Task Load Balancing

You are given an array of non-negative integers, where each integer represents the duration of a task, and an integer m representing the number of available machines. Your goal is to assign every task to one of the m machines such that the maximum total duration across all machines is minimized.

Implement a function:

def minimize_maximum_load(tasks: List[int], m: int) -> int:
    # Your code here

Your function should return the minimized maximum load (i.e. the smallest possible value of the maximum sum of task durations assigned to any single machine) under an optimal assignment of tasks.

Example:

Input: tasks = [3, 1, 4, 2, 2], m = 3
Output: 4

Explanation: One possible optimal assignment is:
- Machine 1: [4]
- Machine 2: [3, 1] (sum = 4)
- Machine 3: [2, 2] (sum = 4)

Constraints:

• The number of tasks will be between 1 and 30.
• m will be between 1 and the total number of tasks.
• Each task duration is a non-negative integer.

Design an algorithm to solve this problem. You do not need to return the actual assignment, only the minimized maximum load.