
}
