Maximum combination health of AI modules

A lab is assembling an AI system from n candidate modules. Module i has a health health[i] (how much it contributes) and a stability stability[i] (how reliable it is). Both are non-negative integers.

You may pick a combination of at least 1 and at most k distinct modules. A combination is only as reliable as its weakest member, so its score is:

combination_health = (sum of health of chosen modules) * (minimum stability among chosen modules)

Implement:

def max_combination_health(health: list[int], stability: list[int], k: int) -> int:
    ...

Return the largest possible combination_health. Return 0 if n == 0 or k <= 0.

Constraints

• 0 <= n <= 10^5, len(health) == len(stability)
• 0 <= health[i], stability[i] <= 10^5
• 0 <= k; k may exceed n

Example 1

health    = [4, 9, 2, 6]
stability = [5, 2, 8, 4]
k = 2
-> 40

Choose modules 0 and 3: (4 + 6) * min(5, 4) = 40. Module 1 has the most health, but its stability of 2 pulls any combination containing it down to at most (9 + 6) * 2 = 30.

Example 2

health    = [10, 10, 10]
stability = [1, 1, 100]
k = 3
-> 1000

Module 2 alone scores 10 * 100 = 1000, more than taking all three (30 * 1 = 30).

Aim for better than trying every subset.

Reconstructed from the reported question; details may differ from what interviewers ask.