Employee Benefit Plans - Narrative (Details)	12 Months Ended
	Jan. 01, 2023 USD ($) Year	Jan. 02, 2022 USD ($)	Jan. 03, 2021 USD ($)
Employee Benefit Plan Disclosure [Line Items]
Defined contribution plan eligibility period	6 months
Multiemployer contributions, percentage of total plan contributions, less than	5.00%
Multiemployer plan, employer contribution	$ 2,400,000	$ 2,600,000	$ 2,500,000
Multiemployer plan funded status		95.00%
Defined benefit plan, accumulated other comprehensive (income) loss	$ 27,548,000	$ 53,888,000
Weighted average discount rate for level 3 plan assets, foreign plans	3.72%	1.01%
Minimum
Employee Benefit Plan Disclosure [Line Items]
Unobservable input for level 3 plan assets, foreign plans	3.70%	1.00%
Maximum
Employee Benefit Plan Disclosure [Line Items]
Unobservable input for level 3 plan assets, foreign plans	4.75%	1.85%
401(k) Plan
Employee Benefit Plan Disclosure [Line Items]
Employer matching contribution	$ 3,300,000	$ 3,000,000.0	1,600,000
Employer discretionary contribution	0	0	0
Foreign Plan
Employee Benefit Plan Disclosure [Line Items]
Liability, defined benefit pension plan	5,500,000
Pension expense	2,000,000.0	2,500,000	$ 2,500,000
Defined benefit plan, funded status benefit assets (liability)	(7,955,000)	(38,808,000)
Defined benefit plan, accumulated other comprehensive (income) loss	23,737,000	45,209,000
Defined benefit plan, expected amortization, next fiscal year	$ 600,000
Number of defined benefit plans	3
Defined benefit plan, benefit obligation, period increase (decrease)	$ (129,000,000)
Defined benefit plan, other comprehensive (income) loss	17,100,000
Other comprehensive (income) loss, defined benefit plan, before reclassification adjustment, tax	10,000,000
Defined benefit plan, actuarial gain (loss)	16,400,000
Other comprehensive income (loss), defined benefit plan, gain (loss) arising during period, tax	9,500,000
Defined benefit plan, loss due to amortization	(700,000)
Other comprehensive income (loss), defined benefit plan, gain (loss), reclassification adjustment from AOCI, tax	500,000
Defined benefit plan, expected future contributions	2,500,000
Accumulated benefit obligation	195,440,000	324,408,000
Company contributions	4,001,000	5,393,000
Foreign Plan | Accumulated Defined Benefit Plans Adjustment Attributable to Parent
Employee Benefit Plan Disclosure [Line Items]
Defined benefit plan, accumulated other comprehensive income, tax	4,300,000
United States
Employee Benefit Plan Disclosure [Line Items]
Defined benefit plan, other comprehensive (income) loss	4,900,000
Other comprehensive (income) loss, defined benefit plan, before reclassification adjustment, tax	1,900,000
Defined benefit plan, actuarial gain (loss)	4,500,000
Other comprehensive income (loss), defined benefit plan, gain (loss) arising during period, tax	1,700,000
Defined benefit plan, loss due to amortization	(400,000)
Other comprehensive income (loss), defined benefit plan, gain (loss), reclassification adjustment from AOCI, tax	$ 200,000
Normal retirement age | Year	65
Early retirement age | Year	55
Minimum period of service for entitlement in plan	15 years
Minimum period under death benefit feature	10 years
Maximum period for death benefits payable to designated beneficiary	10 years
Accumulated benefit obligation	$ 22,700,000	30,100,000
Company contributions	1,900,000
Nonqualified Savings Plans
Employee Benefit Plan Disclosure [Line Items]
Deferred compensation liability	27,500,000	34,200,000
Deferred compensation investments	27,610,000	35,578,000
Nonqualified Savings Plans | Mutual Funds
Employee Benefit Plan Disclosure [Line Items]
Deferred compensation investments	11,000,000	15,600,000
Nonqualified Savings Plans | Insurance Contracts
Employee Benefit Plan Disclosure [Line Items]
Deferred compensation investments	$ 16,600,000	$ 20,000,000.0