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
k = int(sys.stdin.readline().split()[1])
t = list(map(lambda s: int(s), sys.stdin.readline().split()))
t.sort()
# print(t)
def find(x, a, b):
    while True:
        if a == b:
            if x == t[a]:
                return a
            else:
                return None
        m = a + (b - a) // 2
        if x > t[m]:
            a = m + 1
        else:
            b = m
u = [True for i in t]
s = 0
for i in range(len(t)):
    if u[i]:
        s += 1
        u[i] = False
        j = find(t[i] * k, 0, len(t) - 1)
        # print(t[i] * k, j)
        if j is not None:
            u[j] = False
print(s)