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}.
def binary_search(a, x, lo, hi) : 
    while lo < hi : 
        mid = (lo + hi) / 2
        if a[mid] == x : 
            return True
        elif a[mid] < x : 
            lo = mid + 1
        else : 
            hi = mid
    return False
n, k = map(int, raw_input().split())
a = map(int, raw_input().split())
a.sort()
n = len(a)
if k == 1 : 
    print(n)
else : 
    result = 0
    for i in a : 
        if i % k == 0 and binary_search(a, i / k, 0, n) : 
            pass
        else : 
            add = 1
            j = i * k
            while binary_search(a, j, 0, n) : 
                j *= k
                add += 1
            result += (add + 1) / 2
    print(result)