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Equity-Based Compensation - Narrative (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Oct. 31, 2021	Nov. 01, 2020	Oct. 31, 2021	Nov. 01, 2020	Jul. 31, 2021
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Share based compensation expense	$ 2.7	$ 1.1	$ 22.2	$ 3.1
Unrecognized share based compensation	$ 11.4		$ 11.4
Omnibus Incentive Plan \| Class A common stock
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Shares reserved and available for future issuance					12,600,000
Omnibus Incentive Plan \| Class A common stock \| Stock appreciation rights
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Shares reserved and available for future issuance					633,683