<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 SegTree: 

    def __init__(self, arr: List[int]): 
        self.n = len(arr)
        self.tree = [0] * (2*self.n)
        # for i in range(2*self.n-1, 0, -1): 
        #     if i >= self.n: self.tree[i] = arr[i - self.n]
        #     else: self.tree[i] = max(self.tree[i<<1], self.tree[i<<1|1])

    def query(self, lo: int, hi: int) -> int: 
        ans = 0 
        lo += self.n 
        hi += self.n
        while lo < hi: 
            if lo & 1: 
                ans = max(ans, self.tree[lo])
                lo += 1
            if hi & 1: 
                hi -= 1
                ans = max(ans, self.tree[hi])
            lo >>= 1
            hi >>= 1
        return ans 

    def update(self, i: int, val: int) -> None: 
        i += self.n 
        self.tree[i] = val
        while i > 1: 
            self.tree[i>>1] = max(self.tree[i], self.tree[i^1])
            i >>= 1

class Solution:
    def lengthOfLIS(self, nums: List[int], k: int) -> int:
        m = max(nums)
        ans = 0 
        tree = SegTree([0] * (m+1))
        for x in nums: 
            val = tree.query(max(0, x-k), x) + 1
            ans = max(ans, val)
            tree.update(x, val)
        return ans 
27400