Business Segment Information - Reconciliation of Segment Adjusted EBITDA to Net (Loss) Income (Detail) - USD ($) $ in Millions	3 Months Ended			6 Months Ended
	Apr. 30, 2022	Jan. 31, 2022	Apr. 30, 2021	Apr. 30, 2022	Apr. 30, 2021
Segment Reporting Information [Line Items]
Interest expense, net	$ (3.5)		$ (5.5)	$ (6.9)	$ (11.0)
Benefit (provision) for income taxes	0.4		(7.2)	2.2	(7.2)
Restructuring costs	(2.9)			(6.6)	(1.0)
Stock-based compensation expense				(4.5)	(3.4)
Loss on early extinguishment of debt			(1.4)		(1.4)
Net loss on sale of assets and business held for sale	(0.1)			(0.1)	(3.8)
Net loss	(2.3)	$ (0.7)	20.6
Corporate and Other [Member]
Segment Reporting Information [Line Items]
Adjusted EBITDA	(7.1)		(9.6)	(15.5)	(18.7)
Operating Segment [Member] | Fire & Emergency [Member]
Segment Reporting Information [Line Items]
Adjusted EBITDA	(2.2)		21.7	(0.4)	31.9
Operating Segment [Member] | Commercial [Member]
Segment Reporting Information [Line Items]
Adjusted EBITDA	4.4		8.3	12.2	15.5
Operating Segment [Member] | Recreation [Member]
Segment Reporting Information [Line Items]
Adjusted EBITDA	28.7		25.1	45.8	40.2
Reconciling Items [Member]
Segment Reporting Information [Line Items]
Depreciation and amortization	(8.7)		(8.0)	(18.3)	(16.7)
Interest expense, net	(3.5)		(5.5)	(6.9)	(11.0)
Benefit (provision) for income taxes	0.4		(7.2)	2.2	(7.2)
Transaction expenses	(0.3)		(0.3)	(0.5)	(2.7)
Sponsor expense reimbursement				(0.1)	(0.2)
Restructuring costs	(2.9)			(6.6)	(1.0)
Restructuring related charges	(4.4)		(0.3)	(5.1)	(0.3)
Stock-based compensation expense	(2.2)		(1.7)	(4.5)	(3.6)
Legal matters	(4.4)			(5.2)	(0.4)
Loss on early extinguishment of debt			(1.4)		(1.4)
Net loss on sale of assets and business held for sale	(0.1)			(0.1)	(2.7)
Loss on acquisition of business					(0.4)
Losses attributable to assets held for sale			(0.5)		(0.7)
Net loss	$ (2.3)		$ 20.6	$ (3.0)	$ 20.6