<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 * n)

    def update(self, node, start, end, index, value):
        if start == end:
            self.tree[node] = max(self.tree[node], value)
            return
        
        mid = (start + end) // 2
        if index <= mid:
            self.update(2 * node + 1, start, mid, index, value)
        else:
            self.update(2 * node + 2, mid + 1, end, index, value)
        
        self.tree[node] = max(self.tree[2 * node + 1], self.tree[2 * node + 2])

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

class Solution:
    def lengthOfLIS(self, nums: List[int], k: int) -> int:
        max_val = max(nums)
        seg_tree = SegmentTree(max_val + 1)
        
        for num in nums:
            if num == 1:
                seg_tree.update(0, 0, max_val, num, 1)
            else:
                left = max(1, num - k)
                right = num - 1
                prev_max = seg_tree.query(0, 0, max_val, left, right)
                seg_tree.update(0, 0, max_val, num, prev_max + 1)
        
        return seg_tree.tree[0]
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