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Revenue from Contracts with Customers - Contract Assets and Liabilities (Details) - USD ($)
$ in Thousands
12 Months Ended
Sep. 30, 2023
Sep. 30, 2022
Sep. 30, 2021
Change in Contract with Customer, Liability [Roll Forward]      
Balance, beginning of year $ 1,691,580 $ 1,489,842 $ 1,272,632
Amounts added but not recognized as revenues 1,162,698 1,167,143 1,122,081
Deferred revenue acquired through acquisition of businesses 1,800 10,591 779
Revenues recognized related to the opening balance of deferred revenue (1,080,957) (975,996) (905,650)
Balance, end of year $ 1,775,121 $ 1,691,580 $ 1,489,842