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Goodwill and Intangible Assets - Changes in Carrying Amount of Goodwill (Details) - USD ($)
$ in Thousands
12 Months Ended
Sep. 30, 2022
Sep. 30, 2021
Goodwill And Intangible Assets Disclosure [Abstract]    
Balance $ 1,128,511 $ 1,128,198
Goodwill impairment (213,720)  
Effect of foreign currency translation (23,989) 313
Balance $ 890,802 $ 1,128,511