Question: Which EGOT winning American composer composed Sunshine, Lollipops and Rainbows?

Context paragraphs:
Charles Fox (composer): Charles Ira Fox (born October 30, 1940) is an American composer for film and television.  His most heard compositions are probably the "love themes" (the sunshine pop musical backgrounds which accompanied every episode of the 1970s ABC-TV show "Love, American Style"), and the dramatic theme music to ABC's "Wide World of Sports" and the original "Monday Night Football", as well as his (and Norman Gimbel's) Grammy winning hit song "Killing Me Softly With His Song".

Late piano sonatas (Beethoven): The late piano sonatas of Ludwig van Beethoven usually refer to the last five piano sonatas the composer composed during his late period.

Ben Weisman: Ben Weisman (November 16, 1921 – May 20, 2007) was an American composer significant for having written more songs recorded by Elvis Presley (fifty seven) than any other songwriter in history.  The Mad Professor as Weisman was nicknamed by Elvis, worked with the King from 1956 ("First in Line") to 1971 ("Change of Habit").  Their early association (1957–62) produced many of the most powerful rockers and poignant ballads in Presley's repertoire, including "Got a Lot o' Livin' to Do", "Follow That Dream", "Rock-A-Hula Baby", "Crawfish", "As Long As I Have You", "Pocketful of Rainbows" and "Fame and Fortune".

Sunshine: Music from the Motion Picture: Sunshine: Music from the Motion Picture is the soundtrack album for the 2007 Danny Boyle film "Sunshine".  It is a joint composition by the electronic band Underworld and film score composer John Murphy.  Underworld has a long history of collaboration with Boyle, having been featured on the soundtracks of Boyle's "Trainspotting", "A Life Less Ordinary", and "The Beach".  Murphy composed the scores to Boyle's "28 Days Later" and "Millions".

Sunshine, Lollipops and Rainbows: "Sunshine, Lollipops and Rainbows" is a popular song sung by Lesley Gore.  It was originally released on Gore's 1963 album "Lesley Gore Sings of Mixed-Up Hearts".  The song, composed by Marvin Hamlisch, was released as a single in conjunction with Gore's rendition in the 1965 film, "Ski Party".  It was arranged by Claus Ogerman and produced by Quincy Jones.  The tune peaked at #13 on the "Billboard" Hot 100.

Stephen Paulus: Stephen Paulus (August 24, 1949 – October 19, 2014) was a Grammy winning American composer, best known for his operas and choral music.  His best-known piece is his 1982 opera "The Postman Always Rings Twice", one of several operas he composed for the Opera Theatre of St. Louis, which prompted "The New York Times" to call him "a young man on the road to big things".  His style is essentially tonal, and melodic and romantic by nature.  He received grants from the National Endowment for the Arts and Guggenheim Foundation and won the prestigious Kennedy Center Friedheim Prize.  He was commissioned by such notable organizations as the Minnesota Opera, the Chamber Music Society of Lincoln Center, Opera Theatre of Saint Louis, the Saint Louis Chamber Chorus, the American Composers Orchestra, the Dale Warland Singers, the Harvard Glee Club and the New York Choral Society.  Paulus was a passionate advocate for the works and careers of his colleagues.  He co-founded the American Composers Forum in 1973, the largest composer service organization in the U.S., and served as the Symphony and Concert Representative on the ASCAP Board of Directors from 1990 until his death (from complications following a stroke in July 2013) in 2014.

Donald Martino: Donald James Martino (May 16, 1931 – December 8, 2005) was a Pulitzer Prize winning American composer.

Marvin Hamlisch: Marvin Frederick Hamlisch (June 2, 1944August 6, 2012) was an American composer and conductor.  Hamlisch was one of only twelve people to win Emmy, Grammy, Oscar and Tony awards.  This collection of all four is referred to as an "EGOT".  He is one of only two people (along with Richard Rodgers) to have won those four prizes and a Pulitzer Prize.

Lollipops and Roses (song): "Lollipops and Roses" is a song composed by Tony Velona.  The best-known version was a Grammy Award winning recording by Jack Jones in 1962.  The Jack Jones recording went to number twelve on the Easy Listening chart.  The song was used for the end credits of episode 3 of season 2 of Mad Men.

Thomas Young (tenor): Thomas Young is a Grammy and Clio-award winning American lyric tenor.  His first appearance at New York City Opera was in the roles of Street and Elijah Muhammed in the world première performance of Anthony Davis's "X, The Life and Times of Malcolm X".  He made his Lyric Opera of Chicago debut in the world première of "Amistad" by the same composer, portraying the Trickster God.  Davis then composed another role for Young in his opera "Under the Double Moon", which received its première at the Opera Theatre of Saint Louis.

Supporting paragraphs: Sunshine, Lollipops and Rainbows Marvin Hamlisch
Answer: Marvin Hamlisch