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Benefit Plans - Amounts Recognized in Other Comprehensive Income (Details) - USD ($) $ in Thousands | 12 Months Ended
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Oct. 02, 2021 | Oct. 03, 2020 | Sep. 28, 2019
Defined Benefit Plan Disclosure [Line Items] |  |  |
Net (gain) loss | $ 289 | $ (12,185) | $ (24,300)
Pension Plan |  |  |
Defined Benefit Plan Disclosure [Line Items] |  |  |
Interest cost | 4,227 | 4,947 | 6,047
Expected return on plan assets | (7,777) | (7,384) | (7,619)
Amortization of net loss | 1,861 | 1,720 | 2,758
Net periodic benefit (income) expense | (1,689) | (717) | 1,186
Net (gain) loss | (16,038) | 4,671 | 26,083
Amortization of net loss | (1,861) | (1,720) | (2,758)
Total recognized in other comprehensive (income) loss | (17,899) | 2,951 | 23,325
Total recognized in net periodic pension benefit (income) expense and other comprehensive (income) loss | $ (19,588) | $ 2,234 | $ 24,511

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