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)

#region インクルード
using System;
using System.Collections.Generic;
using System.Collections;
using System.Linq;
using System.IO;
using System.Threading;
using System.Text;
using System.Text.RegularExpressions;
using System.Diagnostics;
using static util;
using P = pair<int, int>;
using static System.Math;
#endregion

class Solver
{
    #region Template
    StreamWriter sw;
    Scan sc;
    void Prt(string a) => sw.WriteLine(a);
    void Prt<T>(IEnumerable<T> a) => Prt(string.Join(" ", a));
    void Prt(params object[] a) => Prt(string.Join(" ", a));
    public Solver(StreamWriter sw)
    {
        this.sw = sw;
        this.sc = new Scan();
    }
    #endregion 
    static int[] A;
    static int K;
    static int N;
    static long[] ans;
    public void solve()
    {
        var NK = sc.IntArr;
        N = NK[0];
        K = NK[1];
        A = new int[N];
        var Seg = new SegmentTree(new int[300001]);
        for (int i = 0; i < N; i++)
        {
            A[i] = sc.Int;
        }
        for (int i = (int)N - 1; i >= 0; i--)
        {
            var tmp = Seg.GetMin(A[i] - K, A[i] + K + 1);
            Seg.Update(A[i], tmp - 1);
        }
        Prt((-1)*Seg.GetMin(0, 300002));
    }


    class SegmentTree
    {
        // 元の配列の大きさ
        public int N { get; set; }
        // セグメント木のデータ(2^n-1)
        public int[] Node { get; set; }

        // 元データの配列を引数で渡す
        public SegmentTree(int[] a)
        {
            // 要素数を2のべき乗とする
            N = 1;
            while (N < a.Length) N *= 2;

            // セグメント木の管理する要素数を 2^n-1 で初期化する
            this.Node = new int[2 * N - 1];
            for (int i = 0; i < this.Node.Length; i++) this.Node[i] = INF;

            // 各ノードの値を初期化する
            // 葉は元の配列のデータ
            for (int i = 0; i < a.Length; i++) this.Node[N + i - 1] = a[i];
            // 子ノードを比較して親ノードの値を決めていく
            for (int i = N - 2; i >= 0; i--)
            {
                this.Node[i] = this.Compare(this.Node[2 * i + 1], this.Node[2 * i + 2]);
            }
        }

        // x番目のデータをvに更新する
        public void Update(int x, int v)
        {
            // 元の配列のデータが格納される葉のデータを更新する
            x += (this.N - 1);
            this.Node[x] = v;

            // 更新したノードの親をさかのぼってルートまで更新する
            while (x > 0)
            {
                // 親ノードのインデックス
                x = (x - 1) / 2;
                this.Node[x] = this.Compare(this.Node[2 * x + 1], this.Node[2 * x + 2]);
            }
        }
        // [a, b) の区間最小値を求める
        public int GetMin(int a, int b)
        {
            return this.GetMin(a, b, 0, 0, this.N);
        }
        // [a, b) の区間最小値を求める
        // 現在のノードはk番目、[l, r)
        private int GetMin(int a, int b, int k, int l, int r)
        {
            // 1. 現在のノードの対応区間が、求める区間に含まれない場合
            //    対象外の区間のデータなので、最小値に関係のない値(INF)を返す
            if (r <= a || b <= l) return INF;

            // 2. 現在のノードの対応区間が、求める区間に完全に含まれる場合
            //    現在のノードの値が最小値の候補になるのでそのまま返す
            if (a <= l && r <= b) return this.Node[k];

            // 3. 上記以外の場合、現在のノードの対応区間が、求める区間を一部を含む場合
            //    子ノードを評価し、比較した結果を返す
            var vl = this.GetMin(a, b, 2 * k + 1, l, (l + r) / 2);
            var vr = this.GetMin(a, b, 2 * k + 2, (l + r) / 2, r);
            return this.Compare(vl, vr);
        }

        // 2要素を比較して小さい値を返す
        private int Compare(int a, int b) { return Math.Min(a, b); }
    }
    public static int INF = int.MaxValue;
}



#region メインクラス
class Program
{
    static void Main(string[] args)
    {
        var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
        var solver = new Solver(sw);
        // var t = new Thread(solver.solve, 1 << 26); // 64 MB
        // t.Start();
        // t.Join();
        solver.solve();
        sw.Flush();
    }
}
#endregion
#region pair
class pair<T, U> : IComparable<pair<T, U>>
{
    public T v1;
    public U v2;
    public pair() : this(default(T), default(U)) { }
    public pair(T v1, U v2) { this.v1 = v1; this.v2 = v2; }
    public int CompareTo(pair<T, U> a)
    {
        int c = Comparer<T>.Default.Compare(v1, a.v1);
        return c != 0 ? c : Comparer<U>.Default.Compare(v2, a.v2);
    }
    public override string ToString() => v1 + " " + v2;
    public void Deconstruct(out T a, out U b) { a = v1; b = v2; }
}
#endregion
#region util:使える小技集
static class util
{
    public static readonly int M = 1000000007;
    // public static readonly int M = 998244353;
    public static readonly long LM = 1L << 60;
    public static readonly double eps = 1e-11;
    public static void DBG(string a) => Console.Error.WriteLine(a);
    public static void DBG<T>(IEnumerable<T> a) => DBG(string.Join(" ", a));
    public static void DBG(params object[] a) => DBG(string.Join(" ", a));
    public static void Assert(params bool[] conds)
    {
        if (conds.Any(x => !x)) throw new Exception();
    }
    public static pair<T, U> make_pair<T, U>(T v1, U v2) => new pair<T, U>(v1, v2);
    public static int CompareList<T>(IList<T> a, IList<T> b) where T : IComparable<T>
    {
        for (int i = 0; i < a.Count && i < b.Count; i++)
            if (a[i].CompareTo(b[i]) != 0) return a[i].CompareTo(b[i]);
        return a.Count.CompareTo(b.Count);
    }
    public static bool inside(int i, int j, int h, int w) => i >= 0 && i < h && j >= 0 && j < w;
    static readonly int[] dd = { 0, 1, 0, -1 };
    // static readonly string dstring = "RDLU";
    public static P[] adjacents(int i, int j)
        => Enumerable.Range(0, dd.Length).Select(k => new P(i + dd[k], j + dd[k ^ 1])).ToArray();
    public static P[] adjacents(int i, int j, int h, int w)
        => Enumerable.Range(0, dd.Length).Select(k => new P(i + dd[k], j + dd[k ^ 1]))
                                         .Where(p => inside(p.v1, p.v2, h, w)).ToArray();
    public static P[] adjacents(this P p) => adjacents(p.v1, p.v2);
    public static P[] adjacents(this P p, int h, int w) => adjacents(p.v1, p.v2, h, w);
    public static Dictionary<T, int> compress<T>(this IEnumerable<T> a)
        => a.Distinct().OrderBy(v => v).Select((v, i) => new { v, i }).ToDictionary(p => p.v, p => p.i);
    public static Dictionary<T, int> compress<T>(params IEnumerable<T>[] a) => compress(a.Aggregate(Enumerable.Union));
    public static T[] inv<T>(this Dictionary<T, int> dic)
    {
        var res = new T[dic.Count];
        foreach (var item in dic) res[item.Value] = item.Key;
        return res;
    }
    public static void swap<T>(ref T a, ref T b) where T : struct { var t = a; a = b; b = t; }
    public static void swap<T>(this IList<T> a, int i, int j) where T : struct { var t = a[i]; a[i] = a[j]; a[j] = t; }
    public static T[] copy<T>(this IList<T> a)
    {
        var ret = new T[a.Count];
        for (int i = 0; i < a.Count; i++) ret[i] = a[i];
        return ret;
    }
    public static void Deconstruct<T>(this IList<T> v, out T a)
    {
        a = v[0];
    }
    public static void Deconstruct<T>(this IList<T> v, out T a, out T b)
    {
        a = v[0]; b = v[1];
    }
    public static void Deconstruct<T>(this IList<T> v, out T a, out T b, out T c)
    {
        a = v[0]; b = v[1]; c = v[2];
    }
    public static void Deconstruct<T>(this IList<T> v, out T a, out T b, out T c, out T d)
    {
        a = v[0]; b = v[1]; c = v[2]; d = v[3];
    }
    public static void Deconstruct<T>(this IList<T> v, out T a, out T b, out T c, out T d, out T e)
    {
        a = v[0]; b = v[1]; c = v[2]; d = v[3]; e = v[4];
    }
}
#endregion
#region スキャナー
class Scan
{
    StreamReader sr;
    public Scan() { sr = new StreamReader(Console.OpenStandardInput()); }
    public Scan(string path) { sr = new StreamReader(path); }
    public int Int => int.Parse(Str);
    public long Long => long.Parse(Str);
    public double Double => double.Parse(Str);
    public string Str => sr.ReadLine().Trim();
    public pair<T, U> Pair<T, U>()
    {
        T a; U b;
        Multi(out a, out b);
        return new pair<T, U>(a, b);
    }
    public P P => Pair<int, int>();
    public int[] IntArr => StrArr.Select(int.Parse).ToArray();
    public long[] LongArr => StrArr.Select(long.Parse).ToArray();
    public double[] DoubleArr => StrArr.Select(double.Parse).ToArray();
    public string[] StrArr => Str.Split(new[] { ' ' }, StringSplitOptions.RemoveEmptyEntries);
    bool eq<T, U>() => typeof(T).Equals(typeof(U));
    T ct<T, U>(U a) => (T)Convert.ChangeType(a, typeof(T));
    T cv<T>(string s) => eq<T, int>() ? ct<T, int>(int.Parse(s))
                       : eq<T, long>() ? ct<T, long>(long.Parse(s))
                       : eq<T, double>() ? ct<T, double>(double.Parse(s))
                       : eq<T, char>() ? ct<T, char>(s[0])
                                         : ct<T, string>(s);
    public void Multi<T>(out T a) => a = cv<T>(Str);
    public void Multi<T, U>(out T a, out U b)
    {
        var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]);
    }
    public void Multi<T, U, V>(out T a, out U b, out V c)
    {
        var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]);
    }
    public void Multi<T, U, V, W>(out T a, out U b, out V c, out W d)
    {
        var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]);
    }
    public void Multi<T, U, V, W, X>(out T a, out U b, out V c, out W d, out X e)
    {
        var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); e = cv<X>(ar[4]);
    }
}
#endregion