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Earnings per Share - Schedule of Calculation of Numerator and Denominator in Earnings Per Share (Details) - USD ($) $ / shares in Units, $ in Millions	12 Months Ended
	Sep. 30, 2025	Sep. 30, 2024	Sep. 30, 2023
Numerator:
Net income	$ 305.9	$ 260.8	$ 238.5
Less: Allocation to participating securities	(10.4)	(9.1)	(8.1)
Net income allocated to common stockholders, basic	295.5	251.7	230.4
Net income allocated to common stockholders, diluted	$ 295.5	$ 251.7	$ 230.4
Denominator:
Common shares outstanding (in shares)	47,431,675	45,808,855	44,904,000
Dilutive potential common shares outstanding:
Share-based awards (in shares)	2,692,827	1,628,688	1,489,516
Diluted shares outstanding (in shares)	50,124,502	47,437,543	46,393,516
Earnings per share:
Earnings per share - basic (in dollar per share)	$ 6.22	$ 5.49	$ 5.14
Earnings per share - diluted (in dollar per share)	$ 5.89	$ 5.31	$ 4.97

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