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Pension and Other Postretirement Benefit Plans - Schedule of Amount Recognized in Accompanying Balance Sheets (Details) - USD ($) $ in Thousands | Oct. 01, 2021 | Oct. 02, 2020
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Defined Benefit Plan Disclosure [Line Items] |  |
Liabilities relating to defined benefit pension and retirement plans | $ 418,080 | $ 568,176
Pension Plan | U.S. Plans |  |
Defined Benefit Plan Disclosure [Line Items] |  |
Prepaid benefit cost included in noncurrent assets | 0 | 0
Accrued benefit cost included in current liabilities | 84 | 85
Liabilities relating to defined benefit pension and retirement plans | 19,215 | 57,919
Net amount recognized at the end of the year | 19,299 | 58,004
Pension Plan | Non-U.S. Plans |  |
Defined Benefit Plan Disclosure [Line Items] |  |
Prepaid benefit cost included in noncurrent assets | 48,340 | 1,037
Accrued benefit cost included in current liabilities | 3,873 | 4,375
Liabilities relating to defined benefit pension and retirement plans | 216,612 | 339,049
Net amount recognized at the end of the year | $ 172,145 | $ 342,387

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