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())
ai = list(map(int,input().split()))
def binsearch(num):
    high = n-1
    low = 0
    mid = (high + low) // 2
    while high >= low:
        if ai[mid] < num:
            low = mid + 1
        elif ai[mid] > num:
            high = mid - 1
        else:
            return mid
        mid = (high + low) // 2
    return -1
ai.sort()
ar = [0]*n
ans = 0
for i in range(n):
    if ar[i]:
        continue
    num = binsearch(ai[i] * k)
    if num != -1:
        ar[num] = 1
        ans += 1
if k == 1:
    ans = 0
print(n - ans)
