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,raw_input().split())

a = {}

if n==1:
 print 1
 exit()

b = [ int(x) for x in raw_input().split()]
b.sort()

lenb = len(b)

#print b
for i in xrange(lenb):
 a[b[i]]=i

#print a
for i in xrange(lenb):
 #print b[i],i
 next = b[i]*k
 if b[i]!=-1 and next in a and b[i] != next:
  b[a[next]]= -1
  #print "here",a[b[i]*k]
  del a[b[i]*k]
  n-=1 
 #print a
print n
