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, raw_input().split())
a = map(int, raw_input().split())
b = {}
fa = [i for i in range(n)]
num = [1 for i in range(n)]
def find_set(i):
    if fa[i] == i:
        return i
    fa[i]=find_set(fa[i])
    return fa[i]
def union(i, j):
    i1 = find_set(i)
    j1 = find_set(j)
    fa[i1] = j1
    num[j1] += num[i1]
for i in range(n):
    if a[i]%k==0:
        tmp = b.get(a[i]/k)
        if tmp != None:
            union(i, tmp)
    tmp = b.get(a[i]*k)
    if tmp != None:
        union(tmp, i)
    b[a[i]] = i
s = 0
for i in range(n):
    if fa[i] == i:
        s += (num[i]+1)/2
print s
