Employee Benefit Plans - Narrative (Details)	12 Months Ended
	Jan. 02, 2022 USD ($) Year	Jan. 03, 2021 USD ($)	Dec. 29, 2019 USD ($)
Employee Benefit Plan Disclosure [Line Items]
Defined contribution plan eligibility period	6 months
Multiemployer contributions percentage	5.00%
Multiemployer plan, pension, insignificant, employer contribution, cost	$ 2,600,000	$ 2,500,000
Multiemployer plan funded status		95.00%
Defined benefit plan, accumulated other comprehensive income (loss)	$ 53,888,000	$ 69,288,000
Weighted average discount rate for level 3 plan assets, foreign plans	1.01%	0.52%
Minimum
Employee Benefit Plan Disclosure [Line Items]
Unobservable input for level 3 plan assets, foreign plans	1.00%	0.50%
Maximum
Employee Benefit Plan Disclosure [Line Items]
Unobservable input for level 3 plan assets, foreign plans	1.85%	1.30%
401(k) Plan
Employee Benefit Plan Disclosure [Line Items]
Employer matching contribution	$ 3,000,000.0	$ 1,600,000	$ 3,300,000
Employer discretionary contribution	0	0	0
Foreign Plan
Employee Benefit Plan Disclosure [Line Items]
Curtailment, net actuarial gain recognized in accumulated other comprehensive income			2,400,000
Accumulated net actuarial loss, after impact of curtailment			16,700,000
Curtailment, reclassification of prior service cost from accumulated other comprehensive income			500,000
Liability, defined benefit pension plan	4,500,000
Pension expense	2,500,000	2,500,000	$ 2,300,000
Defined benefit plan, funded status benefit assets (liability)	38,808,000	60,912,000
Defined benefit plan, accumulated other comprehensive income (loss)	45,209,000	58,257,000
Defined benefit plan, expected amortization, next fiscal year	$ 1,400,000
Number of defined benefit plans	3
Defined benefit plan, other comprehensive (income) loss	$ 11,800,000
Other comprehensive (income) loss, defined benefit plan, before reclassification adjustment, tax	3,900,000
Defined benefit plan, actuarial gain (loss)	10,300,000
Other comprehensive income (loss), defined benefit plan, gain (loss) arising during period, tax	3,400,000
Defined benefit plan, loss due to amortization	(1,500,000)
Other comprehensive income (loss), defined benefit plan, gain (loss), reclassification adjustment from AOCI, tax	500,000
Defined benefit plan, expected future contributions	4,100,000
Accumulated benefit obligation	324,408,000	364,443,000
Company contributions	5,393,000	4,451,000
Foreign Plan | Accumulated Defined Benefit Plans Adjustment Attributable to Parent
Employee Benefit Plan Disclosure [Line Items]
Defined benefit plan, accumulated other comprehensive income, tax	15,400,000
United States
Employee Benefit Plan Disclosure [Line Items]
Defined benefit plan, other comprehensive (income) loss	2,300,000
Other comprehensive (income) loss, defined benefit plan, before reclassification adjustment, tax	1,000,000
Defined benefit plan, actuarial gain (loss)	1,800,000
Other comprehensive income (loss), defined benefit plan, gain (loss) arising during period, tax	800,000
Defined benefit plan, loss due to amortization	(500,000)
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	$ 30,100,000	33,800,000
Company contributions	2,000,000.0
Nonqualified Savings Plans
Employee Benefit Plan Disclosure [Line Items]
Deferred compensation liability	34,200,000	33,100,000
Deferred compensation investments	35,578,000	33,939,000
Nonqualified Savings Plans | Mutual Funds
Employee Benefit Plan Disclosure [Line Items]
Deferred compensation investments	15,600,000
Nonqualified Savings Plans | Insurance Contracts
Employee Benefit Plan Disclosure [Line Items]
Deferred compensation investments	$ 20,000,000.0	$ 33,900,000