Please solve the programming task below using a self-contained code snippet in a markdown code block.

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.
 
Please complete the following python code precisely:
```python
class Solution:
    def lengthOfLIS(self, nums: List[int], k: int) -> int:
```