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 11.0.6) (judge verdict: Accepted)

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;

 
public class Main {
	static final long MOD1=1000000007;
	static final long MOD2=998244353;
	public static void main(String[] args) {
		PrintWriter out = new PrintWriter(System.out);
		InputReader sc=new InputReader(System.in);
		int N=sc.nextInt();
		int K=sc.nextInt();
		int[] A=sc.nextIntArray(N);
		SegTree<Integer> segTree=new SegTree<Integer>(300001, (x,y)->Math.max(x, y), 0);
		for (int i = 0; i < A.length; i++) {
			int max=segTree.prod(Math.max(0, A[i]-K), Math.min(300001, K+A[i]+1));
			segTree.set(A[i], max+1);
		}
		System.out.println(segTree.allProd());
	}
	static class SegTree<S> {
		    final int MAX;

		    final int N;
		    final java.util.function.BinaryOperator<S> op;
		    final S E;

		    final S[] data;

		    @SuppressWarnings("unchecked")
		    public SegTree(int n, java.util.function.BinaryOperator<S> op, S e) {
		        this.MAX = n;
		        int k = 1;
		        while (k < n) k <<= 1;
		        this.N = k;
		        this.E = e;
		        this.op = op;
		        this.data = (S[]) new Object[N << 1];
		        java.util.Arrays.fill(data, E);
		    }

		    public SegTree(S[] dat, java.util.function.BinaryOperator<S> op, S e) {
		        this(dat.length, op, e);
		        build(dat);
		    }

		    private void build(S[] dat) {
		        int l = dat.length;
		        System.arraycopy(dat, 0, data, N, l);
		        for (int i = N - 1; i > 0; i--) {
		            data[i] = op.apply(data[i << 1 | 0], data[i << 1 | 1]);
		        }
		    }

		    public void set(int p, S x) {
		        exclusiveRangeCheck(p);
		        data[p += N] = x;
		        p >>= 1;
		        while (p > 0) {
		            data[p] = op.apply(data[p << 1 | 0], data[p << 1 | 1]);
		            p >>= 1;
		        }
		    }

		    public S get(int p) {
		        exclusiveRangeCheck(p);
		        return data[p + N];
		    }

		    public S prod(int l, int r) {
		        if (l > r) {
		            throw new IllegalArgumentException(
		                String.format("Invalid range: [%d, %d)", l, r)
		            );
		        }
		        inclusiveRangeCheck(l);
		        inclusiveRangeCheck(r);
		        S sumLeft = E;
		        S sumRight = E;
		        l += N; r += N;
		        while (l < r) {
		            if ((l & 1) == 1) sumLeft = op.apply(sumLeft, data[l++]);
		            if ((r & 1) == 1) sumRight = op.apply(data[--r], sumRight);
		            l >>= 1; r >>= 1;
		        }
		        return op.apply(sumLeft, sumRight);
		    }

		    public S allProd() {
		        return data[1];
		    }

		    public int maxRight(int l, java.util.function.Predicate<S> f) {
		        inclusiveRangeCheck(l);
		        if (!f.test(E)) {
		            throw new IllegalArgumentException("Identity element must satisfy the condition.");
		        }
		        if (l == MAX) return MAX;
		        l += N;
		        S sum = E;
		        do {
		            l >>= Integer.numberOfTrailingZeros(l);
		            if (!f.test(op.apply(sum, data[l]))) {
		                while (l < N) {
		                    l = l << 1;
		                    if (f.test(op.apply(sum, data[l]))) {
		                        sum = op.apply(sum, data[l]);
		                        l++;
		                    }
		                }
		                return l - N;
		            }
		            sum = op.apply(sum, data[l]);
		            l++;
		        } while ((l & -l) != l);
		        return MAX;
		    }

		    public int minLeft(int r, java.util.function.Predicate<S> f) {
		        inclusiveRangeCheck(r);
		        if (!f.test(E)) {
		            throw new IllegalArgumentException("Identity element must satisfy the condition.");
		        }
		        if (r == 0) return 0;
		        r += N;
		        S sum = E;
		        do {
		            r--;
		            while (r > 1 && (r & 1) == 1) r >>= 1;
		            if (!f.test(op.apply(data[r], sum))) {
		                while (r < N) {
		                    r = r << 1 | 1;
		                    if (f.test(op.apply(data[r], sum))) {
		                        sum = op.apply(data[r], sum);
		                        r--;
		                    }
		                }
		                return r + 1 - N;
		            }
		            sum = op.apply(data[r], sum);
		        } while ((r & -r) != r);
		        return 0;
		    }

		    private void exclusiveRangeCheck(int p) {
		        if (p < 0 || p >= MAX) {
		            throw new IndexOutOfBoundsException(
		                String.format("Index %d out of bounds for the range [%d, %d).", p, 0, MAX)
		            );
		        }
		    }

		    private void inclusiveRangeCheck(int p) {
		        if (p < 0 || p > MAX) {
		            throw new IndexOutOfBoundsException(
		                String.format("Index %d out of bounds for the range [%d, %d].", p, 0, MAX)
		            );
		        }
		    }
		}

	static class UnionFindTree{
    	int[] par;
    	int[] rank;
    	int[] size;
    	int[] diff_weight;
    	int arraysize;
    	public UnionFindTree(int n) {
    		this.par=new int[n];
    		this.rank=new int[n];
    		this.size=new int[n];
    		this.diff_weight=new int[n];
    		arraysize=n;
    		for (int i = 0; i < arraysize; i++) {
				set(i);
			}
    	}
    	public void set(int i) {
    		par[i]=i;
    		rank[i]=0;
    		size[i]=1;
    		diff_weight[i]=0;
    	}
    	public void union(int x,int y,int w) {
    		w += weight(x); 
    		w -= weight(y);
    		int rootx=find(x);
    		int rooty=find(y);
    		if (rootx==rooty) {
				return;
			}
    		if (rank[rootx]>rank[rooty]) {
				par[rooty]=rootx;
				diff_weight[rooty] = w;
				size[rootx]+=size[rooty];
			}
    		else if (rank[rootx]<rank[rooty]) {
				par[rootx]=rooty;
				w=-w;
				diff_weight[rootx] = w;
				size[rooty]+=size[rootx];
			}
    		else {
    			par[rooty]=rootx;
    			diff_weight[rooty] = w;
    			rank[rootx]++;
				size[rootx]+=size[rooty];
			}
    	}
    	public int find(int x) {
    		if(par[x] == x) return x;
    		int r = find(par[x]);
    		diff_weight[x] += diff_weight[par[x]];
    		return par[x] = r;
    	}
    	public int weight(int x) {
    		find(x);
    		return diff_weight[x];
    	}
    	public int size(int i) {
            return size[find(i)];
        }
    	public int diff(int x, int y) {
    		return weight(y) - weight(x);
    	}
    	public boolean same(int x, int y) {
            return find(x) == find(y);
        }
    }

		static class InputReader { 
		private InputStream in;
		private byte[] buffer = new byte[1024];
		private int curbuf;
		private int lenbuf;
		public InputReader(InputStream in) {
			this.in = in;
			this.curbuf = this.lenbuf = 0;
		}
 
		public boolean hasNextByte() {
			if (curbuf >= lenbuf) {
				curbuf = 0;
				try {
					lenbuf = in.read(buffer);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (lenbuf <= 0)
					return false;
			}
			return true;
		}
 
		private int readByte() {
			if (hasNextByte())
				return buffer[curbuf++];
			else
				return -1;
		}
 
		private boolean isSpaceChar(int c) {
			return !(c >= 33 && c <= 126);
		}
 
		private void skip() {
			while (hasNextByte() && isSpaceChar(buffer[curbuf]))
				curbuf++;
		}
 
		public boolean hasNext() {
			skip();
			return hasNextByte();
		}
 
		public String next() {
			if (!hasNext())
				throw new NoSuchElementException();
			StringBuilder sb = new StringBuilder();
			int b = readByte();
			while (!isSpaceChar(b)) {
				sb.appendCodePoint(b);
				b = readByte();
			}
			return sb.toString();
		}
 
		public int nextInt() {
			if (!hasNext())
				throw new NoSuchElementException();
			int c = readByte();
			while (isSpaceChar(c))
				c = readByte();
			boolean minus = false;
			if (c == '-') {
				minus = true;
				c = readByte();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res = res * 10 + c - '0';
				c = readByte();
			} while (!isSpaceChar(c));
			return (minus) ? -res : res;
		}
 
		public long nextLong() {
			if (!hasNext())
				throw new NoSuchElementException();
			int c = readByte();
			while (isSpaceChar(c))
				c = readByte();
			boolean minus = false;
			if (c == '-') {
				minus = true;
				c = readByte();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res = res * 10 + c - '0';
				c = readByte();
			} while (!isSpaceChar(c));
			return (minus) ? -res : res;
		}
 
		public double nextDouble() {
			return Double.parseDouble(next());
		}
 
		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;
		}
 
		public char[][] nextCharMap(int n, int m) {
			char[][] map = new char[n][m];
			for (int i = 0; i < n; i++)
				map[i] = next().toCharArray();
			return map;
		}
	}
}