Angie is going on vacation!
But she has too much stuff she wants to bring! She has ~N~ items, each with a height of ~h_i~. However, her suitcase is quite special, it can fit as many items in it as she wants as long as they have a height range of ~K~ or less. The height range is the absolute difference between the maximum height of any item in the suitcase and the minimum height of any item in the suitcase.
Being a logical person, Angie wants to fit as many items in her suitcase as she can. Can you help her figure out how many?
For all subtasks:
~1 \le h_i, K \le 10^9~
Subtask 1 [10%]
~1 \le N \le 20~
Subtask 2 [15%]
~1 \le N \le 2 \times 10^3~
Subtask 3 [75%]
~1 \le N \le 2 \times 10^5~
The first line contains the space separated integers ~N~ and ~K~.
The second line of input contains ~N~ space separated integers ~h_1, h_2, h_3, ..., h_n~.
Output the most amount of items Angie can bring in her suitcase.
5 3 25 9 1 6 8
She can bring items ~2~, ~4~, and ~5~ for a height range of ~3~.