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

def split_evenly(total_cents: int, ways: int) -> list:
    if not isinstance(total_cents, int) or total_cents < 0:
        raise ValueError("total_cents must be a non-negative integer")
    if not isinstance(ways, int) or ways <= 0:
        raise ValueError("ways must be a positive integer")
    
    # Calculate the initial shares
    shares = [total_cents // ways] * ways
    
    # Distribute the remaining cents
    remainder = total_cents % ways
    for i in range(remainder):
        shares[i] += 1
    
    # Sort the shares in non-increasing order
    shares.sort(reverse=True)
    
    return shares


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
```