```ts
const LADDER: [string, number][] = [["m", 1000], ["cm", 10], ["mm", 1]];

export function splitLength(mm: number): string {
  if (!Number.isInteger(mm) || mm < 0) {
    throw new Error("Invalid length");
  }

  const result: string[] = [];
  for (const [unit, factor] of LADDER) {
    if (mm >= factor) {
      const count = Math.floor(mm / factor);
      result.push(`${count}${unit}`);
      mm %= factor;
    }
  }

  return result.join(" ");
}
```