Employee Retirement Plans Summary of the Plans' Net Periodic Pension Cost, Benefit Obligations, Funded Status, and Net Balance Sheet Position (Details) - USD ($) $ in Thousands	12 Months Ended
	Jan. 03, 2026	Dec. 28, 2024
Defined Benefit Plan, Amounts for Asset (Liability) Recognized in Statement of Financial Position [Abstract]
Liability, Defined Benefit Pension Plan, Noncurrent	$ 7,629	$ 9,573
Pre-tax components in accumulated other comprehensive income at period end:
Long-lived assets	711,682	628,226
Non US Plans
Net Periodic Pension Cost:
Interest cost	47,206	43,330
Defined Benefit Plan, Expected Return (Loss) on Plan Assets	(56,794)	(61,613)
Defined Benefit Plan, Amortization of Gain (Loss)	(149)	(152)
Defined Benefit Plan, Amortization of Prior Service Cost (Credit)	2,715	2,637
Defined Benefit Plan, Net Periodic Benefit Cost	(6,724)	(15,494)
Defined Benefit Plan, Change in Benefit Obligation [Roll Forward]
Defined Benefit Plan, Benefit Obligation, Beginning Balance	855,777	976,187
Interest cost	47,206	43,330
Defined Benefit Plan, Benefit Obligation, Actuarial Gain (Loss)	(6,615)	(92,821)
Defined Benefit Plan, Benefit Obligation, Benefits Paid	(62,512)	(60,720)
Exchange effect	59,918	(10,199)
Defined Benefit Plan, Benefit Obligation, Ending Balance	893,774	855,777
Defined Benefit Plan, Change in Fair Value of Plan Assets [Roll Forward]
Defined Benefit Plan, Plan Assets, Amount, Beginning Balance	946,168	1,013,914
Defined Benefit Plan, Plan Assets, Contributions by Employer	(168)	(72)
Defined Benefit Plan Investment Gain Loss	50,235	4,660
Defined Benefit Plan Fair Value Of Plan Assets Benefits Paid	(62,512)	(60,720)
Defined Benefit Plan, Plan Assets, Foreign Currency Translation Gain (Loss)	66,495	(11,614)
Defined Benefit Plan, Plan Assets, Amount, Ending Balance	1,000,218	946,168
Defined Benefit Plan, Amounts for Asset (Liability) Recognized in Statement of Financial Position [Abstract]
Liability, Defined Benefit Pension Plan, Noncurrent	106,444	90,391
Pre-tax components in accumulated other comprehensive income at period end:
Net actuarial loss	62,335	61,082
Other Comprehensive Income (Loss), Defined Benefit Plan, Gain (Loss) Arising During Period, before Tax	688	(36,035)
Defined Benefit Plan, Amount Recognized in Net Periodic Benefit Cost (Credit) and Other Comprehensive (Income) Loss, before Tax	788	(153)
Other Comprehensive (Income) Loss, Defined Benefit Plan, Prior Service Cost (Credit), before Tax	(223)	(3,078)
Other Comprehensive Income (Loss), Defined Benefit Plan, Gain (Loss), after Reclassification Adjustment, before Tax	(1,253)	39,266
Defined Benefit Plan, Accumulated Benefit Obligation	$ 893,774	$ 855,777
Defined Benefit Plan, Assumptions Used Calculating Benefit Obligation, Discount Rate	5.60%	5.50%
Defined Benefit Plan, Assumptions Used Calculating Net Periodic Benefit Cost, Expected Long-Term Rate of Return on Plan Assets	5.90%	5.90%
USPlans
Net Periodic Pension Cost:
Interest cost	$ 1,321	$ 1,267
Defined Benefit Plan, Expected Return (Loss) on Plan Assets	(942)	(926)
Defined Benefit Plan, Amortization of Gain (Loss)	(51)	(281)
Defined Benefit Plan, Amortization of Prior Service Cost (Credit)	0	0
Defined Benefit Plan, Net Periodic Benefit Cost	430	622
Defined Benefit Plan, Change in Benefit Obligation [Roll Forward]
Defined Benefit Plan, Benefit Obligation, Beginning Balance	25,581	27,659
Interest cost	1,321	1,267
Defined Benefit Plan, Benefit Obligation, Actuarial Gain (Loss)	289	(1,598)
Defined Benefit Plan, Benefit Obligation, Benefits Paid	(1,793)	(1,747)
Exchange effect	0	0
Defined Benefit Plan, Benefit Obligation, Ending Balance	25,398	25,581
Defined Benefit Plan, Change in Fair Value of Plan Assets [Roll Forward]
Defined Benefit Plan, Plan Assets, Amount, Beginning Balance	16,008	15,751
Defined Benefit Plan, Plan Assets, Contributions by Employer	(1,186)	(1,244)
Defined Benefit Plan Investment Gain Loss	2,368	760
Defined Benefit Plan Fair Value Of Plan Assets Benefits Paid	(1,793)	(1,747)
Defined Benefit Plan, Plan Assets, Foreign Currency Translation Gain (Loss)	0	0
Defined Benefit Plan, Plan Assets, Amount, Ending Balance	17,769	16,008
Defined Benefit Plan, Amounts for Asset (Liability) Recognized in Statement of Financial Position [Abstract]
Liability, Defined Benefit Pension Plan, Noncurrent	7,629	9,573
Pre-tax components in accumulated other comprehensive income at period end:
Net actuarial loss	(891)	297
Other Comprehensive Income (Loss), Defined Benefit Plan, Gain (Loss) Arising During Period, before Tax	(1,136)	(1,432)
Defined Benefit Plan, Amount Recognized in Net Periodic Benefit Cost (Credit) and Other Comprehensive (Income) Loss, before Tax	(51)	(281)
Other Comprehensive (Income) Loss, Defined Benefit Plan, Prior Service Cost (Credit), before Tax	0	0
Other Comprehensive Income (Loss), Defined Benefit Plan, Gain (Loss), after Reclassification Adjustment, before Tax	1,187	1,713
Defined Benefit Plan, Accumulated Benefit Obligation	$ 25,398	$ 25,581
Defined Benefit Plan, Assumptions Used Calculating Benefit Obligation, Discount Rate	5.20%	5.40%
Defined Benefit Plan, Assumptions Used Calculating Net Periodic Benefit Cost, Expected Long-Term Rate of Return on Plan Assets	6.00%	6.00%