Match logs to prior queries

Question

You receive a stream of strings, each beginning with either "Q:" (query) or "L:" (log). A query consists of space-separated words and should be indexed when it arrives. For every subsequent log line, output all previously seen queries for which every word in the query appears at least once in the log (case-sensitive, word boundaries by space). Design and implement an efficient algorithm/data structure to support this online matching and output.