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Benefit Plans - Narrative (Details) | 12 Months Ended
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Sep. 30, 2023 USD ($) installment shares | Oct. 01, 2022 USD ($) shares | Oct. 02, 2021 USD ($) shares
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Share-based compensation expense | $ 21,300,000 | $ 23,300,000 | $ 24,800,000
Employer matching contribution, percent of eligible earnings (up to) | 4.00% |  |
Amount of contributions made to 401K | $ 9,800,000 | 9,300,000 | 9,300,000
SERP |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Amount of contributions made to participants' SERP accounts | 900,000 | 800,000 | $ 700,000
Total value of assets held by trust | 12,400,000 | 10,000,000 |
Deferred compensation liability | 12,400,000 | $ 10,000,000 |
RSUs |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Award unrecognized compensation expense | $ 21,100,000 |  |
Award, unrecognized compensation expense, weighted average period of recognition | 1 year 4 months 24 days |  |
PSUs |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Award unrecognized compensation expense | $ 7,100,000 |  |
Award, unrecognized compensation expense, weighted average period of recognition | 1 year 10 months 24 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] |  |  |
Payout, Percent of Shares Granted | 170.00% |  |
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] |  |  |
Payout, Percent of Shares Granted | 200.00% |  |
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 | $ 100,000 | $ 600,000 | $ 5,400,000
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% |  |
Payout, Percent of Shares Granted | 100.00% |  |
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] |  |  |
Performance period | 3 years |  |
Vesting percentage | 50.00% |  |
Terms of Award | three |  |

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- Definition Fair value of options vested. Excludes equity instruments other than options, for example, but not limited to, share units, stock appreciation rights, restricted stock. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Topic 718 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (d)(2) -Publisher FASB -URI https://asc.fasb.org//1943274/2147480429/718-10-50-2 + Details
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