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Income Taxes - Reconciliation of Income Tax Expense, Net of Federal Income Tax Rate (Detail) - USD ($) $ in Millions | 12 Months Ended
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Jan. 01, 2022 | Jan. 02, 2021 | Dec. 28, 2019
Income Taxes [Line Items] |  |  |
Income taxes at U.S. statutory rate of 21% | $ 16.9 | $ (38.7) | $ 30.6
State income taxes, net of federal income tax | (1.1) | (8.1) | 0.5
Adjustments for uncertain tax positions | (1.3) | (1.4) | (1.0)
Change in valuation allowance | 2.2 | 4.7 | (0.2)
Change in state tax rates | 0.0 | 0.0 | (1.5)
Global Intangible Low Tax Income Tax | 3.2 | 2.5 | 2.1
Foreign Derived Intangible Income Tax Credit | (3.7) | (1.6) | (4.4)
Deferred Tax Assets, Tax Deferred Expense, Compensation and Benefits, Share-based Compensation Cost | 5.2 | 1.6 | 2.0
Effective Income Tax Rate Reconciliation, Nondeductible Expense, Share-based Payment Arrangement, Amount | (3.7) | (4.6) | (5.1)
Effective Income Tax Rate Reconciliation Deferred ax on Future Dividends Due To TCJA | (0.9) | 1.0 | 0.6
Tax Adjustments, Settlements, and Unusual Provisions | 2.5 | 0.0 | 0.0
Deferred Income Taxes and Tax Credits | (1.2) | 0.0 | 0.0
Other Permanent adjustments and non-deductible expenses | (0.3) | 1.0 | (0.6)
Other | (0.4) | 0.2 | (0.3)
Income tax expense (benefit) | 13.3 | (45.5) | 17.0
HONG KONG |  |  |
Income Taxes [Line Items] |  |  |
Foreign earnings taxed at rates different from the U.S. statutory rate: | (7.2) | (3.3) | (8.5)
OTHER JURISDICTIONS |  |  |
Income Taxes [Line Items] |  |  |
Foreign earnings taxed at rates different from the U.S. statutory rate: | $ 3.1 | $ 1.2 | $ 2.8

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- Definition Amount before allocation of valuation allowances of deferred tax asset attributable to deductible temporary differences from compensation and benefits costs. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 740 -SubTopic 10 -Section 50 -Paragraph 8 -URI http://asc.fasb.org/extlink&oid=121826272&loc=d3e32632-109319 Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef -Publisher FASB -Name Accounting Standards Codification -Topic 740 -SubTopic 10 -Section 50 -Paragraph 6 -URI http://asc.fasb.org/extlink&oid=121826272&loc=d3e32621-109319 + Details
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