<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, n):
        self.n = n
        self.tree = [0] * 4 * self.n

    def update(self, pos, val):
        def updateTree(left, right, node):
            if left == right:
                self.tree[node] = val
                return
            mid = (left + right) // 2
            left_node = 2 * node + 1
            right_node = 2 * node + 2
            if pos <= mid:
                updateTree(left, mid, left_node)
            else:
                updateTree(mid + 1, right, right_node)
            self.tree[node] = max(self.tree[left_node], self.tree[right_node])

        updateTree(0, self.n, 0)

    def query(self, start, end):
        def queryTree(start, end, left, right, node):
            if end < left or right < start:
                return 0
            if start <= left <= end and start <= right <= end:
                return self.tree[node]
            mid = (left + right) // 2
            left_node = 2 * node + 1
            right_node = 2 * node + 2
            left_max = queryTree(start, end, left, mid, left_node)
            right_max = queryTree(start, end, mid + 1, right, right_node)
            return max(left_max, right_max)

        return queryTree(start, end, 0, self.n, 0)


class Solution:
    def lengthOfLIS(self, nums: list[int], k: int) -> int:
        mx = max(nums)
        segmentTree = SegmentTree(mx)
        lis = 0
        for num in nums:
            left = max(0, num - k)
            right = num - 1
            max_lis = segmentTree.query(left, right)
            lis = max(lis, max_lis + 1)
            segmentTree.update(num, max_lis + 1)
        return lis
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