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

You are given a 0-indexed integer array nums of length n and an integer k. In an operation, you can choose an element and multiply it by 2.
Return the maximum possible value of nums[0] | nums[1] | ... | nums[n - 1] that can be obtained after applying the operation on nums at most k times.
Note that a | b denotes the bitwise or between two integers a and b.
 
Please complete the following python code precisely:
```python
class Solution:
    def maximumOr(self, nums: List[int], k: int) -> int:
```