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Benefit Plans - Narrative (Details)
12 Months Ended
Oct. 01, 2022
USD ($)
installment
shares
Oct. 02, 2021
USD ($)
shares
Oct. 03, 2020
USD ($)
shares
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Share-based compensation expense $ 23,300,000 $ 24,800,000 $ 24,300,000
Employer matching contribution, percent of eligible earnings (up to) 4.00%    
Amount of contributions made to 401K $ 9,300,000 9,300,000 9,800,000
SERP      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Amount of contributions made to participants' SERP accounts 800,000 700,000 $ 700,000
Total value of assets held by trust 10,000,000 14,100,000  
Deferred compensation liability 10,000,000 $ 14,100,000  
RSUs      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Award unrecognized compensation expense $ 18,000,000    
Award, unrecognized compensation expense, weighted average period of recognition 1 year 3 months 18 days    
PSUs      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Award unrecognized compensation expense $ 6,600,000    
Award, unrecognized compensation expense, weighted average period of recognition 1 year 9 months 18 days    
Vested (in shares) | shares 100,000    
Granted (in shares) | shares 100,000 100,000 100,000
PSUs | Minimum      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Number of shares that may be issued (in shares) | shares 0    
PSUs | Maximum      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Number of shares that may be issued (in shares) | shares 500,000    
PSUs | Vest Based on Market Condition - Relative TSR of Common Stock Compared to Companies in Russell 3000 Index or S&P 400 Index      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Share-based Compensation Arrangement by Share-based Payment Award, Payout, Percent of Shares Granted 145.00%    
PSUs | Vest Based on Market Condition - Relative TSR of Common Stock Compared to Companies in Russell 3000 Index or S&P 400 Index | Minimum | S&P 400      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Vesting percentage 0.00%    
PSUs | Vest Based on Market Condition - Relative TSR of Common Stock Compared to Companies in Russell 3000 Index or S&P 400 Index | Maximum | S&P 400      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Vesting percentage 150.00%    
PSUs | Vest Based on Performance Condition - Three-Point Annual Average of Absolute Economic Return      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Share-based Compensation Arrangement by Share-based Payment Award, Payout, Percent of Shares Granted 200.00%    
Share-based Compensation Arrangement by Share-based Payment Award, Payout, Average Economic Return Threshold, Percent 2.50%    
PSUs | Vest Based on Performance Condition - Three-Point Annual Average of Absolute Economic Return | Minimum | Russell 3000      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Vesting percentage 0.00%    
PSUs | Vest Based on Performance Condition - Three-Point Annual Average of Absolute Economic Return | Maximum | Russell 3000      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Vesting percentage 200.00%    
Options and SARs      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Options and SARS granted in period | shares 0 0 0
Options and SARS fair value vested in period $ 0 $ 0 $ 0
Options and SARS total intrinsic value exercised $ 600,000 $ 5,400,000 $ 10,900,000
2016 Plan      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Maximum number of shares authorized under the plan (in shares) | shares 3,200,000    
2016 Plan | Cash Incentive Awards      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Long-term cash awards per employee that may be granted annually $ 4,000,000    
2016 Plan | Stock Options      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Number of annual vesting installments | installment 2    
Term 10 years    
2016 Plan | SARs      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Number of annual vesting installments | installment 2    
Term 7 years    
2016 Plan | RSUs      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Performance period 3 years    
2016 Plan | PSUs      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Performance period 3 years    
2016 Plan | PSUs | Vest Based on Market Condition - Relative TSR of Common Stock Compared to Companies in Russell 3000 Index or S&P 400 Index      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Vesting percentage 50.00%    
Share-based Compensation Arrangement by Share-based Payment Award, Payout, Percent of Shares Granted 100.00%    
Share-based Compensation Arrangement by Share-based Payment Award, Total Shareholder Return Threshold, Percent 50.00%    
2016 Plan | PSUs | Vest Based on Performance Condition - Three-Point Annual Average of Absolute Economic Return      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Vesting percentage 50.00%    
Performance period 3 years    
Share-Based Compensation Arrangement by Share-Based Payment Award, Terms of Award three