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Intangible Assets - Narrative (Details) - USD ($)
12 Months Ended
Oct. 02, 2021
Oct. 03, 2020
Sep. 28, 2019
Finite-Lived Intangible Assets [Line Items]      
Indefinite lived intangible asset impairment $ 0 $ 0  
Amortization expense for intangible assets $ 2,200,000 $ 3,100,000 $ 2,900,000
Customer relationships      
Finite-Lived Intangible Assets [Line Items]      
Estimated life 20 years    
Minimum | Engineering designs      
Finite-Lived Intangible Assets [Line Items]      
Estimated life 2 years    
Maximum | Engineering designs      
Finite-Lived Intangible Assets [Line Items]      
Estimated life 7 years