Derivative Financial Instruments - Fair Value of Derivative Instruments in the Consolidated Balance Sheet (Details) - USD ($) $ in Thousands	Mar. 31, 2022	Sep. 30, 2021
Derivatives designated as hedging instruments: | Interest rate swap contract | Prepaid expenses and other current assets
Derivatives, Fair Value [Line Items]
Derivative Assets	$ 6,001	$ 0
Derivative Liabilities	0	0
Derivatives designated as hedging instruments: | Interest rate swap contract | Other long-term assets
Derivatives, Fair Value [Line Items]
Derivative Assets	36,902	12,335
Derivative Liabilities	0	0
Derivatives designated as hedging instruments: | Interest rate swap contract | Accrued expenses and other current liabilities
Derivatives, Fair Value [Line Items]
Derivative Assets	0	0
Derivative Liabilities	0	2,995
Derivatives not designated as hedging instruments: | Foreign exchange contracts | Prepaid expenses and other current assets
Derivatives, Fair Value [Line Items]
Derivative Assets	124	0
Derivative Liabilities	0	0
Derivatives not designated as hedging instruments: | Foreign exchange contracts | Accrued expenses and other current liabilities
Derivatives, Fair Value [Line Items]
Derivative Assets	0	0
Derivative Liabilities	$ 489	$ 388