Consolidated Statements of Cash Flows $ in Thousands	12 Months Ended
	Jan. 02, 2022 USD ($)	Jan. 03, 2021 USD ($)	Dec. 29, 2019 USD ($)
Restricted Cash	$ 1,018	$ 578	$ 17
Cash, Cash Equivalents, Restricted Cash and Restricted Cash Equivalents	619,337	402,614	191,894
Operating activities:
Net income	943,157	727,887	227,558
Income (Loss) from discontinued operations and dispositions	126	211	195
Income from continuing operations	943,283	728,098	227,753
Adjustments to reconcile net income from continuing operations to net cash provided by continuing operations:
Restructuring and other costs, net	16,432	8,013	29,428
Depreciation and amortization	358,004	246,507	214,025
Stock-based compensation	32,780	29,126	31,514
Pension and other post-retirement expense	(30,891)	18,012	26,107
Business Combination, Contingent Consideration Arrangements, Change in Amount of Contingent Consideration, Liability	3,119	(8,827)	3,881
Deferred taxes	(49,342)	(29,121)	(61,353)
Deferred Income Tax Expense (Benefit), Continuing Operations, Discontinuing Operations	(49,342)	(29,121)	(61,353)
Contingencies and Non-Cash Tax Matters	1,924	4,518	(424)
Amortization of deferred debt issuance costs, interest rate hedge and accretion of discounts	4,962	3,391	3,846
(Gain) loss on disposition of businesses and assets, net	(1,970)	886	2,469
Amortization of acquired inventory revaluation	35,201	2,793	21,590
Asset Impairment Charges	3,868	7,937	0
Change in fair value of financial securities	(10,985)	(35)	(3,249)
Gain (Loss) on Extinguishment of Debt	0	0	32,541
Changes in assets and liabilities which (used) provided cash, excluding effects from companies purchased and divested:
Accounts receivable, net	155,391	(373,895)	(100,630)
Inventories, net	2,376	(122,513)	(9,607)
Accounts payable	823	62,753	7,351
Accrued expenses and other	(54,225)	314,534	(61,773)
Net cash provided by operating activities	1,410,750	892,177	363,469
Investing activities:
Capital expenditures	(99,888)	(77,506)	(76,331)
Payments to Acquire Investments	(23,130)	(20,059)	(6,387)
Payments to Acquire Intangible Assets	0	0	(5,000)
Proceeds from Divestiture of Businesses	1,460	4,280	550
Proceeds from surrender of life insurance policies	109	282	0
Cash paid for acquisitions, net of cash, cash equivalents and restricted cash acquired	(3,991,309)	(411,495)	(400,405)
Net cash used in investing activities	(4,112,758)	(504,498)	(487,573)
Financing activities:
Payments on revolving credit facility	(1,559,133)	(897,674)	(1,692,489)
Proceeds from Long-term Lines of Credit	1,400,282	714,698	1,599,416
Proceeds from term loan	500,000	0	0
Payments of Senior Debt	(339,605)	0	(530,276)
Proceeds from sale of senior debt	3,086,095	0	847,195
Payments of debt financing and equity issuance costs	(30,983)	0	(9,879)
Proceeds from (Repayments of) Other Debt	(13,670)	(4,494)	(14,975)
Settlement of cash flow hedges	(4,482)	(4,554)	(1,280)
Settlement of swaps	14,314	0	0
Payments for acquisition-related contingent consideration	(2,208)	(10,363)	(29,942)
Proceeds, Issuance of Shares, Share-based Payment Arrangement, Including Option Exercised	25,120	37,671	19,732
Purchases of common stock	(73,072)	(6,944)	(6,313)
Dividends paid	(32,373)	(31,212)	(31,059)
Net cash (used in) provided by financing activities	(2,941,657)	202,872	(150,130)
Effect of Exchange Rate on Cash, Cash Equivalents, Restricted Cash and Restricted Cash Equivalents	(22,926)	25,913	(447)
Net increase in cash, cash equivalents and restricted cash	216,723	210,720	25,579
Cash and cash equivalents at beginning of year	402,036	191,877
Cash and cash equivalents at end of year	618,319	402,036	191,877
Supplemental disclosures of cash flow information
Interest Paid, Excluding Capitalized Interest, Operating Activities	54,120	42,142	82,693
Income taxes	364,565	162,454	77,059
Cash Flow, Noncash Investing and Financing Activities Disclosure [Abstract]
Equity issued for business combination, net of issuance costs	$ 2,638,144	$ 0	$ 0