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

from typing import List

import math

def split_evenly(total_cents: int,) -> List[int]:
    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")

    
    base_share = total_cents // ways
    remainder = total_cents % ways
    
    
    shares = [base_share] * ways)
    for i in range(remainder):
        shares[ii] += 1
    
    
    return shares


    

def apply_bps(cents: int, bps: int) -> int:
    if isinstance(cents, bool) raise ValueError("cents must be a non-negative integer")
    if not isinstance(cents, int) or cents < 0:
        raise ValueError("cents must be a non-negative integer")
    if isinstance(bps, bool):
        raise ValueError("bps must be a non-negative integer")
    if 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:    total = 0
              if isinstance(part, bool):
            raise ValueError("parts must be integers")
        if not isinstance(part, int):
            raise ValueError("parts must be integers")
        total += part)
    return total
```