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 PHP (7.4.4) (judge verdict: Time Limit Exceeded)

<?php
  list($n, $k) = explode(" ", trim(fgets(STDIN)));
  $n=intval($n);
  $k=intval($k);

  $N=1;
  while ($N < 300010) {
    $N *= 2;
  }
  $tree=array_fill(0, $N*2-1, 0);


  for($i=0;$i<$n;++$i){
    $a=trim(fgets(STDIN));
    $a=(int)$a;
    $x = sub_query(max($a-$k,0), min($a+$k,300000)+1, 0, 0, $N) + 1;
    update($a,$x);
  }
  echo sub_query(0,300000, 0, 0, $N);

  function update($i, $value){
    global $tree, $N;
    $i = $N + $i - 1;
    $tree[$i] = $value;
    while ($i > 0) {
      $i = intdiv($i - 1, 2);
      $tree[$i] = max($tree[$i * 2 + 1], $tree[$i * 2 + 2]);
    }
  }

  function sub_query($a, $b, $k, $l, $r){
    global $tree;
    if($r <= $a || $b <= $l){
      return 0;
    }
    if($a <= $l && $r <= $b){
      return $tree[$k];
    }else{
      $mid = intdiv($l+$r, 2);
      $lv = sub_query($a, $b, 2*$k+1, $l, $mid);
      $rv = sub_query($a, $b, 2*$k+2, $mid, $r);
      return max($lv, $rv);
    }
  }