Bill a freelancer's clients for a month with half days, weekend rates, marked-up expenses and prepaid retainers

# Bill a freelancer's clients for October Inputs: `timelog.csv` (hours logged per client per day in October 2026), `clients.json` (each client's day rate and the retainer they have already paid in advance) and `expenses.csv` (re-chargeable expenses; mileage rows give miles instead of an amount). Every amount is in pounds. Billing rules, per client: - A day with 4 hours or more logged for a client is a full day; under 4 hours is a half day. Add up a client's hours per date first. - Days on a Saturday or Sunday are charged at 1.5x the day rate. - Expenses are re-charged at cost plus 10%, except mileage, which is charged at 0.45 per mile with no markup. Round each expense line to the cent half-up. - Deduct the client's retainer from fees plus expenses, but never below zero; any unused retainer carries forward. Write `out/invoices.json`: `{"days_charged": {"<client>": <full-day equivalents, e.g. 3.5>, ...}, "fees": {"<client>": <day-rate charges>, ...}, "expenses": {"<client>": <re-charged expenses>, ...}, "amount_due": {...}, "carry_forward": {"<client>": <unused retainer>, ...}}` with every client in `clients.json` (a client with nothing logged has 0 everywhere except carry_forward). ## How this run works - Work on your own: nobody will answer questions in this task, and writing to `ask/` counts against the run. - Write only under `out/`. Create `out/` if it is missing. Inputs are synthetic; don't fetch anything from the network. - Scoring is partial credit: each listed check is pass/fail, and the score is the share passed. Numbers are compared to within 0.005 unless the task says otherwise.