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

Given an m x n matrix matrix and an integer k, return the max sum of a rectangle in the matrix such that its sum is no larger than k.
It is guaranteed that there will be a rectangle with a sum no larger than k.
 
Please complete the following python code precisely:
```python
class Solution:
    def maxSumSubmatrix(self, matrix: List[List[int]], k: int) -> int:
```