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Revenue from Contracts with Customers - Contract Assets and Liabilities (Details) - USD ($)
$ in Thousands
12 Months Ended
Sep. 30, 2022
Sep. 30, 2021
Sep. 30, 2020
Change in Contract with Customer, Liability [Roll Forward]      
Balance, beginning of year $ 1,489,842 $ 1,272,632 $ 1,198,116
Amounts added but not recognized as revenues 1,167,143 1,122,081 850,022
Deferred revenue acquired through acquisition of businesses 10,591 779 39,000
Revenues recognized related to the opening balance of deferred revenue (975,996) (905,650) (814,506)
Balance, end of year $ 1,691,580 $ 1,489,842 $ 1,272,632