Accumulated Other Comprehensive Loss - Schedule of Accumulated Other Comprehensive Loss (Details) - USD ($) $ in Thousands	12 Months Ended
	Aug. 31, 2022	Aug. 31, 2021	Aug. 31, 2020
Increase (Decrease) In Accumulated Other Comprehensive Loss [Roll Forward]
Beginning balance	$ 839,779		$ 701,296
Total other comprehensive (loss) income, net of tax	(2,535)	$ 2,317	1,892
Ending balance	958,474	839,779
Foreign Currency Translation Adjustments
Increase (Decrease) In Accumulated Other Comprehensive Loss [Roll Forward]
Beginning balance	(31,609)	(34,184)	(35,689)
Other comprehensive income (loss) before reclassifications	(3,070)	2,575	1,505
Income tax (expense) benefit		0	0
Other comprehensive income (loss) before reclassifications, net of tax	(3,070)	2,575	1,505
Amounts reclassified from accumulated other comprehensive loss	0	0	0
Income tax benefit	0	0	0
Amounts reclassified from accumulated other comprehensive loss, net of tax	0	0	0
Total other comprehensive (loss) income, net of tax	(3,070)	2,575	1,505
Ending balance	(34,679)	(31,609)	(34,184)
Pension Obligations, net
Increase (Decrease) In Accumulated Other Comprehensive Loss [Roll Forward]
Beginning balance	(2,945)	(2,687)	(3,074)
Other comprehensive income (loss) before reclassifications	355	(530)	190
Income tax (expense) benefit	(80)	(120)	(42)
Other comprehensive income (loss) before reclassifications, net of tax	275	(410)	148
Amounts reclassified from accumulated other comprehensive loss	336	196	309
Income tax benefit	(76)	(44)	(70)
Amounts reclassified from accumulated other comprehensive loss, net of tax	260	152	239
Total other comprehensive (loss) income, net of tax	535	(258)	387
Ending balance	(2,410)	(2,945)	(2,687)
Accumulated Other Comprehensive Loss
Increase (Decrease) In Accumulated Other Comprehensive Loss [Roll Forward]
Beginning balance	(34,554)	(36,871)	(38,763)
Other comprehensive income (loss) before reclassifications	(2,715)	2,045	1,695
Income tax (expense) benefit	(80)	120	(42)
Other comprehensive income (loss) before reclassifications, net of tax	(2,795)	2,165	1,653
Amounts reclassified from accumulated other comprehensive loss	336	196	309
Income tax benefit	(76)	(44)	(70)
Amounts reclassified from accumulated other comprehensive loss, net of tax	260	152	239
Total other comprehensive (loss) income, net of tax	(2,535)	2,317	1,892
Ending balance	$ (37,089)	$ (34,554)	$ (36,871)