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 <iostream>
#include <vector>
#include <algorithm>
#include <utility>

using namespace std;

#define INF (int)1E6

int main()
{
    int n, k;
    cin >> n >> k;
    vector<int> a(n);
    for (int i = 0; i < n; i++)
    {
        cin >> a[i];
    }

    // a, maxlength
    vector<pair<int,int>> al;
    for(int i=0;i<n;i++){
        if(al.size() == 0){
            al.emplace_back(make_pair(a[i], 1));
        }else{
            sort(al.begin(), al.end());
            auto minIter = lower_bound(al.begin(), al.end(), make_pair(a[i]-k, -INF));
            auto maxIter = upper_bound(al.begin(), al.end(), make_pair(a[i]+k, INF));
            // 該当なし
            if(maxIter - minIter <= 0){
                al.emplace_back(make_pair(a[i], 1));
            }else{
                int minindex = minIter - al.begin();
                sort(minIter, maxIter, [](const auto& l, const auto& r){return l.second > r.second;});
                al.emplace_back(make_pair(a[i], 1 + al[minindex].second));
            }
        }
    }

    sort(al.begin(), al.end(), [](auto const &l, auto const &r) { return l.second > r.second; });
    cout << al[0].second << endl;
}