Deferred Compensation (Details) - USD ($)	3 Months Ended		9 Months Ended
	Oct. 31, 2021	Oct. 31, 2020	Oct. 31, 2021	Oct. 31, 2020	Jan. 31, 2021
Deferred Compensation Arrangement with Individual, Excluding Share-based Payments and Postretirement Benefits [Line Items]
Costs to obtain a contract	$ 110,800,000		$ 110,800,000		$ 120,900,000
Amortization of costs to obtain a contract	29,600,000	$ 23,800,000	83,600,000	$ 70,200,000
Impairment loss	0	$ 0	0	$ 0
Prepaid expenses and other current assets
Deferred Compensation Arrangement with Individual, Excluding Share-based Payments and Postretirement Benefits [Line Items]
Deferred compensation plan assets	7,900,000		7,900,000		7,300,000
Long-term Other Assets
Deferred Compensation Arrangement with Individual, Excluding Share-based Payments and Postretirement Benefits [Line Items]
Deferred compensation plan assets	88,400,000		88,400,000		73,700,000
Rabbi Trust
Deferred Compensation Arrangement with Individual, Excluding Share-based Payments and Postretirement Benefits [Line Items]
Deferred compensation plan assets	96,300,000		96,300,000		81,000,000
Deferred compensation liability	96,300,000		96,300,000		81,000,000
Deferred compensation liability, current	7,900,000		7,900,000		7,300,000
Deferred compensation liability, non-current	$ 88,400,000		$ 88,400,000		$ 73,700,000