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}.
n, k = map(int, input().split())
a = [*map(int, input().split())]

a.sort()

def binary_search(arr, value):
    first, last = 0, len(arr)-1
    while first <= last:
        mid = (first + last) // 2
        if arr[mid] == value:
            return mid
        elif arr[mid] < value:
            first = mid + 1
        else:
            last = mid - 1
    return -1

ans = 0
for i in range(n):
    if a[i] != -1:
        ans += 1
        id = binary_search(a, a[i]*k)
        if id != -1:
            a[id] = -1

print(ans)