import calendar
from datetime import date, timedelta


def get_billing_period(
    billing_day: int,
    date_: date,
) -> tuple[date, date]:
    # Determine the anchor month and year
    if date_.day >= billing_day:
        anchor_month = date_.month
        anchor_year = date_.year
    else:
        # Move to previous month
        if date_.month == 1:
            anchor_month = 12
            anchor_year = date_.year - 1
        else:
            anchor_month = date_.month - 1
            anchor_year = date_.year

    # Calculate start date
    _, last_day = calendar.monthrange(anchor_year, anchor_month)
    start_date = date(anchor_year, anchor_month, min(billing_day, last_day))

    # Calculate next month and year
    if anchor_month == 12:
        next_month = 1
        next_year = anchor_year + 1
    else:
        next_month = anchor_month + 1
        next_year = anchor_year

    # Calculate end date
    _, next_last_day = calendar.monthrange(next_year, next_month)
    end_day = min(billing_day, next_last_day)
    end_date = date(next_year, next_month, end_day) - timedelta(days=1)

    return start_date, end_date