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: Accepted)

#include <iostream>
using namespace std;

int n, k, st[300005<<2], ans;

void update(int x, int l, int r, int u, int d){
    st[x] = max(st[x], d);
    if (l == r) return;
    int mid = (l+r)/2;
    if (u <= mid) update(x<<1, l, mid, u, d);
    else update(x<<1|1, mid+1, r, u, d);
}
int query(int x, int l, int r,int ql, int qr){
    if (ql <= l && r <= qr) return st[x];
    int mid = (l+r)/2;
    int ret = 0;
    if (ql <= mid) ret = max(ret, query(x<<1, l, mid, ql, qr));
    if (mid < qr) ret = max(ret, query(x<<1|1, mid+1, r,  ql, qr));
    return ret;
}

int main() {
    cin >> n >> k;
    for (int i = 0, a, ret; i < n; i++){
        cin >> a;
        ret = query(1, 1, 300000, a-k, a+k);
        ret++;
        ans = max(ans, ret);
        update(1, 1, 300000,  a, ret);
    }
    cout << ans << "\n";
}