Given the task definition and input, reply with output. In this task, five ordered key facts are given. All the given facts are expressed in natural language. Your job is to generate a story 100 to 1000 words long, that includes all the facts given as input in their order of appearance while expanding upon them to produce a broader, yet coherent, narrative.

Fact1: Gill starts telephoning Brummel to chat about murders and state of investigation, Fact2: Brummel 's own overbearing mother wants son to be Away from work more like doctor brother, Fact3: Brummel is scornful of career choice, Fact4: Brummell manages to win over Brummell 's mother, Fact5: Palmer does not fit profile of previous victims
Christopher Gill Rod Steiger is a serial killer fixated on his late mother, a noted stage actress. Gill preys on older women. A Broadway theatre owner and director, he adopts various disguises, e.g., priest, policeman, plumber, hairdresser, etc., to put his victims at ease and avoid being identified before strangling them and painting a pair of lips on their foreheads with garish red lipstick. Detective Morris Brummell George Segal is investigating the murders. Brummel is quoted in the newspaper that the latest murder was wellplanned and wellexecuted. This appeals to Gills ego, so he starts telephoning Brummel to chat about the murders and the state of the investigation. Brummel is able to elicit a few scraps of information about Gill, but for the most part Gill succeeds in taunting him without giving away his identity. Away from work, Brummels own overbearing mother Eileen Heckart wants her son to be more like his doctor brother and settle down. She is scornful of his career choice. Brummells new love interest is Kate Palmer Lee Remick, who glimpsed Gill minutes before he committed the first murder, though not well enough to identify him in a way that would aid the investigation. She manages to win over Brummells mother by claiming she is planning to become Jewish, and by pretending to dominate her son. In what turns out to be their last phone conversation, Brummel turns the tables on Gill and insults him. Gill subsequently targets Kate. This is obviously for reasons other than his mother fixation, as Palmer does not fit the profile of his previous victims. He may be jealous of Kate, or perhaps wants revenge on Brummell for the insults. Gill attacks Kate in her apartment, but is forced to flee before he can do her serious harm. During the police manhunt that follows, Gill is seen entering his theatre via a side door. Investigating the sighting, Brummell chats amiably with Gill the detective at that point cannot be sure the man before him is Kates attacker. When he sees in the theatre lobby a portrait of an actress with her lips highlighted in deep red lipstick, he knows he has his man. Brummel confronts Gill with his suspicions, but Gill remains cool. Brummel goes to check out the costume room, and on his way back as he is passing the theatre stage, Gill attacks him with the backstage rigging. Brummel is staggered, but is able to fatally shoot Gill before he next attacks. In his death swoon Gill revisits the murders he committed, as his deranged mind has recast them.