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}.
from math import ceil

def r():
    return map(int, raw_input().split())

def find(el, cont, low=None, high=None):
    low = low or 0
    high = high or len(cont)
    
    if low == high:
        return None if el != cont[low] else low

    mid = (low + high)/2
    if mid == low:
        return None if el != cont[low] else low

    midel = cont[mid]

    if midel == el:
        return mid 

    return find(el, cont, low if (midel > el) else mid, high if (midel < el) else mid) 

def main():
    n, k = r()
    a = sorted(r())
    s = set()

    for x in a:
        if x % k != 0:
            #print "not dived", x
            s.add(x)
        else:
            xk = x/k
            if find(xk, a) is not None:
                if xk not in s:
                    #print "not found in S", xk
                    s.add(x)
            else:
                #print "not found in seq", xk
                s.add(x)

    print len(s)

if __name__ == "__main__":
    main()