<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 Solution:
    def lengthOfLIS(self, nums: List[int], k: int) -> int:
        n = max(nums)
        seg = [0] * (n * 4)
        def modify(o: int, l: int, r: int, i: int, val: int) -> None:
            if l == r:
                seg[o] = val
                return
            mid = (l + r) // 2
            if i <= mid: modify(o * 2, l, mid, i, val)
            else: modify(o * 2 + 1, mid + 1, r, i, val)
            seg[o] = max(seg[o * 2], seg[o * 2 + 1])
        def find(o: int, l: int, r: int, L: int, R: int) -> int:
            if L <= l and r <= R:
                return seg[o]
            res = 0
            mid = (l + r) // 2
            if L <= mid: res = find(o * 2, l, mid, L, R)
            if R > mid: res = max(res, find(o * 2 + 1, mid + 1, r, L, R))
            return res
        for num in nums:
            if num == 1:
                modify(1, 1, n, 1, 1)
            else:
                res = 1 + find(1, 1, n, max(num - k, 1), num - 1)
                modify(1, 1, n, num, res)
        return seg[1]


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