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Derivatives and Fair Value Measurements - Schedule of Amount of Gain (Loss) on Derivatives Recognized in Income (Details) - USD ($) $ in Thousands | 12 Months Ended
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Sep. 30, 2023 | Oct. 01, 2022 | Oct. 02, 2021
Derivatives not designated as hedging instruments | Miscellaneous, net | Foreign Exchange Forward [Member] |  |  |
Derivative [Line Items] |  |  |
Amount of (Loss) Gain on Derivatives Recognized in Income | $ (1,285) | $ (1,181) | $ 98

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