Consolidated Statements of Cash Flows $ in Thousands	12 Months Ended
	Jan. 01, 2023 USD ($)	Jan. 02, 2022 USD ($)	Jan. 03, 2021 USD ($)
Cash, Cash Equivalents, Restricted Cash and Restricted Cash Equivalents	$ 470,746	$ 619,337	$ 402,614
Operating activities:
Net income	569,179	943,157	727,887
Income (Loss) from discontinued operations and dispositions	(56,503)	(53,721)	(97,327)
Income from continuing operations	512,676	889,436	630,560
Adjustments to reconcile net income from continuing operations to net cash provided by continuing operations:
Restructuring and other costs, net	13,580	(14,358)	(7,661)
Depreciation and amortization	427,000	311,443	201,648
Stock-based compensation	51,518	29,675	26,904
Pension and other post-retirement (income) expense	(23,104)	(28,509)	14,904
Business Combination, Contingent Consideration Arrangements, Change in Amount of Contingent Consideration, Liability	(1,377)	3,119	(8,827)
Deferred taxes	(105,923)	(55,328)	(35,338)
Deferred Income Tax Expense (Benefit), Continuing Operations, Discontinuing Operations	(105,923)	(55,328)	(35,338)
Contingencies and Non-Cash Tax Matters	(1,488)	1,924	4,518
Amortization of deferred debt issuance costs, interest rate hedge and accretion of discounts	7,310	4,962	3,391
(Gain) loss on disposition of businesses and assets, net	(2,887)	(1,970)	886
Amortization of acquired inventory revaluation	45,289	35,201	1,831
Asset Impairment Charges	0	3,868	7,937
Change in fair value of financial securities	15,754	(10,985)	(35)
Gain (Loss) on Extinguishment of Debt	(2,880)	0	0
Changes in assets and liabilities which (used) provided cash, excluding effects from companies purchased and divested:
Accounts receivable, net	66,093	165,590	(398,853)
Inventories, net	(48,634)	32,280	(127,357)
Accounts payable	(43,804)	(7,577)	63,231
Accrued expenses and other	(236,623)	(57,303)	311,659
Net cash provided by operating activities of continuing operations	672,500	1,330,184	704,720
Net cash provided by operating activities of discontinued operations	7,310	80,566	187,457
Net cash provided by operating activities	679,810	1,410,750	892,177
Investing activities:
Capital expenditures	(85,632)	(86,020)	(63,634)
Payments to Acquire Investments	(47,181)	(23,130)	(20,059)
Proceeds from Collection of Notes Receivable	8,890	0	0
Proceeds from Divestiture of Businesses	14,505	1,460	4,280
Proceeds from surrender of life insurance policies	0	109	282
Cash paid for acquisitions, net of cash acquired	(7,518)	(3,982,216)	(411,495)
Net cash used in investing activities of continuing operations	(116,936)	(4,089,797)	(490,626)
Net cash used in investing activities of discontinued operations	(15,915)	(22,961)	(13,872)
Net cash used in investing activities	(132,851)	(4,112,758)	(504,498)
Financing activities:
Payments on revolving credit facility	(240,000)	(1,559,133)	(897,674)
Proceeds from Long-term Lines of Credit	240,000	1,400,282	714,698
Proceeds from term loan	0	500,000	0
Repayments of Term Loan	(500,000)	0	0
Payments of Senior Debt	(57,876)	(339,605)	0
Proceeds from sale of senior debt	0	3,086,095	0
Payments of debt financing and equity issuance costs	0	(30,983)	0
Proceeds from (Repayments of) Other Debt	(1,292)	(13,670)	(4,494)
Settlement of cash flow hedges	(762)	(4,482)	(4,554)
Settlement of swaps	0	14,314	0
Payments for acquisition-related contingent consideration	(5)	(2,208)	(10,363)
Proceeds, Issuance of Shares, Share-based Payment Arrangement, Including Option Exercised	14,114	25,120	37,671
Purchases of common stock	(80,638)	(73,072)	(6,944)
Dividends paid	(35,344)	(32,373)	(31,212)
Net cash (used in) provided by financing activities	(661,803)	2,941,657	(202,872)
Effect of Exchange Rate on Cash, Cash Equivalents, Restricted Cash and Restricted Cash Equivalents	(33,747)	(22,926)	25,913
Net (decrease) increase in cash, cash equivalents and restricted cash	(148,591)	216,723	210,720
Cash and cash equivalents at beginning of year	603,320	387,054
Restricted Cash, Current	1,040	1,018	578
Restricted Cash, Noncurrent	349	0	0
Disposal Group, Including Discontinued Operation, Cash and Cash Equivalents	14,999	14,999	14,982
Cash and cash equivalents at end of year	454,358	603,320	387,054
Supplemental disclosures of cash flow information
Interest Paid, Excluding Capitalized Interest, Operating Activities	97,934	54,120	42,142
Income taxes	323,077	364,565	162,454
Cash Flow, Noncash Investing and Financing Activities Disclosure [Abstract]
Equity issued for business combination, net of issuance costs	$ 0	$ 2,638,144	$ 0