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Debt - Narrative (Details) - USD ($)
3 Months Ended 6 Months Ended
Nov. 21, 2022
Apr. 01, 2023
Apr. 02, 2022
Apr. 01, 2023
Apr. 02, 2022
Oct. 01, 2022
Nov. 24, 2021
Debt Instrument [Line Items]              
Interest expense   $ 5,200,000 $ 2,500,000 $ 9,400,000 $ 5,600,000    
Senior Term Loan | Senior Credit Facility              
Debt Instrument [Line Items]              
Long-term line of credit   $ 141,700,000   $ 141,700,000   $ 151,600,000  
Stated interest rate (as a percent)   10.50%   10.50%   7.90%  
Weighted average effective interest rate (as a percent)   11.60%   11.60%   8.00%  
Revolving Credit Facility | Sixth Amendment to Credit Agreement              
Debt Instrument [Line Items]              
Remaining borrowing capacity $ 10,000,000            
Maximum borrowing capacity 90,000,000            
Line of Credit Facility, Current Borrowing Capacity 80,000,000            
Debt Instrument, Covenant, Maximum Borrowing Capacity to Trigger Stated Rate 50,000,000            
Debt Instrument, Minimum Borrowing Capacity to Trigger Stated Rate 80,000,000            
Debt Instrument, Covenant, Maximum Borrowing Capacity to Trigger Stated Rate, Scenario 2 80,000,000            
Term Loan | Sixth Amendment to Credit Agreement              
Debt Instrument [Line Items]              
Debt Instrument, Periodic Payment, Principal 5,000,000            
Debt Instrument, Face Amount $ 151,600,000            
Revolving Credit Facility | Line of Credit | Third Amendment to the Credit Agreement              
Debt Instrument [Line Items]              
Lender fees and other issuance costs             $ 3,300,000
Revolving Credit Facility | Line of Credit | Third Amendment to the Credit Agreement | Gain (Loss) o Extinguishment of Debt [Member]              
Debt Instrument [Line Items]              
Lender fees and other issuance costs             500,000
Revolving Credit Facility | Line of Credit | Third Amendment to the Credit Agreement | Other Noncurrent Assets              
Debt Instrument [Line Items]              
Lender fees and other issuance costs             1,200,000
Revolving Credit Facility | Line of Credit | Third Amendment to the Credit Agreement | Senior Notes, Noncurrent              
Debt Instrument [Line Items]              
Lender fees and other issuance costs             $ 1,500,000
Revolving Credit Facility | Line of Credit | Senior Revolving Credit Facility              
Debt Instrument [Line Items]              
Long-term line of credit   $ 0   $ 0      
Letters of Credit | Line of Credit | Senior Revolving Credit Facility              
Debt Instrument [Line Items]              
Remaining borrowing capacity   83,700,000   83,700,000      
Letters of credit, amount outstanding   $ 6,300,000   $ 6,300,000