@item_router.get("/")
def get_items(user_id: Optional[str] = None):
    if user_id is None:
        return [{"item_id": "i1", "user_id": "u1"}, {"item_id": "i2", "user_id": "u2"}]
    else:
        return [{"item_id": "i2", "user_id": user_id}]


@item_router.get("/{item_id}")
def get_item(item_id: str, user_id: Optional[str] = None):
    if user_id is None:
        return {"item_id": item_id}
    else: