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Employee Benefit Plans (Tables) - Pension Plans, Defined Benefit
 12 Months Ended
Jan. 01, 2023
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]  
Components of Net Periodic Benefit Cost (Credit) Net periodic pension cost for U.S. and non-U.S. plans included the following components for fiscal years ended:
 
January 1,
2023		January 2,
2022		January 3,
2021
(In thousands)
Service and administrative costs$6,331 $5,174 $7,414 
Interest cost10,751 9,440 12,876 
Expected return on plan assets(22,056)(24,417)(21,786)
Actuarial (gain) loss(23,706)(19,514)20,291 
Net periodic pension (credit) cost$(28,680)$(29,317)$18,795 
Schedule of Net Funded Status
The following table sets forth the changes in the funded status of the principal U.S. pension plan and the principal non-U.S. pension plans and the amounts recognized in the Company’s consolidated balance sheets as of January 1, 2023 and January 2, 2022. The pension liability of the Business at the end of fiscal year 2022 that will transfer upon sale was reclassified to discontinued operations, while the prior year was not restated.
 
 January 1, 2023January 2, 2022
Non-U.S.U.S.Non-U.S.U.S.
(In thousands)
Actuarial present value of benefit obligations:
Accumulated benefit obligations$207,503 $231,492 $337,454 $299,826 
Change in benefit obligations:
Projected benefit obligations at beginning of year$339,390 $299,826 $395,339 $317,679 
Service and administrative costs4,956 1,375 4,924 250 
Interest cost3,671 7,080 2,632 6,808 
Benefits paid and plan expenses(14,978)(19,870)(15,299)(18,693)
Benefit obligation classified in discontinued operations(8,261)— — — 
Actuarial gains(88,724)(56,919)(30,705)(6,218)
Effect of exchange rate changes(28,099)— (17,501)— 
Projected benefit obligations at end of year$207,955 $231,492 $339,390 $299,826 
Change in plan assets:
Fair value of plan assets at beginning of year$181,189 $290,116 $204,744 $268,686 
Actual return on plan assets(46,383)(53,498)(13,115)20,123 
Benefits paid and plan expenses(14,978)(19,870)(15,299)(18,693)
Employer’s contributions6,572 — 6,851 20,000 
Effect of exchange rate changes(19,659)— (1,992)— 
Fair value of plan assets at end of year$106,741 $216,748 $181,189 $290,116 
Net liabilities recognized in the consolidated balance sheets$(101,214)$(14,744)$(158,201)$(9,710)
Net amounts recognized in the consolidated balance sheets consist of:
Other assets$19,521 $— $33,084 $— 
Current liabilities(6,568)— (6,966)— 
Long-term liabilities(114,167)(14,744)(184,319)(9,710)
Net liabilities recognized in the consolidated balance sheets$(101,214)$(14,744)$(158,201)$(9,710)
Actuarial assumptions as of the year-end measurement date:
Discount rate4.12 %4.84 %1.41 %2.44 %
Rate of compensation increase3.16 %None2.78 %None
Actuarial assumptions used to determine net periodic pension cost during the year were as follows:
January 1, 2023January 2, 2022January 3, 2021
Non-U.S.U.S.Non-U.S.U.S.Non-U.S.U.S.
Discount rate1.41 %2.44 %0.92 %2.21 %1.34 %3.01 %
Rate of compensation increase2.78 %None2.78 %None3.36 %None
Expected rate of return on assets1.11 %7.25 %2.10 %7.25 %2.20 %7.25 %
Defined Benefit Plan, Plan with Projected Benefit Obligation in Excess of Plan Assets [Table Text Block]
The following table provides a breakdown of the non-U.S. benefit obligations and fair value of assets for pension plans that have benefit obligations in excess of plan assets:
January 1,
2023		January 2,
2022
(In thousands)
Pension Plans with Projected Benefit Obligations in Excess of Plan Assets
Projected benefit obligations$120,736 $191,285 
Fair value of plan assets— — 
Pension Plans with Accumulated Benefit Obligations in Excess of Plan Assets
Accumulated benefit obligations$120,283 $189,349 
Fair value of plan assets— — 
Schedule of Allocation of Plan Assets Assets of the defined benefit pension plans are primarily equity and debt securities. Asset allocations as of January 1, 2023 and January 2, 2022, and target asset allocations for fiscal year 2023 are as follows:
 Target AllocationPercentage of Plan Assets at
December 31, 2023January 1, 2023January 2, 2022
Asset CategoryNon-U.S.U.S.Non-U.S.U.S.Non-U.S.U.S.
Equity securities0-5%0-10%— %44 %— %46 %
Debt securities0-5%90-100%— %56 %— %54 %
Other95-100%0-10%100 %— %100 %— %
Total100 %100 %100 %100 %100 %100 %
Schedule of Changes in Fair Value of Plan Assets
The fair value of the Company’s pension plan assets as of January 1, 2023 and January 2, 2022 by asset category, classified in the three levels of inputs described in Note 20 to the consolidated financial statements are as follows:
 
 Fair Value Measurements at January 1, 2023 Using:
Total Carrying
Value at
January 1, 2023		Quoted Prices in
Active Markets
(Level 1)		Significant Other
Observable Inputs
(Level 2)		Significant
Unobservable 
Inputs
(Level 3)
(In thousands)
Cash$14,483 $14,483 $— $— 
Equity securities:
U.S. large-cap61,680 61,680 — — 
International large-cap value20,148 20,148 — — 
Emerging markets growth9,902 9,902 — — 
Fixed income securities:
Corporate and U.S. debt instruments105,126 36,346 68,780 — 
Short-term corporate bonds17,088 — 17,088 — 
Other types of investments:
Foreign liability driven instrument95,062 — — 95,062 
Total assets measured at fair value$323,489 $142,559 $85,868 $95,062 
 Fair Value Measurements at January 2, 2022 Using:
Total Carrying
Value at
January 2, 2022		Quoted Prices in
Active Markets
(Level 1)		Significant Other
Observable Inputs
(Level 2)		Significant
Unobservable 
Inputs
(Level 3)
(In thousands)
Cash$22,241 $22,241 $— $— 
Equity Securities:
U.S. large-cap91,601 91,601 — — 
International large-cap value29,803 29,803 — — 
Emerging markets growth12,603 12,603 — — 
Fixed income securities:
Corporate and U.S. debt instruments133,727 41,725 92,002 — 
Corporate bonds15,650 — 15,650 — 
Other types of investments:
Foreign liability driven instrument165,680 — — 165,680 
Total assets measured at fair value$471,305 $197,973 $107,652 $165,680 
Schedule of Effect of Significant Unobservable Inputs, Changes in Plan Assets
A reconciliation of the beginning and ending Level 3 assets for fiscal years 2022, 2021 and 2020 is as follows:
 
 Fair Value Measurements Using
Significant Unobservable Inputs
(Level 3):
Foreign liability driven investmentForeign
Real Estate
Funds		Multi-strategy
Hedge
Funds		Total
(In thousands)
Balance at December 30, 2019$— $22,688 $1,721 $24,409 
Sales— — (1,721)(1,721)
Unrealized gains— 571 — 571 
Balance at January 3, 2021— 23,259 — 23,259 
Sales— (23,115)— (23,115)
Purchases165,680 — — 165,680 
Realized losses— (226)— (226)
Realized gains— 82 — 82 
Balance at January 2, 2022165,680 — — 165,680 
Pension benefits paid(6,639)— — (6,639)
Foreign exchange losses(18,411)— — (18,411)
Return on plan assets(45,568)— — (45,568)
Balance at January 1, 2023$95,062 $— $— $95,062 
Schedule of Expected Benefit Payments
The following benefit payments, which reflect expected future service, as appropriate, are expected to be paid as follows:
 
Non-U.S.U.S.
(In thousands)
2023$11,907 $19,311 
202412,371 19,267 
202512,442 19,218 
202612,835 19,094 
202712,450 18,906 
2028-203264,237 87,807