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++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
#define Int int64_t

using namespace std;

template <typename T>
struct SegmentTree {
private:
	size_t n;
	vector<T> node;
	T M0;

public:
	SegmentTree(const vector<T>& v, T m0) {
		M0 = m0;
		n = 1;
		while (n < v.size()) { n *= 2; }
		node.assign(2*n - 1, M0);

		for (int i = 0; i < v.size(); ++i) {
			node[n - 1 + i] = v[i];
		}
		for (int i = n - 2; i >= 0; --i) {
			node[i] = merge(node[2*i + 1], node[2*i + 2]);
		}
	}

	T merge(T a, T b) { return max(a, b); }

	void update(int x, T val) {
		x += (n - 1);
		node[x] = val;
		while (x > 0) {
			x = (x - 1) / 2;
			node[x] = merge(node[2*x + 1], node[2*x + 2]);
		}
	}

	T query(int a, int b, int k=0, int l=0, int r=-1) {
		if (r < 0) { r = n; }
		if ((r <= a) || (b <= l)) { return M0; }
		if ((a <= l) && (r <= b)) { return node[k]; }

		T vl = query(a, b, 2*k + 1, l, (l + r) / 2);
		T vr = query(a, b, 2*k + 2, (l + r) / 2, r);
		return merge(vl, vr);
	}
};

int main() {
	int N, K;
	cin >> N >> K;
	vector<int> A(N);
	for (int i = 0; i < N; ++i) { cin >> A[i]; }

	constexpr int maxA = 300000;
	SegmentTree<int> seg(vector<int>(maxA + 10, 0), 0);
	for (int i = 0; i < N; ++i) {
		int l = max(0, A[i] - K);
		int r = min(maxA, A[i] + K);
		seg.update(A[i], seg.query(l, r + 1) + 1);
	}
	cout << seg.query(0, maxA + 1) << "\n";

	return 0;
}