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>

#define fast                     \
    ios::sync_with_stdio(false); \
    cin.tie(NULL);               \
    cout.tie(NULL)
#define int long long
#define endl '\n'

using namespace std;

const int N = 3e5 + 77;
int A[N] , dp[N];

int32_t main()
{
    fast;  
    int n , k ; cin >> n >> k ;
    for(int i = 0; i < n ; ++i){
        cin >> A[i];
    }
    int ans = 0;
    dp[0] = 1;
    for(int i = 1 ; i < n ; ++i){
        for(int j = 0 ; j < i ; ++j){
            if(abs(A[i]-A[j]) <= k)
                dp[i] = max(dp[i],dp[j]+1);
        }
    }
    for(int i = 0; i < n ; ++i) ans = max(dp[i],ans);
    // for(int i = 0; i < n ; ++i) cout << dp[i] << ' ' ; cout << endl;
    cout << ans << endl;
    return 0;
}