<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 seg_tree():
    def __init__(self, size):
        n = 1
        while n < size: n<<=1
        self.n = n
        self.x = [0] * 2*n
            
    def update(self, index, val):
        index += self.n
        self.x[index] = val
        while index > 1:
            index //= 2
            self.x[index] = max(self.x[2*index], self.x[2*index+1])
    
    def query(self, l, r):
        ans = 0
        l += self.n
        r += self.n
        while l <= r:
            if l%2 == 1:
                ans = max(ans, self.x[l])
                l += 1
            if r%2 == 0:
                ans = max(ans, self.x[r])
                r -=1
            l, r = l//2, r//2
        return ans


class Solution:
    def lengthOfLIS(self, nums: List[int], k: int) -> int:
        if not nums:
            return 0
        maxx = max(nums)
        tree = seg_tree(maxx)
        ans = 1
        for val in nums: 
            l = max(1, val-k)-1
            r = val-2
            if l <= r: 
                length = tree.query(l, r)+1
            else:
                length = 1
            ans = max(ans, length)
            tree.update(val-1, length)
        return ans
27900