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Derivative Financial Instruments - Gains Losses on Derivative Financial Instruments Recorded in Consolidated Statements of Income (Details) - USD ($)
$ in Thousands
12 Months Ended
Sep. 30, 2022
Sep. 30, 2021
Sep. 30, 2020
Foreign Currency Forward Contracts      
Derivative [Line Items]      
Gain (loss) on foreign currency forward contracts $ (2,748) $ 2,064 $ (347)