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 C# (.NET Core 3.1.201) (judge verdict: Time Limit Exceeded)

using System;
using System.Linq;
using System.Collections.Generic;

using E = System.Linq.Enumerable;

public class Program
{
    public static void Main()
    {
        var nk = Console.ReadLine().Split().Select(x => int.Parse(x)).ToArray();
        var (n, k) = (nk[0], nk[1]);
        var seqA = Console.In.ReadToEnd().Split().Where(x => !string.IsNullOrWhiteSpace(x)).Select(x => int.Parse(x)).ToArray();

        var max = Dfs(k, seqA, -1, 0);

        Console.WriteLine(max);
    }

    static int Dfs(int k, Span<int> xs, int t, int length)
    {
        if (xs.Length < 1)
        {
            return length;
        }

        var d = t < 0 ? 0 : Math.Abs(xs[0] - t);
        var l = Dfs(k, xs[1..], t, length);
        if (d > k)
        {
            return l;
        }

        return Math.Max(l, Dfs(k, xs[1..], xs[0], length + 1));
    }
}