Minimize Maximum Task Execution Time Solution

Problem Statement

You are given an integer array `costs` of length `n`, where `costs[i]` represents the time multiplier for the `i`-th processor to process a single task. You are also given an integer `k` representing the total number of tasks to be distributed. You must distribute all `k` tasks among the `n` processors such that each processor is assigned a non-negative integer number of tasks, and the sum of tasks assigned to all processors is exactly `k`. If processor `i` is assigned $x_i$ tasks, its total execution time is $x_i \times \text{costs}[i]$. Return the minimum possible maximum execution time among all processors after an optimal distribution of tasks.

Constraints

• 1 <= costs.length <= 10^5
• 1 <= costs[i] <= 10^6
• 0 <= k <= 10^9

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