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 Rust (1.42.0) (judge verdict: Accepted)

use input_mcr::*;
use std::cmp::*;

pub struct SegmentTree<T> {
    n: usize,
    ini: T,
    xs: Vec<T>,
}

impl<T: Clone + Copy + PartialOrd> SegmentTree<T> {
    pub fn new(n: usize, ini: T) -> SegmentTree<T> {
        let n = (n + 3).next_power_of_two();
        SegmentTree {
            n,
            ini,
            xs: vec![ini; 2 * n],
        }
    }
    pub fn update(&mut self, i: usize, x: T) {
        let mut i = i + self.n;
        self.xs[i] = x;
        i = i / 2;
        while i != 0 {
            self.xs[i] = if self.xs[2 * i] > self.xs[2 * i + 1] {
                self.xs[2 * i]
            } else {
                self.xs[2 * i + 1]
            };
            i /= 2;
        }
    }
    pub fn get_range_max(&self, l: usize, r: usize) -> T {
        let mut l = l + self.n;
        let mut r = r + self.n;
        let mut res = self.ini;
        while l < r {
            if l & 1 != 0 {
                res = if res > self.xs[l] { res } else { self.xs[l] };
                l += 1;
            }
            if r & 1 != 0 {
                r -= 1;
                res = if res > self.xs[r] { res } else { self.xs[r] };
            }
            l /= 2;
            r /= 2;
        }
        res
    }
    pub fn get(&self, i: usize) -> T {
        let i = i + self.n;
        self.xs[i]
    }
}

fn main() {
    input! {
        n: usize,
        w: usize,
        xs: [i64; n],
    }
    let mut seg = SegmentTree::new(400000, 0i64);
    for &x in &xs {
        let l = max(0, x as i64 - w as i64) as usize;
        let r = min(x as usize + w + 1, 400000) as usize;
        let t = seg.get_range_max(l, r) + 1;
        seg.update(x as usize, t);
    }
    let res = seg.get_range_max(0, 400000);
    println!("{}", res);
}
pub mod input_mcr {
    // ref: tanakh <https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8>
    #[macro_export(local_inner_macros)]
    macro_rules! input {
        (source = $s:expr, $($r:tt)*) => {
            let mut parser = Parser::from_str($s);
            input_inner!{parser, $($r)*}
        };
        (parser = $parser:ident, $($r:tt)*) => {
            input_inner!{$parser, $($r)*}
        };
        (new_stdin_parser = $parser:ident, $($r:tt)*) => {
            let stdin = std::io::stdin();
            let reader = std::io::BufReader::new(stdin.lock());
            let mut $parser = Parser::new(reader);
            input_inner!{$parser, $($r)*}
        };
        ($($r:tt)*) => {
            input!{new_stdin_parser = parser, $($r)*}
        };
    }

    #[macro_export(local_inner_macros)]
    macro_rules! input_inner {
        ($parser:ident) => {};
        ($parser:ident, ) => {};
        ($parser:ident, $var:ident : $t:tt $($r:tt)*) => {
            let $var = read_value!($parser, $t);
            input_inner!{$parser $($r)*}
        };
    }

    #[macro_export(local_inner_macros)]
    macro_rules! read_value {
        ($parser:ident, ( $($t:tt),* )) => {
            ( $(read_value!($parser, $t)),* )
        };
        ($parser:ident, [ $t:tt ; $len:expr ]) => {
            (0..$len).map(|_| read_value!($parser, $t)).collect::<Vec<_>>()
        };
        ($parser:ident, chars) => {
            read_value!($parser, String).chars().collect::<Vec<char>>()
        };
        ($parser:ident, char_) => {
            read_value!($parser, String).chars().collect::<Vec<char>>()[0]
        };
        ($parser:ident, usize1) => {
            read_value!($parser, usize) - 1
        };
        ($parser:ident, line) => {
            $parser.next_line()
        };
        ($parser:ident, line_) => {
            $parser.next_line().chars().collect::<Vec<char>>()
        };
        ($parser:ident, $t:ty) => {
            $parser.next::<$t>().expect("Parse error")
        };
    }

    use std::collections::VecDeque;
    use std::io;
    use std::io::BufRead;
    use std::str;

    pub struct Parser<R> {
        pub reader: R,
        buf: VecDeque<u8>,
        parse_buf: Vec<u8>,
    }

    impl Parser<io::Empty> {
        pub fn from_str(s: &str) -> Parser<io::Empty> {
            Parser {
                reader: io::empty(),
                buf: VecDeque::from(s.as_bytes().to_vec()),
                parse_buf: vec![],
            }
        }
    }

    impl<R: BufRead> Parser<R> {
        pub fn new(reader: R) -> Parser<R> {
            Parser {
                reader: reader,
                buf: VecDeque::new(),
                parse_buf: vec![],
            }
        }
        pub fn update_buf(&mut self) {
            loop {
                let (len, complete) = {
                    let buf2 = self.reader.fill_buf().unwrap();
                    self.buf.extend(buf2.iter());
                    let len = buf2.len();
                    (len, buf2.last() < Some(&0x20))
                };
                self.reader.consume(len);
                if complete {
                    break;
                }
            }
        }
        pub fn next<T: str::FromStr>(&mut self) -> Result<T, T::Err> {
            loop {
                while let Some(c) = self.buf.pop_front() {
                    if c > 0x20 {
                        self.buf.push_front(c);
                        break;
                    }
                }
                self.parse_buf.clear();
                while let Some(c) = self.buf.pop_front() {
                    if c <= 0x20 {
                        self.buf.push_front(c);
                        break;
                    } else {
                        self.parse_buf.push(c);
                    }
                }
                if self.parse_buf.is_empty() {
                    self.update_buf();
                } else {
                    return unsafe { str::from_utf8_unchecked(&self.parse_buf) }.parse::<T>();
                }
            }
        }
        pub fn next_line(&mut self) -> String {
            loop {
                while let Some(c) = self.buf.pop_front() {
                    if c >= 0x20 {
                        self.buf.push_front(c);
                        break;
                    }
                }
                self.parse_buf.clear();
                while let Some(c) = self.buf.pop_front() {
                    if c < 0x20 {
                        self.buf.push_front(c);
                        break;
                    } else {
                        self.parse_buf.push(c);
                    }
                }
                if self.parse_buf.is_empty() {
                    self.update_buf();
                } else {
                    return unsafe { str::from_utf8_unchecked(&self.parse_buf) }.to_string();
                }
            }
        }
    }
}