<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:
 def del_by_idx(tree, idxs):
 """ Delete a key entry based on numerical indexes into subtree lists. """

    if len(idxs) == 0:
        tree['item'] = None
        tree['subtrees'] = []
    else:
        hidx, tidxs = idxs[0], idxs[1:]
        del_by_idx(tree['subtrees'][hidx][1], tidxs)
        if len(tree['subtrees'][hidx][1]['subtrees']) == 0:
            del tree['subtrees'][hidx]