Problem:
Score : 400 points

Problem Statement

You are given a sequence A_1, A_2, ..., A_N and an integer K.

Print the maximum possible length of a sequence B that satisfies the following conditions:

B is a (not necessarily continuous) subsequence of A.

For each pair of adjacents elements of B, the absolute difference of the elements is at most K.

Constraints

1 \leq N \leq 300,000

0 \leq A_i \leq 300,000

0 \leq K \leq 300,000

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K
A_1
A_2
:
A_N

Output

Print the answer.

Sample Input 1

10 3
1
5
4
3
8
6
9
7
2
4

Sample Output 1

7

For example, B = (1, 4, 3, 6, 9, 7, 4) satisfies the conditions.

It is a subsequence of A = (1, 5, 4, 3, 8, 6, 9, 7, 2, 4).

All of the absolute differences between two adjacent elements (|1-4|, |4-3|, |3-6|, |6-9|, |9-7|, |7-4|) are at most K = 3.

Solution in Haskell (GHC 8.8.3) (judge verdict: Time Limit Exceeded)


import Control.Monad
import Data.List

solveSub a [] k = [a]
solveSub a (b:s) k
    | abs (a - b) <= k = a : (solveSub b (s) k)
    | otherwise = (solveSub a (s) k)

solve [] k = []
solve (a:s) k = (length (solveSub a s k)) : (solve s k)


main = do
    [n,k] <- map read . words <$> getLine :: IO [Int]
    ass <- replicateM n (map read . words <$> getLine) :: IO [[Int]]
    let as = (concat ass)
    print $ maximum $ solve as k