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 traceback
import math
from collections import defaultdict
from functools import lru_cache


def main():
    N, k = map(int, input().split())
    nums = list(map(int, input().split()))
    nums.sort()
    s = set(nums)
    g1, g2 = [], []
    done = set()
    for n in nums:
        if n in done:
            g2.append(n*k)
        else:
            g1.append(n)
            if n*k in s:
                done.add(n*k)
    return len(max([g1, g2], key=len))


ans = main()
print(ans)

# try:
#     ans = main()
#     print(ans)
# except Exception as e:
#     # print(e)
#     traceback.print_exc()