Acquisitions (Assets Acquired and Liabilities Assumed) (Details) - USD ($) $ in Thousands			9 Months Ended
	Aug. 01, 2022	May 02, 2022	Oct. 01, 2022	Oct. 02, 2021	Jan. 01, 2022
Business Acquisition [Line Items]
Goodwill			$ 1,900,267		$ 1,219,116
Long-term contingent consideration			161,278		$ 0
Cash paid for acquisition, net of cash acquired			$ 1,760,139	$ 2,059
FASA Group
Business Acquisition [Line Items]
Accounts receivable	$ 108,495
Inventories	44,079
Other current assets	13,603
Property, plant and equipment	142,931
Identifiable intangible assets	161,182
Goodwill	400,504
Operating lease right-of-use assets	583
Other assets	51,161
Accounts payable	(18,052)
Current portion of long-term debt	(10,779)
Accrued expenses	(44,362)
Long-term debt, net of current portion	(41,926)
Long-term operating lease liabilities	(583)
Deferred tax liability	(79,691)
Other noncurrent liabilities	(503)
Non-controlling interests	(18,212)
Purchase price, net of cash acquired	708,430
Less hold-back	21,705
Long-term contingent consideration	168,128
Cash paid for acquisition, net of cash acquired	$ 518,597
Acquired Finite-lived Intangible Assets, Weighted Average Useful Life	11 years 6 months
FASA Group | Collection Routes [Member]
Business Acquisition [Line Items]
Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Finite-Lived Intangibles	$ 150,200
Acquired Finite-lived Intangible Assets, Weighted Average Useful Life	12 years
Valley Proteins
Business Acquisition [Line Items]
Accounts receivable		$ 68,558
Inventories		58,246
Other current assets		13,825
Property, plant and equipment		409,405
Identifiable intangible assets		389,200
Goodwill		355,141
Operating lease right-of-use assets		16,380
Other assets		14,164
Accounts payable		(47,615)
Current portion of long-term debt		(2,043)
Current operating lease liabilities		(4,779)
Accrued expenses		(61,802)
Long-term debt, net of current portion		(5,995)
Long-term operating lease liabilities		(11,601)
Other noncurrent liabilities		(19,436)
Purchase price, net of cash acquired		$ 1,171,648
Acquired Finite-lived Intangible Assets, Weighted Average Useful Life		15 years
Valley Proteins | Collection Routes [Member]
Business Acquisition [Line Items]
Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Finite-Lived Intangibles		$ 292,100
Acquired Finite-lived Intangible Assets, Weighted Average Useful Life		15 years