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}.
import io, os
input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline

n, k = map(int, input().split())
a = list(map(int, input().split()))
a.sort()

def search(a, t):
    l = 0
    r = len(a)-1
    
    while (r-l)>=0:
        mid = (l+r)//2
        if a[mid] == t:
            return mid
        if a[mid] < t:
            l = mid+1
        if a[mid] > t:
            r = mid-1
            
    return -1

if k == 1:
    print(n)
else:
    v = [0]*n
    ct = 0
    
    for i in range(n):
        if not v[i]:
            q = a[i]
            in_ct = 0
            while search(a, q) != -1:
                v[search(a, q)] = 1
                in_ct += 1
                q *= k
                
            ct += (in_ct+1)//2
            
    print(ct)