Stockholders' Equity - Accumulated Other Comprehensive Loss (Details) - USD ($) $ in Millions	Jan. 31, 2020	Jan. 31, 2019	Jan. 31, 2018	Jan. 31, 2017
Accumulated Other Comprehensive Income (Loss) [Line Items]
Stockholders' equity	$ 3,335.4	$ 3,130.9	$ 3,248.2	$ 3,028.4
Foreign currency translation adjustments
Accumulated Other Comprehensive Income (Loss) [Line Items]
Stockholders' equity	(130.4)	(108.2)
Deferred hedging gain (loss)
Accumulated Other Comprehensive Income (Loss) [Line Items]
Stockholders' equity	5.4
Deferred hedging gain (loss)
Accumulated Other Comprehensive Income (Loss) [Line Items]
Stockholders' equity		(24.5)
Net unrealized loss on benefit plans
Accumulated Other Comprehensive Income (Loss) [Line Items]
Stockholders' equity	(148.2)	(72.1)
Accumulated Other Comprehensive Loss
Accumulated Other Comprehensive Income (Loss) [Line Items]
Stockholders' equity	$ (273.2)	$ (204.8)	$ (138.0)	$ (256.2)