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Stockholders' Deficit (Details) $ / shares in Units, $ in Thousands, shares in Millions | 12 Months Ended
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Sep. 29, 2024 USD ($) restaurant $ / shares shares | Oct. 01, 2023 USD ($) $ / shares | Oct. 02, 2022 USD ($) $ / shares
Dividends Payable [Line Items] |  |  |
Shares repurchased (in shares) | shares | 1.1 |  |
Cost of shares repurchased | $ | $ 70,592 | $ 90,731 | $ 25,000
Remaining amount under stock repurchase program | $ | $ 180,000 |  |
Number of cash dividends declared | restaurant | 4 |  |
Cash dividends declared per common share (in usd per share) | $ 1.76 | $ 1.76 | $ 1.76
Total cash dividends | $ | $ 34,200 |  |
Dividends Declared, Tranche One |  |  |
Dividends Payable [Line Items] |  |  |
Cash dividends declared per common share (in usd per share) | $ 0.44 |  |
Dividends Declared, Tranche Two |  |  |
Dividends Payable [Line Items] |  |  |
Cash dividends declared per common share (in usd per share) | 0.44 |  |
Dividends Declared, Tranche Three |  |  |
Dividends Payable [Line Items] |  |  |
Cash dividends declared per common share (in usd per share) | 0.44 |  |
Dividends Declared, Tranche Four |  |  |
Dividends Payable [Line Items] |  |  |
Cash dividends declared per common share (in usd per share) | $ 0.44 |  |

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