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 PyPy3 (7.3.0) (judge verdict: Time Limit Exceeded)

import sys
import heapq, math
from itertools import zip_longest, permutations, combinations, combinations_with_replacement
from itertools import accumulate, dropwhile, takewhile, groupby
from functools import lru_cache
from copy import deepcopy


def input():
    return sys.stdin.readline()[:-1]


class SegmentTree:

    def __init__(self, n, fn=lambda x, y: min(x, y), unity=(1 << 31) - 1):
        self.n = 1
        while self.n < n:
            self.n *= 2

        self.arr = [unity] * (2 * self.n - 1)
        self.fn = fn
        self.unity = unity

    def update(self, i, x):
        k = self.n + i - 1
        self.arr[k] = x

        while k > 0:
            k = (k - 1) // 2
            self.arr[k] = self.fn(self.arr[2 * k + 1], self.arr[2 * k + 2])

    def query(self, l, r):
        return self._inner_query(l, r, 0, 0, self.n)

    def _inner_query(self, l, r, k, il, ir):
        if ir <= l or r <= il:
            return self.unity

        elif l <= il and ir <= r:
            return self.arr[k]

        vl = self._inner_query(l, r, k * 2 + 1, il, (il + ir) // 2)
        vr = self._inner_query(l, r, k * 2 + 2, (il + ir) // 2, ir)
        return self.fn(vl, vr)

    def __str__(self):
        return self.arr[0: 2 * self.n].__str__()


N, K = map(int, input().split())
MAX = 300000

st = SegmentTree(MAX + 10, fn=lambda x, y: max(x, y), unity=0)
ans = 0

while N > 0:
    A = int(input())
    minimum, maximum = max(A - K, 0), min(A + K, MAX)
    x = st.query(minimum, maximum + 1) + 1
    ans = max(ans, x)
    st.update(A, x)
    N -= 1

print(ans)