Design a stop-order trigger engine

Design an engine holding resting stop orders:

• add_stop(side, stop_price), register a stop. A buy stop fires when the last trade price rises to stop_price or above; a sell stop fires when the last price falls to stop_price or below. Return an order id.
• cancel(order_id), remove a resting stop.
• on_price(last), feed a new last-trade price; return the list of stops that fire now (each fires at most once).

b = eng.add_stop("buy", 105)
s = eng.add_stop("sell", 95)
eng.on_price(100)   -> []              # inside the band, nothing fires
eng.on_price(106)   -> [("buy", 105)]  # price crossed up through 105

Every operation should be $O(\log n)$ amortized.