Flatten Fractional-Share Inventory and Record Trade Logs

Process customer buy and sell orders while keeping a firm's fractional-share inventory in `[0,1)` for every symbol after each order. The exchange trades only whole shares. Also return an inventory-perspective log of each exchange and customer transfer. Implement `fractional_inventory(orders: string[], inventory: string[]) -> string[][]`. Return exactly two rows: the final inventory strings in input order, and the ordered log strings. ### Input and Numeric Contract - Inventory entries are `SYMBOL/quantity`, where integer quantity counts hundredths of a share. `50` means 0.50 shares. Symbols are unique, nonempty ASCII letters/digits/underscores. Initial quantities lie in `[0,99]`. - Orders are `SYMBOL/B_OR_S/quantityOrDollars/price`. B means the customer buys from inventory; S means the customer sells to inventory. Every symbol appears in the inventory input. - An unprefixed integer quantity counts hundredths of a share. A quantity prefixed by `$` counts cents of money. Price is positive integer cents per whole share. For dollar orders, share hundredths equal `moneyCents * 100 / priceCents`. - The report does not define rounding. This practice contract admits only dollar orders whose conversion is an exact integer number of share hundredths. No fractional hundredth or rounding is required. - At most 100000 orders and 1000 symbols. Numeric inputs are at most 1000000; use wide arithmetic for multiplication. Order quantities are positive. ### Processing and Logging Logs use `SYMBOL/quantity/side/contra`, where quantity is a positive integer in share hundredths, side is B or S **from inventory's perspective**, and contra is `MARKET` or `CUSTOMER`. For a customer buy, obtain enough whole shares from the market first if current inventory is insufficient, then deliver the full requested quantity to the customer. Record a MARKET/B transfer only if needed, followed by a CUSTOMER/S transfer. For a customer sell, record the CUSTOMER/B transfer first. Then sell all whole shares from inventory to the market, recording MARKET/S only if needed. Never emit zero-quantity logs. After either case, inventory must be nonnegative and below 100 hundredths. This string-log encoding and transaction order are explicit practice choices that preserve the source's inventory perspective and example of buying from the market before delivering to a customer. ### Example ```text inventory = ["ABC/0","XYZ/75"] orders = ["ABC/B/150/1000","ABC/B/40/1000","ABC/S/75/1000"] result = [["ABC/85","XYZ/75"], ["ABC/200/B/MARKET","ABC/150/S/CUSTOMER", "ABC/40/S/CUSTOMER","ABC/75/B/CUSTOMER"]] ``` With inventory `ABC/20`, a customer buy of 50 hundredths requires a market purchase of 100 and leaves `ABC/70`. With inventory `ABC/75`, a customer sell of 50 produces a customer buy log of 50, a market sell log of 100, and final inventory 25. Explain how a single flattening invariant simplifies the cases and why language-specific negative-remainder behavior needs care. This exercise models quantity accounting only; it does not simulate prices, fees, settlement, or actual market execution.