Accumulated Other Comprehensive Loss - Components of Accumulated Other Comprehensive Loss, Net of Tax (Details) - USD ($) $ in Thousands		3 Months Ended		9 Months Ended
		May 31, 2025	May 25, 2024	May 31, 2025	May 25, 2024
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period		$ 2,143,556	$ 2,049,685	$ 2,108,511	$ 2,003,960
Other comprehensive income (loss)		8,535	(592)	(773)	130
Balance at end of period		2,174,791	2,075,608	2,174,791	2,075,608
Foreign Currency Translation
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period		(35,340)	(25,736)	(25,966)	(26,504)
Other comprehensive income (loss) before reclassification		8,619	(598)	(755)	170
Amounts reclassified from accumulated other comprehensive loss		0	0	0	0
Other comprehensive income (loss)		8,619	(598)	(755)	170
Balance at end of period		(26,721)	(26,334)	(26,721)	(26,334)
Pension-related
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period	[1]	2,234	2,582	2,234	2,582
Other comprehensive income (loss) before reclassification	[1]	0	0	0	0
Amounts reclassified from accumulated other comprehensive loss	[1]	0	0	0	0
Other comprehensive income (loss)	[1]	0	0	0	0
Balance at end of period	[1]	2,234	2,582	2,234	2,582
Derivative Financial Instruments
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period	[1]	154	115	88	161
Other comprehensive income (loss) before reclassification	[1]	(60)	30	78	28
Amounts reclassified from accumulated other comprehensive loss	[1]	(24)	(24)	(96)	(68)
Other comprehensive income (loss)	[1]	(84)	6	(18)	(40)
Balance at end of period	[1]	70	121	70	121
Accumulated Other Comprehensive Loss
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period		(32,952)	(23,039)	(23,644)	(23,761)
Other comprehensive income (loss) before reclassification		8,559	(568)	(677)	198
Amounts reclassified from accumulated other comprehensive loss		(24)	(24)	(96)	(68)
Other comprehensive income (loss)		8,535	(592)	(773)	130
Balance at end of period		$ (24,417)	$ (23,631)	$ (24,417)	$ (23,631)

[1] Amounts are shown net of tax