Question: Who produced the mixtapes 63 and 19 which includes a collaboration with an American hip hop group from New York City known as the Beastie Boys?

Context articles: Beastie Boys
Run-DMC
3-Minute Rule
63/19
The Young and the Useless
Paul Revere (song)
Foreign Legion (hip hop crew)
Don't Play No Game That I Can't Win
Ill Communication
Rip Slyme

Beastie Boys were an American hip hop group from New York City, formed in 1981.
 For the majority of their career, the group consisted of Michael "Mike D" Diamond (vocals, drums), Adam "MCA" Yauch (vocals, bass) and Adam "Ad-Rock" Horovitz (vocals, guitar).
Run-D.M.C.
 was an American hip hop group from Hollis, Queens, New York, founded in 1981 by Joseph Simmons, Darryl McDaniels, and Jason Mizell.
 Run-D.M.C.
 is widely acknowledged as one of the most influential acts in the history of hip hop culture.
 Run-D.M.C.
 is one of the most famous hip-hop acts of the 1980s who, along with LL Cool J, The Beastie Boys, and Public Enemy, signified the advent of the new school of hip-hop music.
 Run-D.M.C.
 were the first group in the genre to have a gold album ("Run–D.M.C.", 1984) and be nominated for a Grammy Award.
 They were the first to earn a platinum record ("King of Rock", 1985), the first to earn a multiplatinum certification ("Raising Hell", 1986), the first to have videos on MTV, and the first to appear on "American Bandstand" and the cover of "Rolling Stone".
 Run-D.M.C.
 was the only hip hop act to perform at Live Aid in 1985.
"3-Minute Rule" is the 7th track on the album "Paul's Boutique" by American hip hop group the Beastie Boys, released on July 25, 1989.
 The track was produced and written by the Beastie Boys & the Dust Brothers, and engineered by Mario Caldato & Allen Abrahamson.
63 and 19 are mixtapes by Kool A.D, released as a double-album on February 7, 2013.
 The albums include collaborations with Pictureplane, Young L, SKYWLKR, Keyboard Kid, Trackademicks, Fat Tony, Mike Finito, Lakutis and Spank Rock as well as a beat Ad-Rock of the Beastie Boys originally made for Das Racist.
The Young and the Useless were an American punk band formed in the early 1980s that consisted of Adam Trese, Arthur Africano, David Scilken and future Beastie Boys member Adam Horovitz.
 They were managed by former Beastie Boys manager Nick Cooper.
 Their first recording "Real Men Don't Floss" was released by Ratcage Records.
 It is rumoured that they recorded a second album, but it was never released and its whereabouts is unknown.
 They played shows in New York City clubs including: A7, CBGB, Rock Lounge, Mudd Club, Club 57, Rock Hotel and 2+2; and played with Bad Brains, The Stimulators, Dead Kennedys, Ramones, P.I.L., Hüsker Dü, the Mob, the Necros, Adrenalin O.D. and the Beastie Boys.
"Paul Revere" is a song by American hip hop group Beastie Boys, released as the third single from their debut album "Licensed to Ill" (1986).
 It was written by Adam Horovitz, Joseph Simmons, Darryl McDaniels, and Rick Rubin.
 It was produced by Rick Rubin and the Beastie Boys.
 The song tells a fictional story of how the Beastie Boys met.
The story of Foreign Legion began in the bay area in the late nineties where rappers Prozack Turner and Marc Stretch were both pursuing their careers as emcees separately.
 The universe brought the two together one fateful afternoon in a run down strip club in a filthy part of town where Stretch was working as the daytime DJ, and Turner working for the company that supplied the strip club with everything from the plastic cups for the “bottomless soda” fountain, to the blue cleaning agent the strippers used to spray down the brass pole between sets.
 Sharing a love for hip hop music, the two quickly became friends and soon after, band mates.
 The two involved themselves with a Hip Hop organization based in Oakland called Ill Crew Universal, which helped to promote Foreign Legion by pushing their demo, booking shows and getting them on Davey D radio show.
 Releasing their first single “Full Time B Boy” on ABB Records in 1999 with DJ Design, the group quickly became popular in the bay area, Los Angeles, New York and overseas due to their on stage presence and high powered live shows, complete with costume changes, theatrics and a cynical brand of humor, not normally found in hip hop circles.
 Releasing their first full length “Kidnapper Van” on Insiduous Urban Records in 2000, led to more critical acclaim, a U.S., European and two Australian tours, and being courted by the Beastie Boys Mike D. and his then label, Grand Royal.
"Don't Play No Game That I Can't Win" is a song by American hip hop group the Beastie Boys, from their eighth studio album "Hot Sauce Committee Part Two".
 Featuring American singer Santigold, the song was released as the fourth single from the album on July 26, 2011.
 "Don't Play No Game That I Can't Win" was written and produced by group members Michael "Mike D" Diamond, Adam "MCA" Yauch and Adam "Ad-Rock" Horovitz, with additional writing by Santigold.
Ill Communication is the fourth studio album by American hip hop group Beastie Boys.
 It was released on May 31, 1994 by Grand Royal Records.
 Co-produced by Beastie Boys and Mario C., the album is among the band's most varied releases, drawing from hip hop, punk rock, jazz and funk.
 As with their prior release "Check Your Head", this album continues the band's trend away from sampling and towards live instruments.
Rip Slyme (often stylized as RIP SLYME) is a Japanese hip hop group.
 It is composed of four MCs; Ryo-Z, Ilmari, Pes & Su, and a DJ, Fumiya.
 Their sound derives its influences from old school hip hop and other hip hop such as The Pharcyde, De La Soul, Public Enemy, Jurassic 5, the Beastie Boys, DJ Premier and Leaders of the New School.