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 sys
import math

MAXNUM = math.inf
MINNUM = -1 * math.inf


def getInts():
    return map(int, sys.stdin.readline().rstrip().split(" "))


def getString():
    return sys.stdin.readline().rstrip()


def solve(n, k, ints):
    cache = {}
    total = 0

    for ele in ints:
        length = 1
        if (ele * k) in cache:
            after = ele * k
            end = cache[after][1]  # 1 is end of series
            total -= ((cache[after][2]) + 1) // 2  # max length of this sequence
            length += cache[after][2]
        else:
            end = ele

        if ele % k == 0 and (ele // k) in cache:
            before = ele // k
            start = cache[before][0]  # 0 is start of series
            total -= ((cache[before][2]) + 1) // 2  # length
            length += cache[before][2]
        else:
            start = ele

        cache[start] = (start, end, length)
        cache[end] = (start, end, length)
        total += ((length) + 1) // 2

    return total


def printOutput(ans):
    sys.stdout.write(str(ans))


def readinput():
    n, k = getInts()
    ints = list(getInts())
    printOutput(solve(n, k, ints))


readinput()
