Income Taxes - Additional Information (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Oct. 31, 2018	Oct. 31, 2017	Oct. 31, 2018	Oct. 31, 2017
Discrete tax items [Line Items]
Effective income tax rate (as a percentage)	17.10%	33.40%	21.60%	32.90%
Provision (benefit) for income taxes	$ 19.6	$ 50.2	$ 105.2	$ 150.9
Decrease in unrecognized tax benefits and accrued interest and penalties	$ 1.1		4.4
Increase in gross unrecognized tax benefits			$ 2.7
True-up of Prior Year Tax Provision [Member]
Discrete tax items [Line Items]
Effective income tax rate, reconciliation	(3.80%)		(0.90%)
Provision (benefit) for income taxes			$ 4.4
2017 Tax Act [Member]
Discrete tax items [Line Items]
Effective income tax rate, reconciliation		(2.40%)	(0.60%)
Provision (benefit) for income taxes			$ (2.7)
Lapse in Statute of Limitations [Member]
Discrete tax items [Line Items]
Effective income tax rate, reconciliation			(1.60%)
Provision (benefit) for income taxes			$ (8.0)
Transition Tax Estimate Adjustment [Member]
Discrete tax items [Line Items]
Effective income tax rate, reconciliation	(1.00%)
Provision (benefit) for income taxes			$ (5.0)