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}.
def bs (l=0,r=0,val=0):
    l1 =l
    r1 =r
    while (l1 <= r1):
         mid = (l1 + r1) // 2;

         if a[mid]  < val :
              l1= mid+1
         elif a[mid] > val:
              r1 = mid-1
         elif a [mid] == val :
             return mid  ;
    return -1

mark= {}
n,k= map (int,input().split());
a = list (map (int,input().split()))
a.sort()
sum =0
for i in range (0, n):
    if mark.get(i , False) == False:
        temp =bs(i,n-1,a[i]*k);
        mark[temp] = True ;
        sum +=1
print (sum)


