Business Segment Information - Reconciliation of Segment Adjusted EBITDA to Net Income (Detail) - USD ($) $ in Millions	3 Months Ended					9 Months Ended
	Jul. 31, 2022	Apr. 30, 2022	Jan. 31, 2022	Jul. 31, 2021	Apr. 30, 2021	Jul. 31, 2022	Jul. 31, 2021
Segment Reporting Information [Line Items]
Interest expense, net	$ (4.3)			$ (3.4)		$ (11.2)	$ (14.4)
Provision for income taxes	(3.4)			(2.4)		(1.2)	(9.6)
Restructuring costs	(2.3)					(8.9)	(1.0)
Stock-based compensation expense						(6.3)	(5.4)
Loss on early extinguishment of debt							(1.4)
Net gain (loss) on sale of assets and business held for sale				1.0		(0.1)	(2.8)
Net income	9.5	$ (2.3)	$ (0.7)	23.7	$ 20.6
Corporate and Other [Member]
Segment Reporting Information [Line Items]
Adjusted EBITDA	(8.1)			(8.0)		(23.6)	(26.6)
Operating Segment [Member] | Fire & Emergency [Member]
Segment Reporting Information [Line Items]
Adjusted EBITDA	1.0			15.8		0.6	47.6
Operating Segment [Member] | Commercial [Member]
Segment Reporting Information [Line Items]
Adjusted EBITDA	6.8			9.7		19.0	25.1
Operating Segment [Member] | Recreation [Member]
Segment Reporting Information [Line Items]
Adjusted EBITDA	29.8			24.1		75.6	64.3
Reconciling Items [Member]
Segment Reporting Information [Line Items]
Depreciation and amortization	(6.9)			(7.6)		(25.2)	(24.2)
Interest expense, net	(4.3)			(3.4)		(11.2)	(14.4)
Provision for income taxes	(3.4)			(2.4)		(1.2)	(9.6)
Transaction expenses	(0.1)			(0.5)		(0.6)	(3.2)
Sponsor expense reimbursement						(0.1)	(0.2)
Restructuring costs	(2.3)					(8.9)	(1.0)
Restructuring related charges						(5.1)	(0.3)
Stock-based compensation expense	(1.8)			(1.9)		(6.3)	(5.5)
Legal matters	(1.2)			(2.8)		(6.4)	(3.1)
Loss on early extinguishment of debt							(1.4)
Net gain (loss) on sale of assets and business held for sale				1.0		(0.1)	(1.7)
Loss on acquisition of business							(0.4)
Losses attributable to assets held for sale				(0.3)			(1.0)
Net income	$ 9.5			$ 23.7		$ 6.5	$ 44.4