Question: Are Henry Koster and Johnnie To both film directors?

full_context: Document 1: Henry Kolker: Joseph Henry Kolker (November 13, 1874) [some sources 1870] Berlin, Prussia, Germany – July 15, 1947, Los Angeles, California) was an American stage and film actor and director.
Document 2: Michael Curtiz: Michael Curtiz ( ; born Manó Kaminer, December 24, 1888 April 10, 1962) was a Hungarian-born American film director, recognized as one of the most prolific directors in history. He directed classic films from the silent era and numerous others during Hollywood's Golden Age, when the studio system was prevalent.
Document 3: Das häßliche Mädchen: Das häßliche Mädchen ("The Ugly Girl", sometimes translated "The Ugly Duckling") is a German comedy film made in early 1933, during the transition from the Weimar Republic to Nazi Germany, and premièred in September that year. It was the first or second film directed by Hermann Kosterlitz, who left Germany before the film was completed and later worked in the United States under the name Henry Koster, and the last German film in which Dolly Haas appeared; she also later emigrated to the US. A riot broke out at the première to protest the male lead, Max Hansen, who was supposedly "too Jewish." The film's representation of the "ugly girl" as outsider has been described as a metaphorical way to explore the outsider existence of Jews.
Document 4: Sherry Hormann: Sherry Hormann (born 20 April 1960) is an American film director. She was married to film director Dominik Graf. In October 2011, she married cinematographer Michael Ballhaus; he died in April 2017.
Document 5: Wong Kar-wai: Wong Kar-wai, BBS (born 17 July 1958) is a Hong Kong Second Wave filmmaker, internationally renowned as an auteur for his visually unique, highly stylized work, including "As Tears Go By" (1988), "Days of Being Wild" (1990), "Ashes of Time" (1994), "Chungking Express" (1994), "Fallen Angels" (1995), "Happy Together" (1997), "2046" (2004) and "The Grandmaster" (2013). His film "In the Mood for Love" (2000), starring Maggie Cheung and Tony Leung, notably garnered widespread critical acclaim.
Document 6: John Woo: John Woo SBS (Ng Yu-Sum; born 1 May 1946) is a Chinese-born Hong Kong film director, writer, and producer. He is the owner of Lion Rock Productions. He is considered a major influence on the action genre, known for his highly chaotic action sequences, Mexican standoffs, and frequent use of slow motion. Woo has directed several notable Hong Kong action films, among them, "A Better Tomorrow" (1986), "The Killer" (1989), "Hard Boiled" (1992), and "Red Cliff" (2008/2009).
Document 7: Andrew Lau: Andrew Lau Wai-Keung (born 4 April 1960) is a Hong Kong film director, producer, and cinematographer. Lau began his career in the 1980s and 1990s, serving as a cinematographer to filmmakers such as Ringo Lam, Wong Jing and Wong Kar-wai. In the 1990s, Lau decided to have more creative freedom as a cinematographer by becoming a film director and producer. Apart from making films in his native Hong Kong, Lau has also made films in China, Korea and the United States. A highly prolific filmmaker, Lau has made films in a variety of genres, and is most notable in the West for his action and crime films which include the "Young and Dangerous" film series, the "Infernal Affairs" trilogy (the latter co-directed together with Alan Mak), and "Revenge of the Green Dragons" (executive produced by Martin Scorsese).
Document 8: Donnie Yen: Donnie Yen (born 27 July 1963), also known as Yen Chi Tan (甄子丹), is a Hong Kong actor, martial artist, film director, producer, action choreographer, and multiple-time world wushu tournament champion.
Document 9: Dario Argento: Dario Argento (] ; born 7 September 1940) is an Italian film director, producer, film critic and screenwriter. He is best known for his work in the horror film genre during the 1970s and 1980s, particularly in the subgenre known as "giallo", and for his influence on modern horror movies.
Document 10: The Great Opportunity: The Great Opportunity (German:Die große Gelegenheit) is a 1925 German silent film directed by Lorand von Kabdebo and starring Kurt Vespermann, Lia Eibenschütz and Colette Brettel. The production is notable as marking the filmmaking debut of Henry Koster, who co-wrote the screenplay. Koster would go on to become a top Hollywood film director.
Document 11: Johnnie To: Johnnie To (born 22 April 1955), also known as To Kei-Fung (杜琪峯), is a Hong Kong film director and producer. Popular in his native Hong Kong, To has also found acclaim overseas. Intensely prolific, To has made films in a variety of genres, though in the West he is best known for his action and crime movies, which have earned him critical respect and a cult following (which include Quentin Tarantino, who once said that he really loves to watch To's gangster films).
Document 12: Kurt Gerron: Kurt Gerron (11 May 1897 – 28 October 1944) was a German Jewish actor and film director.
Document 13: Henry Koster: Henry Koster (born Hermann Kosterlitz, May 1, 1905 – September 21, 1988) was a German-born film director. He was the husband of actress Peggy Moran.
Document 14: Quentin Tarantino: Quentin Jerome Tarantino ( ; born March 27, 1963) is an American director, writer, and actor. His films are characterized by nonlinear storylines, satirical subject matter, an aestheticization of violence, extended scenes of dialogue, ensemble casts consisting of established and lesser-known performers, references to popular culture, soundtracks primarily containing songs and score pieces from the 1960s to the 1980s, and features of neo-noir film. He is widely considered one of the greatest filmmakers of his generation.
Document 15: Fruit Chan: Fruit Chan Gor (; born 15 April 1959) is an independent Hong Kong Second Wave screenwriter, filmmaker and producer, who is best known for his style of film reflecting the everyday life of Hong Kong people. He is well known for using amateur actors (such as Sam Lee in "Made in Hong Kong", Wong Yau-Nam in "Hollywood Hong Kong") in his films. His name became familiar to many Hong Kongers only after the success of the 1997 film "Made in Hong Kong", which earned many local and international awards. Chan was deeply influenced by the era of sixties film in Japan, for the reason that they were not afraid to produce realistic movies that addressed society's problems. In particular, Nagisa Oshima, a Japanese director during the sixties was someone who Chan looked up to and thought of when directing Made in Hong Kong.
ground_truth: yes