Deferred Compensation (Additional Information) (Details) - USD ($)	3 Months Ended		9 Months Ended
	Oct. 31, 2019	Oct. 31, 2018	Oct. 31, 2019	Oct. 31, 2018	Jan. 31, 2019
Deferred Compensation Arrangement with Individual, Excluding Share-based Payments and Postretirement Benefits [Line Items]
Marketable securities	$ 68,300,000		$ 68,300,000		$ 67,600,000
Costs to obtain a contract	75,900,000		75,900,000		93,000,000.0
Amortization of costs to obtain a contract	25,200,000	$ 26,900,000	75,400,000	$ 80,000,000.0
Impairment loss			0	$ 0
Rabbi Trust
Deferred Compensation Arrangement with Individual, Excluding Share-based Payments and Postretirement Benefits [Line Items]
Deferred compensation liability	68,300,000		68,300,000		60,300,000
Deferred compensation liability, current	5,900,000		5,900,000		5,000,000.0
Deferred compensation liability, non-current	$ 62,400,000		$ 62,400,000		$ 55,300,000