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Revenue from Contracts with Customers - Contract Assets and Liabilities (Details) - USD ($)
$ in Thousands
6 Months Ended
Mar. 31, 2022
Mar. 31, 2021
Change in Contract with Customer, Liability [Roll Forward]    
Beginning Balance $ 1,489,841 $ 1,272,632
Amounts added but not recognized as revenues 723,631 680,124
Deferred revenue acquired through acquisition of businesses 10,591 779
Revenues recognized related to the opening balance of deferred revenue (624,327) (586,632)
Ending Balance $ 1,599,736 $ 1,366,903