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Income Taxes - Additional Information (Detail) - USD ($)
$ in Millions
3 Months Ended 9 Months Ended
Oct. 31, 2018
Oct. 31, 2017
Oct. 31, 2018
Oct. 31, 2017
Income Tax Contingency [Line Items]        
Effective tax rates 5.30% 20.40% 6.60% 11.00%
Maximum [Member]        
Income Tax Contingency [Line Items]        
Provisional amounts measurement period     1 year  
Effect on Provision for Income Taxes [Member]        
Income Tax Contingency [Line Items]        
Excess tax benefits recognized $ 12.0 $ 8.6 $ 31.0 $ 37.3