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Stockholders' Deficit (Details) $ / shares in Units, $ in Thousands, shares in Millions | 3 Months Ended | 4 Months Ended | 12 Months Ended
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Oct. 03, 2021 USD ($) $ / shares | Jul. 04, 2021 $ / shares | Apr. 11, 2021 $ / shares | Jan. 17, 2021 $ / shares | Oct. 03, 2021 USD ($) restaurant $ / shares shares | Sep. 27, 2020 USD ($) $ / shares | Sep. 29, 2019 USD ($) $ / shares
Stockholders' Equity Note [Abstract] |  |  |  |  |  |  |
Shares repurchased (in shares) | shares |  |  |  |  | 1.9 |  |
Cost of shares repurchased |  |  |  |  | $ 200,000 | $ 153,550 | $ 125,317
Remaining amount under stock repurchase program | $ 0 |  |  |  | $ 0 |  |
Number of cash dividends declared | restaurant |  |  |  |  | 4 |  |
Amount of each of the three cash dividends declared per common share (in usd per share) | $ / shares | $ 0.44 | $ 0.44 | $ 0.40 | $ 0.40 | $ 1.68 | $ 1.20 | $ 1.60
Total cash dividends |  |  |  |  | $ 37,600 |  |

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