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: Runtime Error)

import sys,io,os
z=io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
class SegmentTree:
    def __init__(self, data, default=0, func=max):
        self._default = default
        self._func = func
        self._len = len(data)
        self._size = _size = 1 << (self._len - 1).bit_length()
        self.data = [default] * (2 * _size)
        self.data[_size:_size + self._len] = data
        for i in reversed(range(_size)):
            self.data[i] = func(self.data[i + i], self.data[i + i + 1])
    def __delitem__(self, idx):
        self[idx] = self._default
    def __getitem__(self, idx):
        return self.data[idx + self._size]
    def __setitem__(self, idx, value):
        idx += self._size
        self.data[idx] = value
        idx >>= 1
        while idx:
            self.data[idx] = self._func(self.data[2 * idx], self.data[2 * idx + 1])
            idx >>= 1
    def __len__(self):
        return self._len
    def query(self, start, stop):
        start += self._size
        stop += self._size
        res_left = res_right = self._default
        while start < stop:
            if start & 1:
                res_left = self._func(res_left, self.data[start])
                start += 1
            if stop & 1:
                stop -= 1
                res_right = self._func(self.data[stop], res_right)
            start >>= 1
            stop >>= 1
        return self._func(res_left, res_right)
    def __repr__(self):
        return "SegmentTree({0})".format(self.data)

n,k=map(int,z().split())
M=300001
s=SegmentTree([0]*300001)
for i in range(n):
    a=int(z())
    s[a]=1+s.query(a-k,max(a+k+1,M+1))
print(s.query(0,300001))