```python
from typing import List

def sift_marks(entries: List[str], mark: str) -> List[List[str]]:
    if not entries or not mark:
        return ([], [])

    left_run = []
    right_run = []

    for entry in entries:
        if entry.startswith(mark):
            left_run.append(entry)
        else:
            right_run.append(entry)

    return [left_run, right_run]
```