Income Tax - Additional Information (Details) - USD ($) $ in Millions	3 Months Ended
	Apr. 30, 2021	Apr. 30, 2020
Tax Credit Carryforward [Line Items]
Benefit (provision) for income taxes	$ 24.2	$ (24.0)
(Loss) income before income taxes	131.4	$ 90.5
Unrecognized tax benefits	200.5
Unrecognized tax benefits that would impact effective tax rate	168.4
Effect of change in unrecognized tax benefits	8.2
SEC Schedule, 12-09, Valuation Allowance, Tax Credit Carryforward
Tax Credit Carryforward [Line Items]
Unrecognized tax benefits that would impact effective tax rate	$ 32.1