A. Wallpaper
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Igor is renovating again! Once more! This wallpaper! It's everywhere! On every wall!

This renovation is maddening; the next stage of wallpapering has begun. Igor has a very unusual house: it has $$$n$$$ walls, each is $$$3$$$ meters high and $$$a_i$$$ meters wide. Igor came to the hardware store to buy wallpaper. It turns out that there is an infinite number of rolls, each measuring $$$k$$$ meters wide and $$$3$$$ meters high. Our hero wants to save money, so he wants to buy as few rolls as possible. To wallpaper each wall, Igor decided to buy enough rolls so that, for each of wall, all but possibly one roll would be used to its full width of $$$k$$$. If a section less than $$$k$$$ meters wide remains uncovered with wallpaper, Igor cuts the needed piece from a full roll and then doesn't use that roll again for aesthetic reasons (yes, he wants to save money on buying rolls, but not too much). Help Igor calculate how many rolls of wallpaper he needs.

Input

The first line contains two integers $$$n$$$, $$$k$$$ $$$(1 \leq n, k \leq 10^6)$$$ — the number of walls in Igor's house and the width of the wallpaper roll.

The second line contains $$$n$$$ integers $$$a_i$$$ $$$(1 \leq a_i \leq 10^9)$$$ — the width of the $$$i$$$-th wall in Igor's house.

Output

Help Igor determine how many rolls of wallpaper he will need! Igor is too exhausted to calculate it himself.

Examples
Input
4 5
10 13 20 21
Output
14
Input
3 1
5 6 3
Output
14
Input
4 8
8 16 32 33
Output
12
Note

In the first test example, each wall will require 2, 3, 4 and 5 rolls, respectively.