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 with AC Library v1.1) (judge verdict: Wrong Answer)

#include<bits/stdc++.h>
#include<atcoder/all>
using namespace std;
using namespace atcoder;

#define INF 1000000010
#define EPS 1e-9

#define debug(x) cout<<x<<endl;
#define repi(i,x,n) for(int i=x;i<n;i++)
#define rep(i,n) repi(i,0,n)
#define lp(i,n) repi(i,0,n)
#define repn(i,n) for(int i=n;i>=0;i--)
//#define int long long
#define endl "\n"

int op(int a, int b) { return max(a, b); }
int e() { return -1; }

typedef pair<int,int> PII;
typedef pair<int,string> PIS;
typedef pair<string,int> PSI;


signed main(){
  cin.tie(0);	
  ios::sync_with_stdio(false);
  int n,k;
  cin>>n>>k;
  
  segtree<int, op, e> seg(300010);

  int ans=0;
  
  rep(i,n){
    int x;
    cin>>x;
    int l=max(0,x-k);
    int r=min(300010,x+k+1);
    int g=seg.prod(l,r);
    int d=g+1;
    seg.set(x,d);
    if(ans<d) ans=d;
  }
  cout<<ans<<endl;


  return 0;
}