from datetime import datetime, timedelta, timezone
from typing import Optional


def add_months(base_dt: datetime, months_to_add: int) -> datetime:
    """Add calendar months to a datetime, clamping the day to the month's length.

    Preserves tzinfo from base_dt.
    """
    year = base_dt.year
    month = base_dt.month + months_to_add
    day = base_dt.day

    # Normalize year and month
    year += (month - 1) // 12
    month = ((month - 1) % 12) + 1

    # Determine last day of target month by rolling to next month's first day and subtracting 1 day
    if month == 12:
        next_month_first = datetime(year + 1, 1, 1, tzinfo=base_dt.tzinfo)
    else:
        next_month_first = datetime(year, month + 1, 1, tzinfo=base_dt.tzinfo)
    last_day = (next_month_first - timedelta(days=1)).day

    clamped_day = min(day, last_day)
    return base_dt.replace(year=year, month=month, day=clamped_day)


def month_start(base_dt: Optional[datetime] = None) -> datetime:
    """Return the first instant of the month in UTC for a datetime."""
    moment = base_dt or datetime.now(timezone.utc)
    if moment.tzinfo is None:
        moment = moment.replace(tzinfo=timezone.utc)
    else:
        moment = moment.astimezone(timezone.utc)
    return datetime(moment.year, moment.month, 1, tzinfo=timezone.utc)
