Share-Based Compensation (Summary of Share Based Compensation Additional Information) (Details) - USD ($) $ / shares in Units, $ in Thousands	12 Months Ended
Aug. 31, 2025	Aug. 31, 2024	Aug. 31, 2023
Share-Based Payment Arrangement [Abstract]
Intrinsic value of stock options exercised	$ 958	$ 217	$ 23
Cash received from stock option exercises	1,507	479	32
Tax benefit realized from stock option exercises	$ 225	$ 18	$ 1
Weighted average grant-date fair value of stock options vested	$ 28.05	$ 27.14	$ 40.66

Amount of deferred tax (expense) benefit from write-off of the deferred tax asset related to deductible stock options at exercise.

No definition available.

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- Definition

Share based compensation arrangement by share based payment award equity instruments stock options grants in period weighted average grant date fair value.

+ References

No definition available.

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- References

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- Definition

Amount of cash inflow from exercise of option under share-based payment arrangement.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Section 45
-Paragraph 14
-Subparagraph (a)
-SubTopic 10
-Topic 230
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482740/230-10-45-14

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Section 50
-Paragraph 2A
-Subparagraph (a)
-SubTopic 10
-Topic 718
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480429/718-10-50-2A

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- Definition

Amount by which current fair value of underlying stock exceeds exercise price of fully vested and expected to vest exercisable or convertible options. Includes, but is not limited to, unvested options for which requisite service period has not been rendered but that are expected to vest based on achievement of performance condition, if forfeitures are recognized when they occur.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (e)(2)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480429/718-10-50-2

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