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 Ruby (2.7.1) (judge verdict: Accepted)

class ST
	def initialize n
		@l = (1<<(n-1).bit_length)-1
		@h = [0]*(@l+@l+1)
	end
 
	def max
		return @h[0]
	end
 
	def [] l,r
		return if r < l
		l,r = @l+l+1,@l+r+1
		lx,rx = @h[l-1],@h[r-1]
		while l <= r
			lx = @h[l-1] if lx < @h[l-1]
			rx = @h[r-1] if rx < @h[r-1]
			l = (l+1)/2
			r = (r-1)/2
		end
		return lx < rx ? rx : lx
	end
 
	def []= i,v
		j = @l+i+1
		@h[j-1] = v
		@h[j-1] = v while 0 < (j/=2) && @h[j-1] < v
		return v
	end
end

N,K = gets.split.map(&:to_i)
max = ST.new 3000001
N.times{
	a = gets.to_i
	max[a] = 1+max[[a-K,0].max,[300000,a+K].min]
}
p max.max