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:64000000")
using namespace std;
const int INF = 1000 * 1000 * 1000;
const long long LINF = 1000000000000000000LL;
const double eps = 1e-9;
void prepare() {}
const int nmax = 100005;
set<long long> q;
int n, k;
int a[nmax];
bool solve() {
  scanf("%d%d", &n, &k);
  for (int i = 0; i < n; i++) {
    scanf("%d", &a[i]);
    q.insert(a[i]);
  }
  if (k == 1) {
    cout << n << endl;
    return false;
  }
  sort(a, a + n);
  for (int i = 0; i < n; i++) {
    if (q.find(a[i]) != q.end()) q.erase((long long)a[i] * k);
  }
  cout << (int)q.size() << endl;
  return false;
}
int main() {
  prepare();
  while (solve())
    ;
  return 0;
}
