```python
from typing import List, Tuple

def cut_roll(length: int, board: List[Tuple[int, int]]) -> dict:
    if isinstance(length, bool) or not isinstance(length, int) or length < 0:
        raise ValueError("length must be a non-negative whole number")
    order = sorted(board, key=lambda entry: -entry[0])
    best = [0] * (length + 1)
    taken = [0] * (length + 1)
    for metres in range(1, length + 1):
        best[metres] = -1
        for piece, price in order:
            if piece <= metres and price + best[metres - piece] > best[metres]:
                best[metres] = price + best[metres - piece]
                taken[metres] = piece
        if best[metres - 1] > best[metres]:
            best[metres] = best[metres - 1]
            taken[metres] = 0
    pieces: List[int] = []
    for metres in range(length, 0, -1):
        if taken[metres] > 0:
            pieces.append(taken[metres])
            metres -= taken[metres]
        else:
            metres -= 1
    return {"takings": best[length], "pieces": pieces}
```