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. 28, 2024	Dec. 30, 2023
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	$ 1,557,545	$ 1,452,813
Comprehensive income (loss)	12,146	1,426
Amortization of share-based awards	3,648	4,169
Restricted share activity, including net share settlement	(1,811)	(1,919)
Issuance of common stock, including net share settlement of stock options	1,790	(1,581)
Repurchase of stock	(52,141)	(1,422)
Distribution to Noncontrolling interest	(1,346)	(900)
Ending balance	1,519,831	1,452,586
Total
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	1,555,654	1,451,353
Comprehensive income (loss)	11,974	1,289
Amortization of share-based awards	3,648	4,169
Restricted share activity, including net share settlement	(1,811)	(1,919)
Issuance of common stock, including net share settlement of stock options	1,790	(1,581)
Repurchase of stock	(52,141)	(1,422)
Ending balance	1,519,114	1,451,889
Additional Paid In Capital
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	598,098	594,282
Amortization of share-based awards	3,648	4,169
Restricted share activity, including net share settlement	(1,810)	(1,918)
Issuance of common stock, including net share settlement of stock options	1,789	(1,583)
Repurchase of stock	(14,948)	(438)
Ending balance	586,777	594,512
Retained Earnings
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	959,511	859,370
Comprehensive income (loss)	14,009	430
Repurchase of stock	(37,176)	(984)
Ending balance	936,344	858,816
Accumulated Other Comprehensive Income (Loss)
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	(2,626)	(2,970)
Comprehensive income (loss)	(2,035)	859
Ending balance	(4,661)	(2,111)
Noncontrolling Interest
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	1,891	1,460
Comprehensive income (loss)	172	137
Distribution to Noncontrolling interest	(1,346)	(900)
Ending balance	717	697
Common Stock | Common Stock
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	111	111
Repurchase of stock	(4)
Ending balance	107	111
Class A Common Stock | Common Stock
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	544	544
Restricted share activity, including net share settlement	$ (1)	$ (1)
Issuance of common stock, including new shares settlement of stock options (in shares)	1	2
Repurchase of stock	$ (13)
Ending balance	531	$ 545
Class B Stock | Common Stock
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	16	16
Ending balance	$ 16	$ 16