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, k, cnt;
vector<long long> vit;
vector<long long> num;
void find_(long long l, long long r, long long m) {
  if (l > r) return;
  long long mid = (r + l) / 2;
  if (num[mid] == m) {
    cnt++;
    vit[mid] = 1;
    find_(mid + 1, n - 1, m * k);
  } else if (m < num[mid]) {
    find_(l, mid - 1, m);
  } else if (m > num[mid]) {
    find_(mid + 1, r, m);
  }
}
int main() {
  while (cin >> n >> k) {
    num.clear();
    for (long long i = 0; i < n; i++) {
      long long number;
      cin >> number;
      num.push_back(number);
    }
    vit.resize(num.size());
    sort(num.begin(), num.end());
    long long sum = 0;
    long long p;
    for (long long i = 0; i < num.size(); i++) {
      if (vit[i] == 0) {
        cnt = 1;
        vit[i] = 1;
        find_(0, n - 1, num[i] * k);
        sum += (cnt + 1) / 2;
      }
    }
    printf("%lld\n", sum);
  }
  return 0;
}
