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Summary of Significant Accounting Policies - Revenue Recognition and Allowances for Accounts Receivable and Unbilled Services (Details) - USD ($) $ in Thousands | 12 Months Ended |  |  |  |
--- | --- | --- | --- | --- | ---
Dec. 31, 2022 | Jan. 01, 2022 | Jan. 02, 2021 | Dec. 29, 2019 | Dec. 28, 2019
Revenue Recognition |  |  |  |  |
Cumulative effect of a change in accounting principle | $ 211,154 | $ 205,834 | $ 209,019 |  | $ 197,751
Cumulative Effect Period of Adoption, Adjustment |  |  |  |  |
Revenue Recognition |  |  |  |  |
Cumulative effect of a change in accounting principle |  |  |  | $ (200) | $ (203)
Minimum |  |  |  |  |
Revenue Recognition |  |  |  |  |
Period in which engagements are generally completed (months) | 3 months |  |  |  |
Maximum |  |  |  |  |
Revenue Recognition |  |  |  |  |
Period in which engagements are generally completed (months) | 6 months |  |  |  |

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