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Income Taxes - Tax (Benefit) Expense (Details) - USD ($)
$ in Thousands
 3 Months Ended 12 Months Ended
Sep. 30, 2022
Jun. 30, 2022
Mar. 31, 2022
Dec. 31, 2021
Sep. 30, 2021
Jun. 30, 2021
Mar. 31, 2021
Dec. 31, 2020
Sep. 30, 2022
Sep. 30, 2021
Sep. 30, 2020
Income from domestic operations before income tax expense                 $ 235,200 $ 98,600 $ 52,900
Income from foreign operations before income tax expense                 315,400 310,200 179,700
Current:                      
Federal                 22,800 32,200 21,800
State                 16,000 6,800 12,700
Foreign                 75,800 53,200 55,700
Total current income tax expense                 114,600 92,200 90,200
Deferred:                      
Federal                 22,100 (28,800) (21,800)
State                 11,800 18,800 12,800
Foreign                 (12,400) 6,800 (35,400)
Total income tax expense $ 33,000 $ 44,500 $ 36,000 $ 22,600 $ 46,100 $ (17,800) $ 35,100 $ 25,600 136,051 89,011 45,753
Total                      
Deferred:                      
Total deferred income tax benefit                 21,500 (3,200) (44,400)
Total income tax expense                 $ 136,100 $ 89,000 $ 45,800