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Stockholders' Equity - Changes in Accumulated Other Comprehensive Income by Component, Net of Tax (Details) - USD ($) $ in Millions |  | 12 Months Ended
--- | --- | ---
Mar. 01, 2022 | Dec. 31, 2023 | Jan. 01, 2023 | Jan. 02, 2022
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward] |  |  |  |
Balance at beginning of year |  | $ 1,254.2 | $ 1,336.2 |
Balance at end of year |  | 1,253.7 | 1,254.2 | $ 1,336.2
Other Expense |  |  |  |
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward] |  |  |  |
Amounts reclassified from accumulated other comprehensive income (loss) |  | (1.4) |  |
Gain (Loss) on Disposal of Assets |  |  |  |
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward] |  |  |  |
Amounts reclassified from accumulated other comprehensive income (loss) |  | 1.4 |  |
PersolKelly Pte. Ltd. |  |  |  |
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward] |  |  |  |
Amounts reclassified from accumulated other comprehensive income (loss) | $ 1.9 |  |  |
Foreign currency translation adjustments: |  |  |  |
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward] |  |  |  |
Balance at beginning of year |  | (7.4) | (25.0) | (0.8)
Other comprehensive income (loss) before classifications |  | 8.0 | (7.5) | (24.2)
Net current-period other comprehensive income (loss) |  | 8.0 | 17.6 | (24.2)
Balance at end of year |  | 0.6 | (7.4) | (25.0)
Foreign currency translation adjustments: | Liquidation of Subsidiary |  |  |  |
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward] |  |  |  |
Amounts reclassified from accumulated other comprehensive income (loss) |  | 0.0 | 20.4 | 0.0
Foreign currency translation adjustments: | Equity Method Investment |  |  |  |
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward] |  |  |  |
Amounts reclassified from accumulated other comprehensive income (loss) |  | 0.0 | 4.7 | 0.0
Foreign currency translation adjustments: | PersolKelly Pte. Ltd. | Other Expense |  |  |  |
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward] |  |  |  |
Amounts reclassified from accumulated other comprehensive income (loss) |  | (1.9) |  |
Pension liability adjustments: |  |  |  |
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward] |  |  |  |
Balance at beginning of year |  | (1.1) | (2.7) | (3.4)
Other comprehensive income (loss) before classifications |  | 0.6 | 1.5 | 0.5
Amounts reclassified from accumulated other comprehensive income (loss) |  | 0.1 | 0.1 | 0.2
Net current-period other comprehensive income (loss) |  | 0.7 | 1.6 | 0.7
Balance at end of year |  | (0.4) | (1.1) | (2.7)
Accumulated Other Comprehensive Income (Loss) |  |  |  |
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward] |  |  |  |
Balance at beginning of year |  | (8.5) | (27.7) | (4.2)
Balance at end of year |  | $ 0.2 | $ (8.5) | $ (27.7)

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