Reportable Segments - Reconciliation of Total Reportable Segments' Revenues and EBITDA to Consolidated Revenues and Consolidated Income Before Taxes (Details) - USD ($) $ in Thousands	3 Months Ended
	Apr. 02, 2023	Apr. 03, 2022
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Revenues	$ 641,789	$ 610,371
Depreciation expense	(12,400)	(11,200)
Amortization of intangibles	(9,610)	(8,817)
Severance, restructuring, and acquisition integration costs	(674)	(2,983)
Operating income	85,537	73,521
Interest expense, net	(8,201)	(14,411)
Loss on debt extinguishment	0	(6,392)
Total non-operating pension benefit	488	1,200
Consolidated income from continuing operations before taxes	77,824	53,918
Reportable Segment
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Segment EBITDA	110,992	98,349
Depreciation expense	(12,354)	(11,226)
Amortization of intangibles	(9,610)	(8,817)
Severance, restructuring, and acquisition integration costs	(1,712)	(3,723)
Amortization of software development intangible assets	(1,452)	(1,007)
Adjustments related to acquisitions and divestitures	(298)	0
Operating income	85,537	73,521
Interest expense, net	(8,201)	(14,411)
Loss on debt extinguishment	0	(6,392)
Inventory adjustment	300
Reportable Segment | Segment Revenues
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Revenues	641,789	610,371
Intersegment Eliminations
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Operating income	$ (29)	$ (55)