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Stock-based Compensation Expense (Additional Information) (Details)
$ in Millions
3 Months Ended 9 Months Ended
Oct. 31, 2020
USD ($)
Apr. 30, 2020
USD ($)
Oct. 31, 2019
USD ($)
Oct. 31, 2020
USD ($)
period
shares
Oct. 31, 2019
USD ($)
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
Allocated share-based compensation expense $ 97.4   $ 94.0 $ 291.5 $ 257.4
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       $ 400.6 277.3
Awards granted in period (shares) | shares       2,215,000.0  
Restricted Stock Units (RSUs)          
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
Awards granted in period (shares) | shares       1,900,000  
Allocated share-based compensation expense 74.7   73.8 $ 222.9 192.4
Performance Stock Unit          
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
Awards granted in period (shares) | shares       300,000  
Allocated share-based compensation expense $ 8.7   $ 6.4 $ 26.2 $ 18.6
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]          
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% 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%