Income Taxes - Schedule of Temporary Differences Comprising the Net Deferred Income Tax Liability (Details) - USD ($) $ in Thousands	Oct. 02, 2022	Oct. 03, 2021
Deferred Tax Assets:
State taxes	$ 1,238	$ 1,342
Reserves and contingent liabilities	5,023	6,662
Accounts receivable including the allowance for doubtful accounts	4,986	5,917
Accrued liabilities	35,973	41,657
Lease liabilities, operating leases	49,618	60,181
Stock-based compensation	2,925	3,560
Unbilled revenue	4,885	0
Loss carry-forwards	41,648	54,825
Valuation allowance	(12,286)	(13,040)
Total deferred tax assets	134,010	161,104
Deferred Tax Liabilities:
Unbilled revenue	0	(5,595)
Prepaid expense	(6,065)	(8,136)
Right-of-use assets, operating leases	(49,618)	(60,181)
Intangibles	(42,863)	(40,121)
Undistributed earnings	(2,200)	(3,136)
Property and equipment	(621)	(85)
Total deferred tax liabilities	(101,367)	(117,254)
Net deferred tax assets	$ 32,643	$ 43,850