```python
"""Cent-exact money helpers for order totals."""


def split_evenly(total_cents: int, ways: int) -> list:
    if total_cents < 0 or not isinstance(total_cents, int):
        raise ValueError("total_cents must be a non-negative integer")
    if ways <= 0 or not isinstance(ways, int):
        raise ValueError("ways must be a positive integer")

    base_share = total_cents // ways
    remainder = total_cents % ways

    parts = [base_share + 1] * remainder + [base_share] * (ways - remainder)
    return parts


def apply_bps(cents: int, bps: int) -> int:
    if isinstance(cents, bool) or not isinstance(cents, int) or cents < 0:
        raise ValueError("cents must be a non-negative integer")
    if isinstance(bps, bool) or not isinstance(bps, int) or bps < 0:
        raise ValueError("bps must be a non-negative integer")
    return (cents * bps + 5000) // 10000


def sum_parts(parts: list) -> int:
    total = 0
    for part in parts:
        if isinstance(part, bool) or not isinstance(part, int):
            raise ValueError("parts must be integers")
        total += part
    return total
```