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Benefit Plans - Narrative (Details)
12 Months Ended
Oct. 03, 2020
USD ($)
installment
shares
Sep. 28, 2019
USD ($)
shares
Sep. 29, 2018
USD ($)
shares
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Share-based compensation expense $ 24,300,000 $ 21,300,000 $ 18,000,000.0
Deferred tax benefits recognized related to equity awards $ 8,200,000 9,200,000 8,200,000
Employer matching contribution, percent of eligible earnings (up to) 4.00%    
Amount of contributions $ 9,800,000 9,300,000 8,100,000
SERP      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Deferred compensation liability 12,600,000 12,100,000  
Total value of assets held by trust 12,600,000 12,100,000  
Amount of contributions made to participants' SERP accounts $ 700,000 600,000 1,000,000.0
Other Postretirement Benefit Plan      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Term of deferred compensation agreements 15 years    
Deferred compensation liability $ 100,000 200,000  
Total value of assets held by trust 10,800,000 10,400,000  
Amount of payments made to participants 100,000 $ 100,000 $ 100,000
RSUs      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Unrecognized compensation expense $ 17,000,000.0    
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]      
Performance period 3 years    
Payout, percent of shares granted 100.00%    
Unrecognized compensation expense $ 8,800,000    
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]      
Vesting percentage 0.00%    
Number of shares that may be issued (in shares) | shares 0    
PSUs | Maximum      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Vesting percentage 200.00%    
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      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Payout, percent of shares granted 148.40%    
Payout at target, TSR threshold percent of companies in Russell 3000 Index during performance period 50.00%    
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]      
Payout at target, average economic return threshold percentage over performance period 2.50%    
Options and SARs      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Options and SARS granted in period | shares 0 0 0
Fair value vested $ 0 $ 300,000 $ 1,300,000
Total intrinsic value exercised $ 10,900,000 $ 2,400,000 $ 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 $ 4,000,000.0    
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      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Vesting percentage 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%