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Basis of Presentation - Additional Information (Detail) - USD ($) $ in Thousands	3 Months Ended		4 Months Ended		9 Months Ended		12 Months Ended
	Oct. 08, 2022	Oct. 09, 2021	Apr. 23, 2022	Apr. 24, 2021	Oct. 08, 2022	Oct. 09, 2021	Jan. 01, 2022	Jul. 16, 2022	Mar. 09, 2021	Apr. 03, 2012
Basis of Presentation [Line Items]
Debt instrument face amount	$ 900,000				$ 900,000		$ 900,000
Segment reporting, description					The company has one operating segment based on the nature of products the company sells, intertwined production and distribution model, the internal management structure and information that is regularly reviewed by the chief executive officer (“CEO”), who is the chief operating decision maker, for the purpose of assessing performance and allocating resources.
Investment in unconsolidated affiliate	9,000				$ 9,000			$ 9,000
Business consulting cost	8,100	$ 9,200			$ 28,900	$ 27,400
Recovery on inferior ingredients		(950)				$ (828)
Additional costs associated with receiving inferior ingredients				$ 100
Multi-employer pension plan withdrawal costs	3,300	3,300
Impairment charge			$ 1,000
Acquisition related costs	11,600
Realized foreign currency exchange losses	8,400
Holsum Bakery
Basis of Presentation [Line Items]
Severance costs	1,700
Multi-employer pension plan withdrawal costs	1,300
Asset impairment and equipment relocation charges	3,800
Gluten Free Products
Basis of Presentation [Line Items]
Recovery on inferior ingredients		$ 1,000
Outstanding Trade Receivables \| Wal-Mart/Sam's Club \| Customer Concentration Risk
Basis of Presentation [Line Items]
Concentration risk percentage					25.20%		19.80%
Unsecured Credit Facility
Basis of Presentation [Line Items]
Debt facility available borrowing capacity and cash on hand.	864,300				$ 864,300
2031 Notes
Basis of Presentation [Line Items]
Debt instrument face amount	$ 500,000			$ 500,000	$ 500,000		$ 500,000		$ 500,000
Debt instrument interest rate				2.40%					2.40%
Final Maturity				2031
2022 Notes
Basis of Presentation [Line Items]
Debt instrument face amount				$ 400,000						$ 400,000
Debt instrument interest rate				4.375%						4.375%
Final Maturity				2022