import calendar
from datetime import date

STEP = {"monthly": 1, "quarterly": 3, "yearly": 12}


def _clamp(y: int, m: int, day: int) -> date:
    return date(y, m, min(day, calendar.monthrange(y, m)[1]))


def occurrences(rhythm: str, due_day: int, window_start: date, window_end: date,
                item_start: date | None = None, item_end: date | None = None) -> list[date]:
    step = STEP[rhythm]
    lo = max(window_start, item_start) if item_start else window_start
    hi = min(window_end, item_end) if item_end else window_end
    anchor = item_start or window_start
    d = _clamp(anchor.year, anchor.month, due_day)
    out: list[date] = []
    while d <= hi:
        if d >= lo:
            out.append(d)
        total = d.year * 12 + d.month - 1 + step
        y, m0 = divmod(total, 12)
        d = _clamp(y, m0 + 1, due_day)
    return out