Supplemental Equity Information - Summary of Changes in Carrying Amounts of Equity Attributable to Controlling Interest and Noncontrolling Interest (Details) - USD ($) shares in Thousands, $ in Thousands	3 Months Ended
	Dec. 24, 2022	Dec. 25, 2021
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	$ 1,334,712	$ 1,223,541
Comprehensive loss	(8,067)	8,754
Amortization of share-based awards	4,647	3,886
Restricted share activity, including net share settlement	(590)	(705)
Issuance of common stock, including net share settlement of stock options	1,708	890
Repurchase of stock	(8,966)	(6,660)
Distribution to Noncontrolling interest		(806)
Ending balance	1,323,444	1,228,900
Total
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	1,333,706	1,222,249
Comprehensive loss	(7,651)	8,567
Amortization of share-based awards	4,647	3,886
Restricted share activity, including net share settlement	(590)	(705)
Issuance of common stock, including net share settlement of stock options	1,708	890
Repurchase of stock	(8,966)	(6,660)
Ending balance	1,322,854	1,228,227
Additional Paid In Capital
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	582,056	576,446
Amortization of share-based awards	4,647	3,886
Restricted share activity, including net share settlement	(590)	(705)
Issuance of common stock, including net share settlement of stock options	1,707	890
Repurchase of stock	(2,693)	(1,600)
Ending balance	585,127	578,917
Retained Earnings
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	755,253	646,082
Comprehensive loss	(8,433)	9,009
Repurchase of stock	(6,271)	(5,059)
Ending balance	740,549	650,032
Accumulated Other Comprehensive Income (Loss)
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	(4,145)	(831)
Comprehensive loss	782	(442)
Ending balance	(3,363)	(1,273)
Noncontrolling Interest
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	1,006	1,292
Comprehensive loss	(416)	187
Distribution to Noncontrolling interest		(806)
Ending balance	590	673
Common Stock | Common Stock
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	113	113
Ending balance	113	113
Class A Common Stock | Common Stock
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	$ 413	423
Restricted share activity, including net share settlement		0
Issuance of common stock, including new shares settlement of stock options (in shares)	1
Repurchase of stock (in shares)	(2)
Repurchase of stock		(1)
Ending balance	$ 412	422
Class B Stock | Common Stock
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	16	16
Ending balance	$ 16	$ 16