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: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading.Tasks;
using static System.Math;
using MethodImplAttribute = System.Runtime.CompilerServices.MethodImplAttribute;
using MethodImplOptions = System.Runtime.CompilerServices.MethodImplOptions;
public static class P
{
    public static void Main()
    {
        var nk = Console.ReadLine().Split().Select(int.Parse).ToArray();
        var k = nk[1];
        SegmentTree<int> segTree = new SegmentTree<int>(300001, 0, Max);
        for (int i = 0; i < nk[0]; i++)
        {
            var a = int.Parse(Console.ReadLine());
            segTree[a] = segTree.Query(Max(0, a - k), Min(300000, a + k)) + 1;
        }
        Console.WriteLine(segTree.Query(0, 300000));
    }
}


class SegmentTree<T>
{
    public int Size { get; private set; }
    T Identity;
    T[] Data;
    Func<T, T, T> Merge;
    int LeafCount;

    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public SegmentTree(int size, T identity, Func<T, T, T> merge)
    {
        Init(size, identity, merge);
        for (int i = 1; i < Data.Length; i++) Data[i] = identity;
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public SegmentTree(T[] elems, T identity, Func<T, T, T> merge)
    {
        Init(elems.Length, identity, merge);
        elems.CopyTo(Data, LeafCount);
        for (int i = elems.Length + LeafCount; i < Data.Length; i++) Data[i] = identity;
        for (int i = LeafCount - 1; i >= 1; i--) Data[i] = Merge(Data[i << 1], Data[(i << 1) | 1]);
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    private void Init(int size, T identity, Func<T, T, T> merge)
    {
        Size = size;
        Identity = identity;
        Merge = merge;
        LeafCount = 1;
        while (LeafCount < size) LeafCount <<= 1;
        Data = new T[LeafCount << 1];
    }

    public T this[int index]
    {
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        get { return Data[LeafCount + index]; }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        set { Update(index, value); }
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public void Update(int i, T x) { Data[i += LeafCount] = x; while (0 < (i >>= 1)) Data[i] = Merge(Data[i << 1], Data[(i << 1) | 1]); }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public void Operate(int i, T x) { Data[i += LeafCount] = Merge(Data[i], x); while (0 < (i >>= 1)) Data[i] = Merge(Data[i << 1], Data[(i << 1) | 1]); }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public T Query(int l, int r)
    {
        T lRes = Identity, rRes = Identity;
        for (l += LeafCount, r += LeafCount; l <= r; l = (l + 1) >> 1, r = (r - 1) >> 1)
        {
            if ((l & 1) == 1) lRes = Merge(lRes, Data[l]); if ((r & 1) == 0) rRes = Merge(Data[r], rRes);
        }
        return Merge(lRes, rRes);
    }
}