Summary of Significant Accounting Policies - Narrative (Details) - USD ($) $ in Millions	12 Months Ended
Jan. 02, 2022	Jan. 03, 2021	Dec. 29, 2019
Accounting Policies [Abstract]
Fiscal period duration	364 days	371 days	364 days
Advertising expense	$ 7.5	$ 8.1	$ 9.4
Accounting Policies [Line Items]
Depreciation expense	16.4	16.8	$ 25.3
Intangible assets, accumulated amortization	30.1	17.1
Accounts payable	687.2	536.8
Accrued payroll and related taxes	318.4	293.0
Workers Compensation
Accounting Policies [Line Items]
Liability for claims	1.0
Cloud Computing Arrangements
Accounting Policies [Line Items]
Amortization of intangible assets	2.2	1.0
Intangible assets, accumulated amortization	3.2	1.0
Prepaid Expenses and Other Current Assets \| Cloud Computing Arrangements
Accounting Policies [Line Items]
Short-term hosted software	2.7	2.9
Other Noncurrent Assets \| Cloud Computing Arrangements
Accounting Policies [Line Items]
Long-term hosted software	13.9	7.2
Book overdrafts
Accounting Policies [Line Items]
Accounts payable	5.4	9.3
Accrued payroll and related taxes	$ 39.1	$ 11.0
PersolKelly Pte. Ltd.
Accounting Policies [Line Items]
Equity method investment, ownership percentage	49.00%	49.00%

Accounting Policies

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Long-term Hosted Software

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Short-term Hosted Software

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Sum of the carrying values as of the balance sheet date of obligations incurred through that date and due within one year (or the operating cycle, if longer), including liabilities incurred (and for which invoices have typically been received) and payable to vendors for goods and services received, taxes, interest, rent and utilities, accrued salaries and bonuses, payroll taxes and fringe benefits.

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Amount charged to advertising expense for the period, which are expenses incurred with the objective of increasing revenue for a specified brand, product or product line.

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The aggregate expense charged against earnings to allocate the cost of intangible assets (nonphysical assets not used in production) in a systematic and rational manner to the periods expected to benefit from such assets. As a noncash expense, this element is added back to net income when calculating cash provided by or used in operations using the indirect method.

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The amount of expense recognized in the current period that reflects the allocation of the cost of tangible assets over the assets' useful lives. Includes production and non-production related depreciation.

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Total of the carrying values as of the balance sheet date of obligations incurred through that date and payable for obligations related to services received from employees, such as accrued salaries and bonuses, payroll taxes and fringe benefits. Used to reflect the current portion of the liabilities (due within one year or within the normal operating cycle if longer).

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The percentage of ownership of common stock or equity participation in the investee accounted for under the equity method of accounting.

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Accumulated amount of amortization of assets, excluding financial assets and goodwill, lacking physical substance with a finite life.

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Duration of a fiscal period, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days. Includes, but not limited to, weeks in a year or quarter.

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The amount needed to reflect the estimated ultimate cost of settling claims relating to insured events that have occurred on or before the balance sheet date, whether or not reported to the insurer at that date.

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