```ts
export interface Cut {
  takings: number;
  pieces: number[];
}

function cutRoll(length: number, board: [number, number][]): Cut {
  if (typeof length !== 'number' || !Number.isInteger(length) || length < 0) {
    throw new Error('Length must be a non-negative whole number.');
  }

  const dp: { takings: number; pieces: number[] }[] = Array.from({ length }, () => ({ takings: 0, pieces: [] }));

  for (let i = 1; i <= length; i++) {
    let maxTakings = 0;
    let bestPieces: number[] = [];

    for (const [metres, price] of board) {
      if (i >= metres && dp[i - metres].takings + price > maxTakings) {
        maxTakings = dp[i - metres].takings + price;
        bestPieces = [...dp[i - metres].pieces, metres];
      }
    }

    dp[i] = { takings: maxTakings, pieces: bestPieces };
  }

  return dp[length];
}
```