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Transactions with Related Parties (Details) - USD ($)
$ in Thousands
12 Months Ended
Sep. 28, 2024
Sep. 30, 2023
Sep. 24, 2022
Related Party Transaction [Line Items]      
Accounts payable $ 212,606 $ 190,902  
Contract Packaging, Inc.      
Related Party Transaction [Line Items]      
Percentage of shares held by CPI in Tech Pac 20.00% 20.00% 20.00%
Accounts payable $ 1,400 $ 1,600  
Contract Packaging, Inc. | Tech Pac      
Related Party Transaction [Line Items]      
Purchases products from related party $ 37,000 $ 31,000 $ 41,000