Debt avalanche vs snowball schedule to the cent

# Debt avalanche vs snowball, to the cent `input.json` lists debts and a fixed monthly budget (synthetic). Write `solve.py` (Python 3 standard library only) so that `python solve.py input.json answer.json` simulates both payoff methods month by month. We re-run it on fresh inputs, so do not hard-code anything. ## Input `debts`: list of `{"name", "balance", "apr" (yearly percent, e.g. 21.99), "min_payment"}`; `monthly_budget` (total paid each month, including minimums). ## Rules 1. Work in exact cents (use `decimal.Decimal`; convert input numbers with `Decimal(str(x))`). Round with ROUND_HALF_UP to 0.01. 2. If `monthly_budget` < the sum of all minimum payments, the whole answer is `{"error": "budget_below_minimums"}`. 3. Target order (fixed at the start, using the original balances): **avalanche** = highest apr first, ties by smaller balance, then name; **snowball** = smallest balance first, ties by higher apr, then name. 4. Each month, in this order: (a) every debt with a positive balance gets interest = round(balance * apr / 1200) added to its balance; (b) in input order, each debt with a positive balance is paid min(min_payment, balance) from the budget; (c) whatever is left of the budget goes to debts in target order: pay min(left, balance) to the first target with a positive balance, then any remainder to the next, and so on in the same month. Any budget still left at the end of the month is not used. 5. `payoff_month[name]` = the month number (first month = 1) at whose end the debt's balance is 0. `months` = month at which all are 0. If debts remain after month 600, that method's result is `{"error": "not_paid_off"}`. 6. `total_interest` = all interest added; `total_paid` = all payments. `interest_saved_by_avalanche` = snowball total_interest - avalanche total_interest (only when both methods finish). ## Output `answer.json`: `{"avalanche": R, "snowball": R, "interest_saved_by_avalanche": x}` with R = `{"months", "total_interest", "total_paid", "payoff_month": {name: month}, "order": [names in target order]}`. Money as numbers with 2 decimals. ## Scoring Hidden checks (partial credit = fraction passed; all must pass), money within 0.011, months and orders exact: `orders`, `avalanche_totals`, `snowball_totals`, `payoff_months` (and interest saved) on the given input; `fresh_run_1`, `fresh_run_2` (whole answer on fresh inputs, which can contain 0% debts and equal balances); `budget_below_minimums` (a fresh input whose budget is too small). Each run has a 60-second limit.