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Stock-based Compensation Expense (Additional Information) (Details)
$ in Millions
3 Months Ended 6 Months Ended
Jul. 31, 2020
USD ($)
shares
Apr. 30, 2020
USD ($)
Jul. 31, 2019
USD ($)
shares
Jul. 31, 2020
USD ($)
period
shares
Jul. 31, 2019
USD ($)
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
Allocated share-based compensation expense $ 95.9   $ 88.2 $ 194.1 $ 163.4
Settlement of liability-classified restricted stock units   $ 28.7   28.7 0.0
Market capitalization       $ 2,000.0  
Expected dividend yield (in percentage)       0.00%  
Restricted Stock Units (RSUs) and Performance Shares          
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
Awards vested in period, fair value       $ 132.3 84.3
Awards granted in period (shares) | shares       867,800  
Restricted Stock Units (RSUs)          
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
Awards granted in period (shares) | shares       600,000  
Allocated share-based compensation expense $ 71.3   $ 64.2 $ 148.2 118.6
Performance Stock Unit          
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
Awards granted in period (shares) | shares 0   0 300,000  
Allocated share-based compensation expense $ 10.1   $ 5.7 $ 17.5 $ 12.2
Award vesting period       3 years  
Expected dividend yield (in percentage)       0.00% 0.00%
1998 Employee Qualified Stock Purchase Plan          
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
Awards granted in period (shares) | shares 0   0    
Employee stock purchase plan maximum percentage of compensation to purchase shares by eligible participants       15.00%  
Employee stock purchase plan minimum percentage of common stock fair value defined to purchase shares by eligible participants       85.00%  
Employee stock purchase plan, number of exercise periods | period       4  
Employee stock purchase plan, term of exercise period       6 months  
Employee stock purchase plan, term of offering period       24 months  
Expected dividend yield (in percentage)       0.00% 0.00%
Share-based Compensation Award, Tranche One | Performance Stock Unit          
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
PSU annual vesting percentage       33.33%  
Share-based Compensation Award, Tranche Two | Performance Stock Unit          
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
PSU annual vesting percentage       33.33%  
Share-based Compensation Award, Tranche Three | Performance Stock Unit          
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
PSU annual vesting percentage       33.33%