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

You are given an m x n integer matrix matrix with the following two properties:

Each row is sorted in non-decreasing order.
The first integer of each row is greater than the last integer of the previous row.

Given an integer target, return true if target is in matrix or false otherwise.
You must write a solution in O(log(m * n)) time complexity.
 
Please complete the following python code precisely:
```python
class Solution:
    def searchMatrix(self, matrix: List[List[int]], target: int) -> bool:
```