Accumulated Other Comprehensive Loss - Schedule of Accumulated Other Comprehensive Loss (Details) - USD ($) $ in Thousands	3 Months Ended		9 Months Ended
	May 31, 2022	May 31, 2021	May 31, 2022	May 31, 2021
Increase (Decrease) In Accumulated Other Comprehensive Loss [Roll Forward]
Beginning balance	$ 904,649	$ 734,039	$ 839,779	$ 680,436
Total other comprehensive income, net of tax	193	4,551	309	6,140
Ending balance	967,870	802,583	967,870	802,583
Foreign Currency Translation Adjustments
Increase (Decrease) In Accumulated Other Comprehensive Loss [Roll Forward]
Beginning balance	(32,002)	(32,373)	(31,609)	(34,184)
Other comprehensive (loss) income before reclassifications	153	4,514	240	6,325
Income tax (expense) benefit	0	0	0	0
Other comprehensive (loss) income before reclassifications, net of tax	153	4,514	240	6,325
Amounts reclassified from accumulated other comprehensive loss	0	0	0	0
Income tax (benefit)	0	0	0	0
Amounts reclassified from accumulated other comprehensive loss, net of tax	0	0	0	0
Total other comprehensive income, net of tax	153	4,514	240	6,325
Ending balance	(31,849)	(27,859)	(31,849)	(27,859)
Pension Obligations, net
Increase (Decrease) In Accumulated Other Comprehensive Loss [Roll Forward]
Beginning balance	(2,436)	(2,909)	(2,945)	(2,687)
Other comprehensive (loss) income before reclassifications	0	0	451	(385)
Income tax (expense) benefit	0	0	(101)	87
Other comprehensive (loss) income before reclassifications, net of tax	0	0	350	(298)
Amounts reclassified from accumulated other comprehensive loss	52	49	257	147
Income tax (benefit)	(12)	(12)	(58)	(34)
Amounts reclassified from accumulated other comprehensive loss, net of tax	40	37	199	113
Total other comprehensive income, net of tax	40	37	549	(185)
Ending balance	(2,396)	(2,872)	(2,396)	(2,872)
Accumulated Other Comprehensive Loss
Increase (Decrease) In Accumulated Other Comprehensive Loss [Roll Forward]
Beginning balance	(34,438)	(35,282)	(34,554)	(36,871)
Other comprehensive (loss) income before reclassifications	153	4,514	211	5,940
Income tax (expense) benefit	0	0	(101)	87
Other comprehensive (loss) income before reclassifications, net of tax	153	4,514	110	6,027
Amounts reclassified from accumulated other comprehensive loss	52	49	257	147
Income tax (benefit)	(12)	(12)	(58)	(34)
Amounts reclassified from accumulated other comprehensive loss, net of tax	40	37	199	113
Total other comprehensive income, net of tax	193	4,551	309	6,140
Ending balance	$ (34,245)	$ (30,731)	$ (34,245)	$ (30,731)