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>
using namespace std;
inline int re(){
	char c;
	int w=1;
	while((c=getchar())<'0'||c>'9')if(c=='-')w=-1;
	int res = c-'0';
	while((c=getchar())>='0'&&c<='9')res = res*10+c-'0';
	return res*w;
}
const int maxn = 6e5+5;
int n,k,a[maxn],dp[maxn];
int maxx[maxn<<2];
inline void update(int k,int l,int r,int pos,int v){
	if(l == r)return maxx[k] = max(maxx[k],v),void();
	int mid = l+r>>1;
	if(pos <= mid)update(k<<1,l,mid,pos,v);
	else update(k<<1|1,mid+1,r,pos,v);
	maxx[k] = max(maxx[k<<1],maxx[k<<1|1]);
}
inline int query(int k,int l,int r,int x,int y){
	if(l>y||r<x)return 0;
	if(l>=x&&r<=y)return maxx[k];
	int mid = l+r>>1;
	return max(query(k<<1,l,mid,x,y),query(k<<1|1,mid+1,r,x,y));
}
int main(){
	scanf("%d %d",&n,&k);
	for(int i=1;i<=n;++i)scanf("%d",&a[i]);
	int ans = 0;
	for(int i=1;i<=n;++i){
		dp[i] = query(1,0,6e5,max(0,a[i]-k),a[i]+k)+1;
		update(1,0,6e5,a[i],dp[i]);
		ans = max(ans,dp[i]);
	}
	printf("%d",ans);
	return 0;
}