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Description of Business and Basis of Presentation - Schedule of Percentage Revenues Realized by Contract (Details)
12 Months Ended
Sep. 30, 2022
Oct. 01, 2021
Oct. 02, 2020
Organization, Consolidation and Presentation of Financial Statements [Abstract]      
Cost-reimbursable 74.00% 76.00% 76.00%
Fixed-price 26.00% 24.00% 24.00%