Business Segment Information - Reconciliation of Segment Adjusted EBITDA to Net Income (Detail) - USD ($) $ in Millions	3 Months Ended
	Jan. 31, 2023	Jan. 31, 2022
Segment Reporting Information [Line Items]
Interest expense, net	$ (7.1)	$ (3.4)
Benefit for income taxes	5.1	1.8
Restructuring costs	0.0	(3.7)
Stock-based compensation expense	(5.9)	(2.3)
Net loss	(13.5)	(0.7)
Corporate and Other [Member]
Segment Reporting Information [Line Items]
Adjusted EBITDA	(8.3)	(8.4)
Operating Segment [Member] | Fire & Emergency [Member]
Segment Reporting Information [Line Items]
Adjusted EBITDA	(2.0)	1.8
Operating Segment [Member] | Commercial [Member]
Segment Reporting Information [Line Items]
Adjusted EBITDA	7.3	7.8
Operating Segment [Member] | Recreation [Member]
Segment Reporting Information [Line Items]
Adjusted EBITDA	24.3	17.1
Reconciling Items [Member]
Segment Reporting Information [Line Items]
Depreciation and amortization	(6.9)	(9.6)
Interest expense, net	(7.1)	(3.4)
Benefit for income taxes	5.1	1.8
Transaction expenses	(0.2)	(0.2)
Sponsor expense reimbursement	(0.2)	(0.1)
Restructuring costs		(3.7)
Restructuring related charges	(5.6)	(0.7)
Stock-based compensation expense	(5.9)	(2.3)
Legal matters	(13.8)	(0.8)
Other Items	(0.2)
Net loss	$ (13.5)	$ (0.7)