<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 Solution:
    def lengthOfLIS(self, nums: List[int], k: int) -> int:
        maxnum = max(nums) + 1
        powsz, i = 0, maxnum
        while i:
            powsz, i = powsz + 1, i >> 1
        tree = [[0 for _ in range(1 << p)] for p in range(powsz + 1)]

        def getmax(l: int, r: int, lvl : int, i: int) -> int:
            chw = (1 << (powsz - lvl))
            bgn = i * chw
            if l == bgn and r == bgn + chw - 1:
                return tree[lvl][i]
            chw //= 2
            if l < bgn + chw and r < bgn + chw:
                return getmax(l, r, lvl + 1, i * 2)
            if l >= bgn + chw and r >= bgn + chw:
                return getmax(l, r, lvl + 1, i * 2 + 1)
            return max(getmax(l, bgn + chw - 1, lvl + 1, i * 2), getmax(bgn + chw, r, lvl + 1, i * 2 + 1))

        def update(i: int, val: int) -> None:
            for lvl in reversed(tree):
                lvl[i] = max(lvl[i], val)
                i = i >> 1

        res = 1
        for n in nums:
            maxlen = getmax(max(n - k, 0), n - 1, 0, 0) + 1
            res = max(res, maxlen)
            update(n, maxlen)
        return res

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