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: Time Limit Exceeded)

/*
       ▄▄▄▄▄▄▄▄▄▄▄  ▄▄▄▄▄▄▄▄▄▄▄  ▄▄▄▄▄▄▄▄▄▄
      ▐░░░░░░░░░░░▌▐░░░░░░░░░░░▌▐░░░░░░░░░░▌
      ▐░█▀▀▀▀▀▀▀▀▀ ▐░█▀▀▀▀▀▀▀█░▌▐░█▀▀▀▀▀▀▀█░▌
      ▐░▌          ▐░▌       ▐░▌▐░▌       ▐░▌
      ▐░▌ ▄▄▄▄▄▄▄▄ ▐░▌       ▐░▌▐░▌       ▐░▌
      ▐░▌▐░░░░░░░░▌▐░▌       ▐░▌▐░▌       ▐░▌
      ▐░▌ ▀▀▀▀▀▀█░▌▐░▌       ▐░▌▐░▌       ▐░▌
      ▐░▌       ▐░▌▐░▌       ▐░▌▐░▌       ▐░▌
      ▐░█▄▄▄▄▄▄▄█░▌▐░█▄▄▄▄▄▄▄█░▌▐░█▄▄▄▄▄▄▄█░▌
      ▐░░░░░░░░░░░▌▐░░░░░░░░░░░▌▐░░░░░░░░░░▌
       ▀▀▀▀▀▀▀▀▀▀▀  ▀▀▀▀▀▀▀▀▀▀▀  ▀▀▀▀▀▀▀▀▀▀  
 
 #can_change_the_world_with_the_help_of_0_1
                                    -darshan786    */
 
  
 
 
#include<bits/stdc++.h>
using namespace std;
#define pb push_back
#define mod 1000000007
#define boost ios_base::sync_with_stdio(false);cin.tie(0); 
#define F first 
#define MAXN   1010
#define int long long
#define S second
#define all(v) v.begin(),v.end() 
#define PI pair<int,int>
#define PIS pair<int,string>





int values[41];
   
void value()
{
   values[0]=1;
    for(int i=1;i<=40;i++)
    {
        values[i]=2*values[i-1];
    }
}


int32_t main() {
    boost
     #ifndef ONLINE_JUDGE
     freopen("input.c","r",stdin);
     freopen("output.c","w",stdout);
    #endif

   int n,k;
   cin>>n>>k;
   int s[n+1];
   for(int i=0;i<n;i++)cin>>s[i];

    vector<int> dp(n, 0); 
  
    auto  solve=[&]()
    {
        map<int,int> ma;
      
        for (int i = 0; i < n; i++)  
        { 
      
            int curr = s[i]; 
              
            int low = max(curr - k,0ll); 
              
            int high = min(curr + k,n); 
              
            for (int j = low; j < high + 1; j++) 
                dp[i] = max(dp[i], ma[j] + 1); 
            
            ma[curr] = max(dp[i], ma[curr]); 
        } 
      
        int ans = 0; 
      
        for(int i:dp) ans = max(i, ans); 

          return ans;
    };
  
    cout<<solve()<<endl; 
}