Integer Rescaling

You are given a list of positive integers weights and a positive integer target. Your task is to rescale the integers so that their sum becomes exactly target while keeping the proportions as close as possible. Formally, implement a function rescale(weights, target) that returns a list res of the same length such that:

1. sum(res) == target.
2. Among all integer lists satisfying (1), the one you return minimizes the total absolute error sum(|res[i] - weights[i] * target / total|) where total = sum(weights).

Use the two-step apportionment algorithm: first assign each bucket the floor of its exact share, then distribute the leftover units one-by-one to the buckets with the largest remainders. Break ties by the original index order. If total == 0 (all weights zero), distribute target evenly (as evenly as possible). If target == 0, return all zeros. You must use only integer arithmetic to avoid floating-point precision issues.