import dataclasses
from datetime import datetime
from decimal import Decimal
from typing import Generator


@dataclasses.dataclass(kw_only=True, frozen=True)
class Flow:
    """Time-discrete flow of money paid on the first day of a month"""

    amount: Decimal
    since: None | datetime
    until: None | datetime

    def integrate(self, start: datetime, end: datetime) -> Decimal:
        """Integrate the flow between two dates to an amount of money"""

        payments: int = 0

        if self.since is not None:
            if start < self.since:
                start = self.since

        if self.until is not None:
            if end > self.until:
                end = self.until

        for candidate in monthly_candidates(start):
            if start <= candidate <= end:
                payments += 1
            if candidate > end:
                break

        return self.amount * Decimal(payments)


def monthly_candidates(start: datetime) -> Generator[datetime, None, None]:
    current = datetime(start.year, start.month, 1)
    while True:
        yield current
        if current.month == 12:
            current = datetime(current.year + 1, 1, 1)
        else:
            current = datetime(current.year, current.month + 1, 1)