Retirement Benefit Plans - Additional Information (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 31, 2020	Jan. 31, 2019	Jan. 31, 2018
Defined Contribution Plan Disclosure [Line Items]
Projected benefit obligation of plan assets	$ 103.5	$ 91.6
Accumulated benefit obligation	97.3	85.1
Fair value of plan assets	96.2	80.8
Other long-term liabilities	11.6	10.8
Net periodic (benefit) cost	3.7	(3.1)	$ 6.7
Estimated future employer contributions in next fiscal year	$ 4.9
United States
Defined Contribution Plan Disclosure [Line Items]
Maximum annual contributions per employee	75.00%
Cost Recognized	$ 21.4	17.1	17.3
Foreign Plan
Defined Contribution Plan Disclosure [Line Items]
Contributions paid by employer	$ 28.7	$ 29.6	$ 27.2
Mandatory Retirement Savings, Cash Balance Plan
Defined Contribution Plan Disclosure [Line Items]
Weighted-average interest crediting rate	1.00%	1.00%	1.00%
Supplementary Retirement Savings, Cash Balance Plan
Defined Contribution Plan Disclosure [Line Items]
Weighted-average interest crediting rate	0.10%	0.30%	0.30%