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		6 Months Ended
	Jul. 02, 2023	Jul. 03, 2022	Jul. 02, 2023	Jul. 03, 2022
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Revenues	$ 692,245	$ 666,551	$ 1,334,034	$ 1,276,922
Depreciation expense	(12,700)	(11,400)	(25,000)	(22,600)
Amortization of intangibles	(11,126)	(9,177)	(20,736)	(17,994)
Severance, restructuring, and acquisition integration costs	(1,417)	(1,167)	(2,091)	(4,150)
Operating income	92,597	81,936	178,134	155,457
Interest expense, net	(8,812)	(11,276)	(17,013)	(25,687)
Loss on debt extinguishment	0	0	0	(6,392)
Total non-operating pension benefit	646	1,070	1,134	2,270
Consolidated income from continuing operations before taxes	84,431	71,730	162,255	125,648
Reportable Segment
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Segment EBITDA	122,587	109,947	233,579	208,296
Depreciation expense	(12,682)	(11,370)	(25,036)	(22,596)
Amortization of intangibles	(11,126)	(9,177)	(20,736)	(17,994)
Severance, restructuring, and acquisition integration costs	(4,059)	(5,857)	(5,771)	(9,580)
Amortization of software development intangible assets	(1,820)	(981)	(3,272)	(1,988)
Adjustments related to acquisitions and divestitures	(249)	(576)	(547)	(576)
Operating income	92,597	81,936	178,134	155,457
Interest expense, net	(8,812)	(11,276)	(17,013)	(25,687)
Loss on debt extinguishment	0	0	0	(6,392)
Reportable Segment | Segment Revenues
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Revenues	692,245	666,551	1,334,034	1,276,922
Intersegment Eliminations
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Operating income	$ (54)	$ (50)	$ (83)	$ (105)