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Goodwill and Intangible Assets - Changes in Carrying Value of Goodwill (Details) - USD ($) |  | 3 Months Ended | 12 Months Ended
--- | --- | --- | ---
Jun. 28, 2021 | Sep. 27, 2020 | Oct. 03, 2021 | Sep. 27, 2020 | Sep. 29, 2019
Goodwill [Roll Forward] |  |  |  |  |
Balance at beginning of the period |  |  | $ 993,498,000 | $ 924,820,000 |
Acquisitions |  |  | 90,591,000 | 80,176,000 |
Impairment | $ 0 | $ (15,800,000) | 0 | (15,800,000) | $ (7,755,000)
Translation and other |  |  | 24,489,000 | 4,302,000 |
Balance at end of the period |  | 993,498,000 | 1,108,578,000 | 993,498,000 | 924,820,000
GSG |  |  |  |  |
Goodwill [Roll Forward] |  |  |  |  |
Balance at beginning of the period |  |  | 516,315,000 | 441,802,000 |
Acquisitions |  |  | 15,112,000 | 74,882,000 |
Impairment |  |  |  | 0 |
Translation and other |  |  | 7,006,000 | (369,000) |
Balance at end of the period |  | 516,315,000 | 538,433,000 | 516,315,000 | 441,802,000
CIG |  |  |  |  |
Goodwill [Roll Forward] |  |  |  |  |
Balance at beginning of the period |  |  | 477,183,000 | 483,018,000 |
Acquisitions |  |  | 75,479,000 | 5,294,000 |
Impairment |  |  |  | (15,800,000) |
Translation and other |  |  | 17,483,000 | 4,671,000 |
Balance at end of the period |  | $ 477,183,000 | $ 570,145,000 | $ 477,183,000 | $ 483,018,000

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- Definition Amount after accumulated impairment loss of an asset representing future economic benefits arising from other assets acquired in a business combination that are not individually identified and separately recognized. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 942 -SubTopic 210 -Section S99 -Paragraph 1 -Subparagraph (SX 210.9-03(10)(1)) -URI http://asc.fasb.org/extlink&oid=120398452&loc=d3e534808-122878 Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 350 -SubTopic 20 -Section 45 -Paragraph 5 -URI http://asc.fasb.org/extlink&oid=120320667&loc=SL49117168-202975 Reference 3: http://www.xbrl.org/2003/role/exampleRef -Publisher FASB -Name Accounting Standards Codification -Topic 852 -SubTopic 10 -Section 55 -Paragraph 10 -URI http://asc.fasb.org/extlink&oid=84165509&loc=d3e56426-112766 Reference 4: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 350 -SubTopic 20 -Section 45 -Paragraph 1 -URI http://asc.fasb.org/extlink&oid=99380562&loc=d3e13770-109266 + Details
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