Income Taxes (Details) - USD ($) $ / shares in Units, $ in Thousands	12 Months Ended
	Jan. 02, 2022	Jan. 03, 2021	Dec. 29, 2019	Dec. 30, 2018	Dec. 31, 2017
Income Tax Contingency [Line Items]
Income Tax Holiday, Aggregate Dollar Amount	$ (19,000)	$ (21,800)	$ (10,400)
Effective Tax Rate, Income Tax on Repatriation of Foreign Earnings	$ 37,100
Impact of benefits derived from tax holidays on earnings per share, basic	$ 0.16	$ (0.20)	$ (0.09)
Impact of benefits derived from tax holidays on earnings per share, diluted	$ (0.16)	$ (0.19)	$ (0.09)
Valuation Allowance, Amount	$ 91,503	$ 99,740
Reconciliation of Unrecognized Tax Benefits, Excluding Amounts Pertaining to Examined Tax Returns [Roll Forward]
Unrecognized tax benefits, beginning of period	38,773	35,547	$ 33,009
Gross increases - tax positions in prior period	2,877	4,974	275
Gross decreases - tax positions in prior period	0	(2,471)	(2,183)
Gross increases - current-period tax positions	149	151	152
Unrecognized Tax Benefits, Increase Resulting from Acquisition	22,697	158	4,158
Settlements	(2,252)	0	(45)
Lapse of statute of limitations	(563)	0	0
Foreign currency translation adjustments	(23)	414	181
Unrecognized tax benefits, end of period		38,773	35,547	$ 33,009
Income Tax Penalties and Interest Accrued	7,600	5,800
Income Tax Penalties and Interest Expense	1,800	1,800	1,600
Unrecognized Tax Benefits, Ending Balance	61,658	38,773	35,547
Uncertain tax benefits if recognized that could affect the continuing operations effective tax rate	58,000
Uncertain tax benefits if recognized that could affect the discontinuing operations effective tax rate	1,700
Unrecognized Tax Benefits Expected To Be Resolved With In A Year	1,000
Undistributed Earnings of Foreign Subsidiaries Not Meeting Requirements to be Reinvested	1,200,000
Tax Adjustments, Settlements, and Unusual Provisions	43,200	10,800	(23,400)
Effective Income Tax Rate Reconciliation, Repatriation of Foreign Earnings, Amount	37,147	0	0
2017 Tax Cuts and Jobs Act [Member]
Reconciliation of Unrecognized Tax Benefits, Excluding Amounts Pertaining to Examined Tax Returns [Roll Forward]
Tax Cuts and Jobs Act, Transition Tax for Accumulated Foreign Earnings, Income Tax Expense			2,700	$ (4,600)	$ 85,000
Discrete Income Tax Expense (Benefit), Tax Reform Trueup			2,700
Other Tax Matters [Member]
Reconciliation of Unrecognized Tax Benefits, Excluding Amounts Pertaining to Examined Tax Returns [Roll Forward]
Tax Adjustments, Settlements, and Unusual Provisions	3,900	1,600	1,400
Excess tax benefits on stock compensation [Member]
Reconciliation of Unrecognized Tax Benefits, Excluding Amounts Pertaining to Examined Tax Returns [Roll Forward]
Tax Adjustments, Settlements, and Unusual Provisions	(5,500)	(11,700)	(4,900)
Valuation allowance adjustments [Member]
Reconciliation of Unrecognized Tax Benefits, Excluding Amounts Pertaining to Examined Tax Returns [Roll Forward]
Tax Adjustments, Settlements, and Unusual Provisions		(2,500)	(12,300)
Foreign tax rate changes
Reconciliation of Unrecognized Tax Benefits, Excluding Amounts Pertaining to Examined Tax Returns [Roll Forward]
Tax Adjustments, Settlements, and Unusual Provisions		2,500
Interest on uncertain tax positions
Reconciliation of Unrecognized Tax Benefits, Excluding Amounts Pertaining to Examined Tax Returns [Roll Forward]
Tax Adjustments, Settlements, and Unusual Provisions		4,500
Tax elections adjustments [Member]
Reconciliation of Unrecognized Tax Benefits, Excluding Amounts Pertaining to Examined Tax Returns [Roll Forward]
Tax Adjustments, Settlements, and Unusual Provisions			(3,700)
True-up of Return-to-Provision [Member]
Reconciliation of Unrecognized Tax Benefits, Excluding Amounts Pertaining to Examined Tax Returns [Roll Forward]
Tax Adjustments, Settlements, and Unusual Provisions		1,200	$ (6,700)
Foreign fiscal unity adjustments
Reconciliation of Unrecognized Tax Benefits, Excluding Amounts Pertaining to Examined Tax Returns [Roll Forward]
Tax Adjustments, Settlements, and Unusual Provisions		$ 15,200
Assertions Regarding Reinvestment of Foreign Earnings
Reconciliation of Unrecognized Tax Benefits, Excluding Amounts Pertaining to Examined Tax Returns [Roll Forward]
Tax Adjustments, Settlements, and Unusual Provisions	37,100
Unrecognized tax (benefits) expense [Member]
Reconciliation of Unrecognized Tax Benefits, Excluding Amounts Pertaining to Examined Tax Returns [Roll Forward]
Tax Adjustments, Settlements, and Unusual Provisions	(1,900)
Remeasurement of Deferred Tax Liabilities [Member]
Reconciliation of Unrecognized Tax Benefits, Excluding Amounts Pertaining to Examined Tax Returns [Roll Forward]
Tax Adjustments, Settlements, and Unusual Provisions	14,000
Deferred Tax Assets and Liabilities in Connection with United Kingdom Finance Act 2021 [Member]
Reconciliation of Unrecognized Tax Benefits, Excluding Amounts Pertaining to Examined Tax Returns [Roll Forward]
Tax Adjustments, Settlements, and Unusual Provisions	(1,800)
Discrete Tax Benefits Related a Transaction Completed in Second Quarter of Fiscal Year 2021 [Member]
Reconciliation of Unrecognized Tax Benefits, Excluding Amounts Pertaining to Examined Tax Returns [Roll Forward]
Tax Adjustments, Settlements, and Unusual Provisions	(6,400)
General Business [Member]
Reconciliation of Unrecognized Tax Benefits, Excluding Amounts Pertaining to Examined Tax Returns [Roll Forward]
Tax Credit Carryforward, Amount	600
State and Local Jurisdiction [Member]
Income Tax Contingency [Line Items]
Operating Loss Carryforwards	10,800
Reconciliation of Unrecognized Tax Benefits, Excluding Amounts Pertaining to Examined Tax Returns [Roll Forward]
Tax Credit Carryforward, Amount	15,000
Foreign Tax Authority [Member]
Income Tax Contingency [Line Items]
Operating Loss Carryforwards	452,000
Reconciliation of Unrecognized Tax Benefits, Excluding Amounts Pertaining to Examined Tax Returns [Roll Forward]
Tax Credit Carryforward, Amount	100
Internal Revenue Service (IRS) [Member]
Income Tax Contingency [Line Items]
Operating Loss Carryforwards	$ 74,800