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;
void read(int &x) {
  int flag = 1;
  char ch;
  x = 0;
  for (ch = getchar(); (ch < '0' || ch > '9') && ch != '-'; ch = getchar())
    ;
  if (ch == '-') {
    flag = -1;
    ch = getchar();
  }
  for (; ch >= '0' && ch <= '9'; x = x * 10 + ch - 48, ch = getchar())
    ;
  x *= flag;
}
int a[100005], b[100005], n, k;
int slove(int i) {
  if (!b[i]) {
    return 0;
  }
  int left = i + 1, right = n, mid;
  while (left < right) {
    mid = (left + right) / 2;
    if (a[mid] % k == 0 && a[mid] / k == a[i]) {
      b[mid] = 0;
      return 1;
    } else if (a[mid] / k > a[i] || (a[mid] / k == a[i] && a[mid] % k > 0))
      right = mid;
    else
      left = mid + 1;
  }
  return 1;
}
int main(int argc, char const *argv[]) {
  scanf("%d%d", &n, &k);
  for (int i = 0; i < n; ++i) {
    scanf("%d", a + i);
    b[i] = 1;
  }
  sort(a, a + n);
  int sum = 0;
  for (int i = 0; i < n; ++i) {
    sum += slove(i);
  }
  printf("%d\n", sum);
  return 0;
}
