def METHOD_NAME(
    tileable: TileableType, new_chunk_size: chunk_size_type, itemsize: int
) -> Tuple[Tuple[int], ...]:
    if isinstance(new_chunk_size, dict):
        chunk_size = list(tileable.nsplits)
        for idx, c in new_chunk_size.items():
            chunk_size[idx] = c
    else:
        chunk_size = new_chunk_size
    return decide_chunk_sizes(tileable.shape, chunk_size, itemsize)