Longest Increasing Subsequence II

You are given an integer array `nums` and an integer `k`. Find the longest subsequence of `nums` that meets the following requirements: - The subsequence is **strictly increasing** and - The difference between adjacent elements in the subsequence is **at most** `k`. Return_ the length of the **longest** **subsequence** that meets the requirements._ A **subsequence** is an array that can be derived from another array by deleting some or no elements without changing the order of the remaining elements.   **Example 1:** **Input:** nums = [4,2,1,4,3,4,5,8,15], k = 3 **Output:** 5 **Explanation:** 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. ``` **Example 2:** **Input:** nums = [7,4,5,1,8,12,4,7], k = 5 **Output:** 4 **Explanation:** The longest subsequence that meets the requirements is [4,5,8,12]. The subsequence has a length of 4, so we return 4. ``` **Example 3:** **Input:** nums = [1,5], k = 1 **Output:** 1 **Explanation:** The longest subsequence that meets the requirements is [1]. The subsequence has a length of 1, so we return 1. ```   **Constraints:** - `1 <= nums.length <= 105` - `1 <= nums[i], k <= 105`