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Equity Investment in Affiliate - Narrative (Details)
$ in Thousands
12 Months Ended
Oct. 01, 2022
USD ($)
Oct. 02, 2021
USD ($)
Oct. 03, 2020
USD ($)
Oct. 14, 2009
manufacturer
Schedule of Equity Method Investments [Line Items]        
Number of manufacturers before venture | manufacturer       2
Equity investment in affiliate $ 10,659 $ 14,817    
Equity in net (loss) income of non-consolidated affiliate $ (4,159) 498 $ 3,213  
Micro Bird Holdings, Inc.        
Schedule of Equity Method Investments [Line Items]        
Equity interest in equity method investment (as a percent) 50.00%      
Equity investment in affiliate $ 10,700 14,800    
Equity in net (loss) income of non-consolidated affiliate $ (4,200) $ 500 $ 3,200