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 Python (3.8.2) (judge verdict: Accepted)

import sys
import numpy as np
import numba
from numba import njit, b1, i4, i8, f8

read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines

@njit((numba.types.optional(i8), ) * 2, cache=True)
def seg_f(x, y):
    if x is None:
        return y
    if y is None:
        return x
    return max(x, y)


@njit((i8[:], ), cache=True)
def build(raw_data):
    N = len(raw_data)
    seg = np.empty(N + N, np.int64)
    seg[N:] = raw_data
    for i in range(N - 1, 0, -1):
        seg[i] = seg_f(seg[i << 1], seg[i << 1 | 1])
    return seg


@njit((i8[:], i8, i8), cache=True)
def set_val(seg, i, x):
    N = len(seg) // 2
    i += N
    seg[i] = x
    while i > 1:
        i >>= 1
        seg[i] = seg_f(seg[i << 1], seg[i << 1 | 1])


@njit((i8[:], i8, i8), cache=True)
def fold(seg, l, r):
    vl = vr = None
    N = len(seg) // 2
    l, r = l + N, r + N
    while l < r:
        if l & 1:
            vl = seg_f(vl, seg[l])
            l += 1
        if r & 1:
            r -= 1
            vr = seg_f(seg[r], vr)
        l, r = l >> 1, r >> 1
    return seg_f(vl, vr)


@njit((i8[:], i8, i8), cache=True)
def max_right(seg, l, x):
    """[l,r) が ok であるような最大の r を返す"""
    N = len(seg) // 2

    def is_ok(v):
        return v < x

    v = None
    i, node_l, node_w = l + N, l, 1
    while True:
        if not (i & 1):
            i >>= 1
            node_w <<= 1
            continue
        if node_l + node_w > N:
            break
        v1 = seg_f(v, seg[i])
        if is_ok(v1):
            v, i = v1, (i + 1) >> 1
            node_l, node_w = node_l + node_w, node_w << 1
        else:
            break
    # 奇数セルに居て、とりきれないことが分かっている。偶数をとっていく
    i, node_w = i << 1, node_w >> 1
    while node_w:
        if node_l + node_w > N:
            i, node_w = i << 1, node_w >> 1
            continue
        v1 = seg_f(v, seg[i])
        if is_ok(v1):
            v, i = v1, (i + 1) << 1
            node_l, node_w = node_l + node_w, node_w >> 1
        else:
            i, node_w = i << 1, node_w >> 1
    i >>= 1
    return i - N

@njit((i8, i8[:]), cache=True)
def main(K, A):
    MAX = 300_010
    seg = np.zeros(2 * MAX, np.int64)
    for x in A:
        l, r = max(0, x - K), min(MAX, x + K + 1)
        n = fold(seg, l, r) + 1
        set_val(seg, x, n)
    return fold(seg, 0, MAX)

N, K = map(int, readline().split())
A = np.array(read().split(), np.int64)

print(main(K, A))