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Income Tax - Additional Information (Details) - USD ($) $ in Millions | 3 Months Ended
--- | ---
Apr. 30, 2021 | Apr. 30, 2020
Tax Credit Carryforward [Line Items] |  |
Benefit (provision) for income taxes | $ 24.2 | $ (24.0)
(Loss) income before income taxes | 131.4 | $ 90.5
Unrecognized tax benefits | 200.5 |
Unrecognized tax benefits that would impact effective tax rate | 168.4 |
Effect of change in unrecognized tax benefits | 8.2 |
SEC Schedule, 12-09, Valuation Allowance, Tax Credit Carryforward |  |
Tax Credit Carryforward [Line Items] |  |
Unrecognized tax benefits that would impact effective tax rate | $ 32.1 |

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