<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:
        n = len(nums)
        MAX_NUM = max(nums) + 1
        dp = [0] * n
        segTree = [0] * (4 * MAX_NUM)

        def query(node, start, end, l, r):
            if r < start or end < l:
                return 0
            if l <= start and end <= r:
                return segTree[node]
            mid = (start + end) // 2
            left_query = query(2 * node, start, mid, l, r)
            right_query = query(2 * node + 1, mid + 1, end, l, r)
            return max(left_query, right_query)

        def update(node, start, end, idx, val):
            if start == end:
                segTree[node] = val
                return
            mid = (start + end) // 2
            if idx <= mid:
                update(2 * node, start, mid, idx, val)
            else:
                update(2 * node + 1, mid + 1, end, idx, val)
            segTree[node] = max(segTree[2 * node], segTree[2 * node + 1])

        maxLen = 0
        for i in range(n):
            max_dp_value = query(1, 0, MAX_NUM - 1, max(0, nums[i] - k), nums[i] - 1)
            dp[i] = 1 + max_dp_value
            update(1, 0, MAX_NUM - 1, nums[i], dp[i])
            maxLen = max(maxLen, dp[i])

        return maxLen
57500