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Basis of Presentation and Summary of Significant Accounting Policies - Schedule of Accumulated Other Comprehensive Loss (Details) - USD ($) $ in Thousands | Apr. 03, 2026 | Oct. 03, 2025
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Organization, Consolidation and Presentation of Financial Statements [Abstract] |  |
Pension plan adjustments | $ (18,450) | $ (18,450)
Foreign currency translation adjustments | (155,265) | (161,012)
Cash flow hedges | 16,028 | 12,056
Total accumulated other comprehensive loss | $ (157,687) | $ (167,406)

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