<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 Node:
    def __init__(self, val, L, R):
        self.val = val
        self.left = None
        self.right = None
        self.L = L
        self.R = R

class SegmentTree:
    def __init__(self, n):
        self.root = self.build(0, n)
    
    def build(self, L, R):
        if L == R:
            return Node(0, L, R)
        root = Node(0, L, R)
        M = (L + R) // 2
        root.left = self.build(L, M)
        root.right = self.build(M+1, R)
        root.val = max(root.left.val, root.right.val)
        return root

    def update(self, index, val):
        self.updateHelper(self.root, index, val)

    def updateHelper(self, root, index, val):
        if root.L == root.R:
            root.val = val
            return
        M = (root.L + root.R) // 2
        if index <= M:
            self.updateHelper(root.left, index, val)
        else:
            self.updateHelper(root.right, index, val)
        root.val = max(root.left.val, root.right.val)

    def query(self, L, R):
        return self.queryHelper(self.root, L, R)

    def queryHelper(self, root, L, R):
        if L <= root.L and R >= root.R:
            return root.val
        elif R < root.L or L > root.R:
            return 0
        else:
            return max(self.queryHelper(root.left, L, R), self.queryHelper(root.right, L, R))

class Solution:
    def lengthOfLIS(self, nums: List[int], k: int) -> int:
        st = SegmentTree(max(nums))
        result = 0
        for n in nums:
            start = n-k if n-k > 0 else 0
            val = st.query(start, n-1) + 1
            st.update(n, val)
            result = max(result, val)

        return result
56300