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)

#![allow(non_snake_case,unused_imports,dead_code)]

use std::str::FromStr;
use std::collections::{HashMap,HashSet,VecDeque,BinaryHeap};
use std::cmp::{max,min,Reverse,Ordering};
use std::io::Read;
use std::time::{Duration, Instant};
use rand::Rng;
 
use proconio::input;
use proconio::marker::{Chars,Usize1,Isize1};

fn main() {
    input!{
        N:usize,
        K:usize,
        A:[usize;N],
    }

    let a_INF = 300100;
    let mut T = SegmentTree::new(a_INF,|x,y| max(*x,*y),0);
    let mut dp = vec![1;N];

    for (i,&a) in A.iter().enumerate(){
        let l = max(0,a as isize -K as isize) as usize;
        let r = min(a_INF,a+K+1) as usize;
        dp[i] = T.get(l,r) +1;
        T.operate(a, dp[i]);
    }

    println!("{}",dp.iter().max().unwrap());

}


// #region SegmentTree
struct SegmentTree<N,F>
where F:Fn(&N,&N) ->N{
    n: usize,
    T: Vec<N>,
    func: F,
    identity: N,
}

impl<N:Clone,F> SegmentTree<N,F>
where F:Fn(&N,&N) ->N {
    fn new(n:usize,func:F,identity:N) -> SegmentTree<N,F>{
        let mut T = SegmentTree { n:n,T:Vec::new(),func:func,identity:identity};
        T.init();
        T
    }
    fn init(&mut self){
        self.n = 1<<format!("{:b}",self.n-1).len();
        self.T = vec![self.identity.clone(); 2*self.n-1];
    }
    fn _replace_without_update(&mut self,index:usize,value:N){
        let i = index + self.n - 1;
        self.T[i] = value;
    }
    fn replace(&mut self,index:usize,value:N){
        self._replace_without_update(index, value);
        let i = index + self.n - 1;
        self._update_parent((i-1)/2);
    }
    fn replace_range(&mut self,l:usize,r:usize,array:&Vec<N>){
        let n = array.len();
        let mut j = 0;
        for i in l..r{
            self._replace_without_update(i, array[j].clone());
            j = (j+1)%n;
        }
        self._update_range((l + self.n-2)/2,(r + self.n-2)/2);
    }
    fn _operate_without_update(&mut self,index:usize,value:N){
        let i = index + self.n - 1;
        self.T[i] = (self.func)(&self.T[i],&value);
    }
    fn operate(&mut self,index:usize,value:N){
        self._operate_without_update(index, value);
        let i = index + self.n - 1;
        self._update_parent((i-1)/2);
    }
    fn operate_range(&mut self,l:usize,r:usize,array:&Vec<N>){
        let n = array.len();
        let mut j = 0;
        for i in l..r{
            self._operate_without_update(i, array[j].clone());
            j = (j+1)%n;
        }
        self._update_range((l + self.n-2)/2,(r + self.n-2)/2);
    }
    fn _update(&mut self,i:usize){
        self.T[i] = (self.func)(&self.T[i*2+1],&self.T[i*2+2]);
    }
    fn _update_parent(&mut self,i:usize){
        self._update(i);
        if i>0 { self._update_parent((i-1)/2)}
    }
    fn _update_range(&mut self,l:usize,r:usize){
        for i in l..r{
            self._update(i);
        }
        if l<r{
            self._update_range((l-1)/2,(r-1)/2);
        }
    }
    fn get(&self,l:usize,r:usize) -> N{
    self._get(l,r,0,0,self.n)
    }
    fn _get(&self,l:usize,r:usize,i:usize,a:usize,b:usize) -> N{
        if l<=a && b<=r {
            self.T[i].clone()
        } else if b<=l || r<=a {
            self.identity.clone()
        } else{
            (self.func)(&self._get(l,r,2*i+1,a,(a+b)/2),
                        &self._get(l,r,2*i+2,(a+b)/2,b))
        }
    }
}

//  let mut T_sum = SegmentTree::new(N,|x,y| x+y,0);
//  let INF = 1e15 as isize;
//  let mut T_min = SegmentTree::new(a_INF,|x,y| min(*x,*y),INF);
//  let mut T_max = SegmentTree::new(a_INF,|x,y| max(*x,*y),-INF);
// #endregion