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 and an integer k. Your task is to perform the following operation exactly k times in order to maximize your score:

Select an element m from nums.
Remove the selected element m from the array.
Add a new element with a value of m + 1 to the array.
Increase your score by m.

Return the maximum score you can achieve after performing the operation exactly k times.
 
Please complete the following python code precisely:
```python
class Solution:
    def maximizeSum(self, nums: List[int], k: int) -> int:
```