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Goodwill and Intangible Assets - Narrative (Details) - USD ($) |  | 12 Months Ended
--- | --- | ---
Jul. 03, 2023 | Oct. 01, 2023 | Oct. 02, 2022 | Oct. 03, 2021
Goodwill [Line Items] |  |  |  |
Impairment of goodwill | $ 0 |  |  |
Percentage of excess of fair value over carrying value (less than) | 45.00% |  |  |
Amortization expense for intangible assets |  | $ 41,200,000 | $ 13,200,000 | $ 11,500,000
Reduction in intangible assets, foreign currency translation adjustment |  | 200,000 | 5,300,000 |
GSG |  |  |  |
Goodwill [Line Items] |  |  |  |
Gross amounts of goodwill |  | 677,600,000 | 536,800,000 |
Accumulated impairment |  | 17,700,000 | 17,700,000 |
CIG |  |  |  |
Goodwill [Line Items] |  |  |  |
Gross amounts of goodwill |  | 1,341,800,000 | 712,800,000 |
Accumulated impairment |  | $ 121,500,000 | $ 121,500,000 |

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- Definition The aggregate expense charged against earnings to allocate the cost of intangible assets (nonphysical assets not used in production) in a systematic and rational manner to the periods expected to benefit from such assets. As a noncash expense, this element is added back to net income when calculating cash provided by or used in operations using the indirect method. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Name Accounting Standards Codification -Section 45 -Paragraph 28 -Subparagraph (b) -SubTopic 10 -Topic 230 -Publisher FASB -URI https://asc.fasb.org//1943274/2147482740/230-10-45-28 Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef -Name Accounting Standards Codification -Topic 350 -SubTopic 30 -Section 45 -Paragraph 2 -Publisher FASB -URI https://asc.fasb.org//1943274/2147482686/350-30-45-2 Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef -Name Accounting Standards Codification -Topic 350 -SubTopic 30 -Section 50 -Paragraph 2 -Subparagraph (a)(2) -Publisher FASB -URI https://asc.fasb.org//1943274/2147482665/350-30-50-2 + Details
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