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Revenue from Contracts with Customers - Contract Assets and Liabilities (Details) - USD ($)
$ in Thousands
9 Months Ended
Jun. 30, 2022
Jun. 30, 2021
Change in Contract with Customer, Liability [Roll Forward]    
Beginning Balance $ 1,489,841 $ 1,272,632
Amounts added but not recognized as revenues 973,673 946,186
Deferred revenue acquired through acquisition of businesses 10,591 779
Revenues recognized related to the opening balance of deferred revenue (836,800) (778,987)
Ending Balance $ 1,637,305 $ 1,440,610