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Business Segment Information - Reconciliation of Segment Adjusted EBITDA to Net Income (Detail) - USD ($)
$ in Millions
 3 Months Ended 9 Months Ended
Jul. 31, 2023
Apr. 30, 2023
Jan. 31, 2023
Jul. 31, 2022
Apr. 30, 2022
Jan. 31, 2022
Jul. 31, 2023
Jul. 31, 2022
Segment Reporting Information [Line Items]                
Interest expense, net $ (7.3)     $ (4.3)     $ (21.9) $ (11.2)
Provision for income taxes (3.5)     (3.4)     (4.2) (1.2)
Restructuring costs 0.0     (2.3)     0.0 (8.9)
Stock-based compensation expense             (11.0) (6.3)
Loss on sale of business             (1.1) (0.1)
Net income 14.9 $ 14.2 $ (13.5) 9.5 $ (2.3) $ (0.7) 15.6 6.5
Corporate and Other [Member]                
Segment Reporting Information [Line Items]                
Adjusted EBITDA (8.7)     (8.1)     (24.5) (23.6)
Operating Segment [Member] | Fire & Emergency [Member]                
Segment Reporting Information [Line Items]                
Adjusted EBITDA 18.1     (1.0)     25.6 (0.6)
Operating Segment [Member] | Commercial [Member]                
Segment Reporting Information [Line Items]                
Adjusted EBITDA 11.6     6.8     29.6 19.0
Operating Segment [Member] | Recreation [Member]                
Segment Reporting Information [Line Items]                
Adjusted EBITDA 18.4     29.8     71.9 75.6
Reconciling Items [Member]                
Segment Reporting Information [Line Items]                
Depreciation and amortization (6.3)     (6.9)     (19.7) (25.2)
Interest expense, net (7.3)     (4.3)     (21.9) (11.2)
Provision for income taxes (3.5)     (3.4)     (4.2) (1.2)
Transaction expenses (0.1)     (0.1)     (0.5) (0.6)
Sponsor expense reimbursement             (0.2) (0.1)
Restructuring costs       (2.3)       (8.9)
Restructuring related charges (1.9)           (10.5) (5.1)
Stock-based compensation expense (3.5)     (1.8)     (11.0) (6.3)
Legal matters (1.1)     (1.2)     (16.6) (6.4)
Loss on sale of business             (1.1) (0.1)
Other Items (0.8)           (1.3)  
Net income $ 14.9     $ (9.5)     $ 15.6 $ (6.5)