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 = input()
n = n.split(' ')
(a,b)  = (int(n[0]),int(n[1]))

A = []    # 
S = []    # salidas

k=b   #Multiplicador K

o = map(int,input().split(" "))

A = sorted(list(o))
#o = input()
#O = o.split(' ')

#for i in range(a):   #Cantidad de números
#  A.append(int(o[i]))

for i in A:
  if i % k!=0:    # no es posible que y = xk
    S.append(i)
  elif i//k not in S: #de ser posible, x no se encuentra en la lista
    S.append(i)

l = len(S)
print(l)
 		 		   	 	  		 	 				  		  	