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Debt - Details of Long-term Debt Table (Details) - USD ($)
$ in Thousands
12 Months Ended
Sep. 30, 2022
Sep. 30, 2021
Debt Instruments    
Total $ 1,087,461 $ 1,392,961
Variable-rate tranche    
Debt Instruments    
Total $ 407,500 413,000
Variable-rate tranche | LIBOR    
Debt Instruments    
Percentage points added to the reference rate 2.25%  
Senior notes due Apr. 2025    
Debt Instruments    
Total   300,000
Interest rate (as a percent) 8.75%  
Senior notes due Dec. 2025    
Debt Instruments    
Total $ 679,961 $ 679,961
Interest rate (as a percent) 5.625%