<p>You are given an integer array <code>nums</code> and an integer <code>k</code>.</p>

<p>Find the longest subsequence of <code>nums</code> that meets the following requirements:</p>

<ul>
	<li>The subsequence is <strong>strictly increasing</strong> and</li>
	<li>The difference between adjacent elements in the subsequence is <strong>at most</strong> <code>k</code>.</li>
</ul>

<p>Return<em> the length of the <strong>longest</strong> <strong>subsequence</strong> that meets the requirements.</em></p>

<p>A <strong>subsequence</strong> is an array that can be derived from another array by deleting some or no elements without changing the order of the remaining elements.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [4,2,1,4,3,4,5,8,15], k = 3
<strong>Output:</strong> 5
<strong>Explanation:</strong>
The longest subsequence that meets the requirements is [1,3,4,5,8].
The subsequence has a length of 5, so we return 5.
Note that the subsequence [1,3,4,5,8,15] does not meet the requirements because 15 - 8 = 7 is larger than 3.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [7,4,5,1,8,12,4,7], k = 5
<strong>Output:</strong> 4
<strong>Explanation:</strong>
The longest subsequence that meets the requirements is [4,5,8,12].
The subsequence has a length of 4, so we return 4.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,5], k = 1
<strong>Output:</strong> 1
<strong>Explanation:</strong>
The longest subsequence that meets the requirements is [1].
The subsequence has a length of 1, so we return 1.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= nums[i], k &lt;= 10<sup>5</sup></code></li>
</ul>

class SegmentTree:
    def __init__(self):
        self.t = defaultdict(int)

    def query(self, l, r):
        return self._query(1, 0, 10**5, l, r)
    
    def _query(self, v, tl, tr, l, r):
        if l>tr or r<tl: return 0
        if tr==tl:
            return self.t[v]
        if l<=tl and tr<=r:
            return self.t[v]
        tm = (tl+tr)//2
        return max(self._query(2*v, tl, tm, l, r), self._query(2*v+1, tm+1, tr, l, r))

    def update(self, l, val):
        return self._update(1, 0, 10**5, l, val)

    def _update(self, v, tl, tr, l, val):
        if tl==tr==l:
            self.t[v] = max(self.t[v], val)
            return

        tm = (tl+tr)//2
        if l<=tm:
            self._update(2*v, tl, tm, l, val)
        else:
            self._update(2*v+1, tm+1, tr, l, val)

        self.t[v]=max(self.t[2*v], self.t[2*v+1])

class Solution:
    def lengthOfLIS(self, nums: List[int], k: int) -> int:

        sg = SegmentTree()

        for i in nums:
            mx = sg.query(max(i-k, 0), i-1)
            sg.update(i, mx+1)

        return sg.query(0, 10**5)
48100