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Share-Based Compensation (Narrative) (Details) $ in Thousands | 12 Months Ended
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Aug. 31, 2025 USD ($) Item shares | Aug. 31, 2024 USD ($) shares | Aug. 31, 2023 USD ($) shares
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Pre-tax total unrecognized compensation cost related to nonvested share-based compensation | $ | $ 9,900 |  |
Weighted average period to be recognized | 1 year 9 months 18 days |  |
Outstanding stock options vested | 23,781 | 19,995 | 19,617
Shares outstanding | 167,172 | 142,176 |
Share withheld for payroll tax obligations | $ | $ 1,450 | $ 1,575 | $ 2,471
Restricted Stock Units [Member] |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Vesting period | 3 years |  |
Fair value vested | $ | $ 2,400 | $ 2,300 |
Number of shares vested | 22,349 |  |
Restricted Stock Units Settled In Cash [Member] |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Shares outstanding | 5,793 | 4,742 | 4,039
Performance Stock Units [Member] |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Vesting period | 3 years |  |
Number of shares vested | 11,729 |  |
Performance Stock Units [Member] | Common Stock [Member] |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Number of shares vested | 11,729 | 13,893 | 18,688
Performance Stock Units [Member] | Minimum [Member] |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Percentage of awards actually earned | 0.00% |  |
Performance Stock Units [Member] | Maximum [Member] |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Percentage of awards actually earned | 2.00% |  |
2015 Long-Term Incentive Plan [Member] | Employee Stock Option |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Stock option expire, years | 10 years |  |
Vesting period | 3 years |  |
2025 Long-Term Incentive Plan [Member] |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Plan effective date | Jan. 08, 2025 |  |
Maximum number of shares authorized | 533,491 |  |
Number of shares available | 535,609 |  |
Stock award ratio | Item | 1 |  |
Non Employee Directors [Member] | Restricted Stock Units [Member] |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Vesting period | 9 months |  |

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