from collections import defaultdict
from dataclasses import dataclass
from datetime import date, timedelta
from decimal import Decimal


@dataclass(frozen=True)
class Projection:
    series: list[tuple[date, Decimal]]
    low_point: tuple[date, Decimal]
    first_below_zero: date | None
    first_below_threshold: date | None


def project(start_balance: Decimal, start_date: date,
            cashflows: list[tuple[date, Decimal]], horizon_days: int,
            threshold: Decimal = Decimal("0")) -> Projection:
    end = start_date + timedelta(days=horizon_days)
    by_day: dict[date, Decimal] = defaultdict(lambda: Decimal("0"))
    for d, amount in cashflows:
        if start_date < d <= end:
            by_day[d] += amount
    series: list[tuple[date, Decimal]] = []
    balance = start_balance
    low = (start_date, start_balance)
    below0: date | None = None
    below_t: date | None = None
    d = start_date + timedelta(days=1)
    while d <= end:
        balance += by_day.get(d, Decimal("0"))
        series.append((d, balance))
        if balance < low[1]:
            low = (d, balance)
        if below0 is None and balance < 0:
            below0 = d
        if below_t is None and balance < threshold:
            below_t = d
        d += timedelta(days=1)
    return Projection(series, low, below0, below_t)