<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,L,R):
        self.longest=0
        self.L=L
        self.R=R
        if L==R:
            self.left=None
            self.right=None
        else:
            M=(L+R)//2
            self.left=SegmentTree(L,M)
            self.right=SegmentTree(M+1,R)
    
    def update(self,index,val):
        if self.L==self.R:
            self.longest=val
            return
        M=(self.L+self.R)//2

        if index>M:
            self.right.update(index,val)
        else:
            self.left.update(index,val)
        
        self.longest=max(self.left.longest,self.right.longest)
    
    def rangeQuery(self,L,R):
        if L==self.L and R==self.R:
            return self.longest
        
        M=(self.L+self.R)//2
        if L>M:
            return self.right.rangeQuery(L,R)
        elif R<=M:
            return self.left.rangeQuery(L,R)
        else:
            return max(self.left.rangeQuery(L,M),self.right.rangeQuery(M+1,R))

class Solution:
    
    def lengthOfLIS(self, nums: List[int], k: int) -> int:
        n = max(nums)
        res = 1
        tree = SegmentTree(0, n)
        for num in nums:
            mm = tree.rangeQuery(max(0, num - k), num-1)
            tree.update(num, mm + 1)
            res = max(res, mm + 1)
        return res
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