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: Time Limit Exceeded)

#include<bits/stdc++.h>
using namespace std;
int arr[1000000];
int longest_subseq ( int n , int k) 
{ 
	int i;
    vector<int > dp; 
    int max_length[1000000] ; 
    for (i=0;i<n;i++)
    {
    	max_length[i]=0;
    	dp.push_back(0);
	}
    for (i = 0; i < n; i++)  
    { 
        int curr = arr[i]; 
        int lower = max(0, curr - k); 
        int upper = curr + k; 
        for (int j = lower; j < upper + 1; j++) 
        { 
            dp[i] = max(dp[i], max_length[j] + 1); 
        } 
        max_length[curr] = max(dp[i], max_length[curr]); 
    } 
  
    int ans = 0; 
    for(i = 0; i < n; i++) 
	{
		ans = max(dp[i], ans); 
	}
    return ans; 
} 
int main()
{
    ios_base::sync_with_stdio(false); 
    cin.tie(NULL);   
    //freopen("input.txt", "r", stdin);
    //freopen("output.txt", "w", stdout);
    int i,j,k,x,y,z,n;
    cin>>n>>k;
    for (i=0;i<n;i++)
    {
    	cin>>arr[i];
	}
	y=longest_subseq(n,k);
	cout<<y<<endl;
}