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Fair Value Measurements - Summary of Financial Assets and Liabilities Measured at Fair Value (Details) - USD ($)
$ in Thousands
Mar. 31, 2024
Sep. 30, 2023
Assets:    
Interest rate swap contract $ 1,111 $ 1,409
Liabilities:    
Contingent consideration liabilities 85,908 86,059
Level 2 [Member]    
Assets:    
Interest rate swap contract 1,111 1,409
Level 3 [Member]    
Liabilities:    
Contingent consideration liabilities $ 85,908 $ 86,059