Deferred Compensation (Details) - USD ($)	12 Months Ended
	Jan. 31, 2022	Jan. 31, 2021	Jan. 31, 2020
Deferred Compensation Arrangement with Individual, Excluding Share-based Payments and Postretirement Benefits [Line Items]
Costs to obtain a contract	$ 138,500,000	$ 120,900,000
Amortization of costs to obtain a contract	117,800,000	96,600,000	$ 101,600,000
Contract cost impairment loss	0	0	$ 0
Rabbi Trust
Deferred Compensation Arrangement with Individual, Excluding Share-based Payments and Postretirement Benefits [Line Items]
Deferred compensation liability, current and non-current	89,500,000	81,000,000
Deferred compensation liability, current	7,100,000	7,300,000
Deferred compensation liability, non-current	$ 82,400,000	$ 73,700,000