Accumulated Other Comprehensive Loss - Components of Accumulated Other Comprehensive Loss (Details) - USD ($) $ in Thousands		12 Months Ended
		Aug. 31, 2024	Aug. 26, 2023	Aug. 27, 2022
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period		$ 2,003,960	$ 1,915,871	$ 1,872,952
Change during the year		117	529	546
Balance at end of period		2,108,511	2,003,960	1,915,871
Foreign Currency Translation
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period		(26,504)	(24,803)
Change during the year		538	(1,701)
Balance at end of period		(25,966)	(26,504)	(24,803)
Pension-related
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period	[1]	2,582	452
Change during the year	[1]	(348)	2,130
Balance at end of period	[1]	2,234	2,582	452
Derivative Financial Instruments
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period	[1]	161	61
Change during the year	[1]	(73)	100
Balance at end of period	[1]	88	161	61
Accumulated Other Comprehensive Loss
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period		(23,761)	(24,290)	(24,836)
Change during the year		117	529
Balance at end of period		$ (23,644)	$ (23,761)	$ (24,290)

[1] Amounts are shown net of tax.