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 Java (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;
import java.io.*;
 
public class Main {
    public static void main(String[] args) throws Exception {
        FastScanner sc = new FastScanner(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        StringBuilder sb = new StringBuilder();
        int N = sc.nextInt();
        int K = sc.nextInt();
        int[] a = sc.nextIntArray(N);
        TwoSAT ts = new TwoSAT(N);
        for(int i = 0; i < N; i++){
             for (int j = i + 1; j < N; j++) {
                int x = a[i];
                int y = a[j];
                if(Math.abs(x-y) > K){
                    ts.addNand(i, false, j, false);
                }else{
                    break;
                }
                
            }
        }
        
        if(ts.satisfiable()) {
            int ans = 0;
            boolean[] b = ts.answer();
            //pw.println(Arrays.toString(b));
            for(int i = 0; i < N; i++) {
                if(!b[i]){
                    ans++;
                }
            }
            pw.println(ans);
        }
        pw.flush();
    }

    static class GeekInteger {
        public static void save_sort(int[] array) {
            shuffle(array);
            Arrays.sort(array);
        }
 
        public static int[] shuffle(int[] array) {
            int n = array.length;
            Random random = new Random();
            for (int i = 0, j; i < n; i++) {
                j = i + random.nextInt(n - i);
                int randomElement = array[j];
                array[j] = array[i];
                array[i] = randomElement;
            }
            return array;
        }
 
    }
}

/**
 * @verified https://atcoder.jp/contests/practice2/submissions/16647102
 */
class TwoSAT {
    private final int n;
    private final InternalSCC scc;
    private final boolean[] answer;

    private boolean hasCalledSatisfiable = false;
    private boolean existsAnswer = false;

    public TwoSAT(int n) {
        this.n = n;
        this.scc = new InternalSCC(2 * n);
        this.answer = new boolean[n];
    }

    public void addClause(int x, boolean f, int y, boolean g) {
        scc.addEdge(x << 1 | (f ? 0 : 1), y << 1 | (g ? 1 : 0));
        scc.addEdge(y << 1 | (g ? 0 : 1), x << 1 | (f ? 1 : 0));
    }

    public void addImplication(int x, boolean f, int y, boolean g) {
        addClause(x, !f, y, g);
    }

    public void addNand(int x, boolean f, int y, boolean g) {
        addClause(x, !f, y, !g);
    }

    public boolean satisfiable() {
        hasCalledSatisfiable = true;
        int[] ids = scc.ids();
        for (int i = 0; i < n; i++) {
            if (ids[i << 1 | 0] == ids[i << 1 | 1]) return existsAnswer = false;
            answer[i] = ids[i << 1 | 0] < ids[i << 1 | 1];
        }
        return existsAnswer = true;
    }

    public boolean[] answer() {
        if (!hasCalledSatisfiable) {
            throw new UnsupportedOperationException(
                "Call TwoSAT#satisfiable at least once before TwoSAT#answer."
            );
        }
        if (existsAnswer) return answer;
        return null;
    }

    private static final class EdgeList {
        long[] a;
        int ptr = 0;
        EdgeList(int cap) {a = new long[cap];}
        void add(int upper, int lower) {
            if (ptr == a.length) grow();
            a[ptr++] = (long) upper << 32 | lower;
        }
        void grow() {
            long[] b = new long[a.length << 1];
            System.arraycopy(a, 0, b, 0, a.length);
            a = b;
        }
    }

    private static final class InternalSCC {
        final int n;
        int m;
        final EdgeList unorderedEdges;
        final int[] start;
        InternalSCC(int n) {
            this.n = n;
            this.unorderedEdges = new EdgeList(n);
            this.start = new int[n + 1];
        }
        void addEdge(int from, int to) {
            unorderedEdges.add(from, to);
            start[from + 1]++;
            this.m++;
        }
        static final long mask = 0xffff_ffffl;
        int[] ids() {
            for (int i = 1; i <= n; i++) {
                start[i] += start[i - 1];
            }
            int[] orderedEdges = new int[m];
            int[] count = new int[n + 1];
            System.arraycopy(start, 0, count, 0, n + 1);
            for (int i = 0; i < m; i++) {
                long e = unorderedEdges.a[i];
                orderedEdges[count[(int) (e >>> 32)]++] = (int) (e & mask);
            }
            int nowOrd = 0;
            int groupNum = 0;
            int k = 0;
            int[] par = new int[n];
            int[] vis = new int[n];
            int[] low = new int[n];
            int[] ord = new int[n];
            java.util.Arrays.fill(ord, -1);
            int[] ids = new int[n];
            long[] stack = new long[n];
            int ptr = 0;
            
            for (int i = 0; i < n; i++) {
                if (ord[i] >= 0) continue;
                par[i] = -1;
                stack[ptr++] = i;
                while (ptr > 0) {
                    long p = stack[--ptr];
                    int u = (int) (p & mask);
                    int j = (int) (p >>> 32);
                    if (j == 0) {
                        low[u] = ord[u] = nowOrd++;
                        vis[k++] = u;
                    }
                    if (start[u] + j < count[u]) {
                        int to = orderedEdges[start[u] + j];
                        stack[ptr++] += 1l << 32;
                        if (ord[to] == -1) {
                            stack[ptr++] = to;
                            par[to] = u;
                        } else {
                            low[u] = Math.min(low[u], ord[to]);
                        }
                    } else {
                        while (j --> 0) {
                            int to = orderedEdges[start[u] + j];
                            if (par[to] == u) low[u] = Math.min(low[u], low[to]);
                        }
                        if (low[u] == ord[u]) {
                            while (true) {
                                int v = vis[--k];
                                ord[v] = n;
                                ids[v] = groupNum;
                                if (v == u) break;
                            }
                            groupNum++;
                        }
                    }
                }
            }
            for (int i = 0; i < n; i++) {
                ids[i] = groupNum - 1 - ids[i];
            }
            return ids;
        }
    }
}


class FastScanner {
    private BufferedReader reader = null;
    private StringTokenizer tokenizer = null;
    public FastScanner(InputStream in) {
        reader = new BufferedReader(new InputStreamReader(in));
        tokenizer = null;
    }

    public String next() {
        if (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }

    public String nextLine() {
        if (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                return reader.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken("\n");
    }

    public long nextLong() {
        return Long.parseLong(next());
    }

    public int nextInt() {
        return Integer.parseInt(next());
    }

    public double nextDouble() {
         return Double.parseDouble(next());
    }
    
    public String[] nextArray(int n) {
        String[] a = new String[n];
        for (int i = 0; i < n; i++)
            a[i] = next();
        return a;
    }

    public int[] nextIntArray(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++)
            a[i] = nextInt();
        return a;
    }

    public long[] nextLongArray(int n) {
        long[] a = new long[n];
        for (int i = 0; i < n; i++)
            a[i] = nextLong();
        return a;
    } 
}