Fix: The Invoice That Does Not Balance

An invoicing service splits a total across several line items and then verifies the parts sum back to the whole. It fails intermittently in production with "invoice does not balance", and nobody can reproduce it locally with round numbers. `split_amount(total_cents, weights)` distributes `total_cents` proportionally across `weights` and must return integers that sum to **exactly** `total_cents`. The code below looks reasonable and is wrong. Find the bug and fix it — the hidden tests include the cases production actually hit.