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Stock-Based Compensation Plans (Narrative) (Details) $ / shares in Units, $ in Thousands								12 Months Ended
	Oct. 02, 2020 USD ($) item shares	Oct. 18, 2019 item shares	Jan. 25, 2019 USD ($) $ / shares shares	Oct. 01, 2018 item shares	Nov. 14, 2017 item shares	Oct. 18, 2016 item shares	Nov. 12, 2015 item shares	Aug. 31, 2021 USD ($) item shares	Aug. 31, 2020 USD ($) item shares	Aug. 31, 2019 USD ($) item shares
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Common stock issued from treasury stock								432,564
Shares withheld for tax								147,092
Shares withheld for tax, fair value \| $								$ 3,000
Capitalized stock-based compensation expense \| $								$ 0
Fiscal 2021 Long Term Incentive Plan Award [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Number of tranches \| item	2
Fiscal 2021 Acquisition Of Strive Talent Plan [Member] \| Bonus [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Service period								18 months
Compensation \| $								$ 1,000
Former Principal Owner [Member] \| Fiscal 2021 Acquisition Of Strive Talent Plan [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Compensation \| $								$ 4,200
Trading days								15 days
Shares required to be distributed within, days								45 days
Common Stock [Member] \| 2019 Omnibus Plan [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Shares reserved for payment of consideration								200,000
Stock Options [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Stock options exercised								218,750	350,000
Shares withheld for tax								51,738	102,656
Shares withheld for tax, fair value \| $								$ 1,300	$ 3,600
Intrinsic value of the exercised options \| $								2,900	8,000
Income tax benefit from exercise of the options \| $								700	1,800
Income tax benefit upon exercise of the options \| $								500
Restricted Stock Awards [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Unrecognized compensation expense \| $								200
Whole-share grant per eligible director \| $								$ 100
Vesting period of awards								1 year
Cost of common stock issued from treasury \| $								$ 400	300	$ 400
Weighted-average vesting period for recognition								4 months
Total recognized tax benefit from unvested stock awards \| $								$ 200	200	200
Intrinsic value of unvested stock awards \| $								1,200
Restricted Stock Awards [Member] \| Board Of Directors [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Fair value of shares awarded \| $								$ 700	$ 700	$ 700
Shares issued under terms of the award								28,049	21,420	28,525
Time-Based Award [Member] \| Fiscal 2019 Time Based Award [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Service period			2 years
Price per share \| $ / shares			$ 24.54
Vesting period of awards			2 years
Fair value of shares awarded \| $			$ 300
Shares issued under terms of the award			11,915
Performance-Based Award [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Service period	2 years
Increase Adjusted EBITDA vesting target \| $	$ 2,000
Number of individuals who qualified for award \| item								4	4	4
Performance-Based Award [Member] \| 2019 Omnibus Plan [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Shares available for future grants								8,500
Performance-Based Award [Member] \| Fiscal 2020 Long Term Incentive Plan Award [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Shares may be awarded		25,101
Increase Adjusted EBITDA vesting target \| $								$ 2,000
Shares authorized to be issued		150,630
Number of tranches \| item		3
Life of awards		3 years
Expiration date								Aug. 31, 2024
Percent of shares plan participants are entitled to		25.00%
Vesting period of awards		3 years
Performance-Based Award [Member] \| Fiscal 2019 Long Term Incentive Plan Award [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Shares may be awarded				36,470
Service period								2 years
Increase Adjusted EBITDA vesting target \| $								$ 2,000
Shares authorized to be issued				218,818
Number of tranches \| item				3
Life of awards				3 years
Expiration date								Aug. 31, 2023
Percent of shares plan participants are entitled to				25.00%
Vesting period of awards				3 years
Performance-Based Award [Member] \| Fiscal 2018 Long Term Incentive Plan Award [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Number of tranches \| item					3
Life of awards					3 years
Shares earned by participants								221,067
Performance-Based Award [Member] \| Fiscal 2017 Long Term Incentive Plan Award [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Increase Adjusted EBITDA vesting target \| $								$ 2,000
Remaining unvested shares								0
Shares authorized to be issued						183,381
Number of individual vesting conditions \| item						6
Number of performance measures \| item						2
Life of awards						6 years
Expiration date						Aug. 31, 2022		Aug. 31, 2024
Performance-Based Award [Member] \| Fiscal 2016 Long Term Incentive Plan Award [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Increase Adjusted EBITDA vesting target \| $								$ 2,000
Remaining unvested shares								0
Shares authorized to be issued							231,276
Number of individual vesting conditions \| item							6
Number of performance measures \| item							2
Life of awards							6 years
Expiration date							Aug. 31, 2021	Aug. 31, 2023
Performance-Based Award [Member] \| Common Stock [Member] \| 2019 Omnibus Plan [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Authorized additional shares of common stock for issuance			700,000
Employee Stock Purchase Plan [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Price of common stock as a percent of the average fair market value								85.00%
Shares issued to employee stock purchase plan participants								51,581	41,409	43,073
Cost basis of shares issued to employee stock purchase plan participants \| $								$ 800	$ 600	$ 600
Proceeds from ESPP participants \| $								$ 1,100	$ 1,000	$ 1,000
Employee Stock Purchase Plan [Member] \| 2017 Employee Stock Purchase Plan [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Shares remaining in employee stock purchase plan								810,000
Tranche One [Member] \| Time-Based Award [Member] \| Fiscal 2021 Long Term Incentive Plan Award [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Percent of award shares vest	25.00%
Shares issued under terms of the award	52,696
Tranche One [Member] \| Performance-Based Award [Member] \| Fiscal 2018 Long Term Incentive Plan Award [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Shares may be awarded					42,883
Percent of shares plan participants are entitled to					25.00%
Vesting period of awards					3 years
Tranche Two and Three [Member] \| Performance-Based Award [Member] \| Fiscal 2021 Long Term Incentive Plan Award [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Percent of performance-based objectives	100.00%
Shares issued under terms of the award	158,088
Tranche Two and Three [Member] \| Performance-Based Award [Member] \| Minimum [Member] \| Fiscal 2021 Long Term Incentive Plan Award [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Percent of performance award to be granted	50.00%
Tranche Two and Three [Member] \| Performance-Based Award [Member] \| Minimum [Member] \| Fiscal 2020 Long Term Incentive Plan Award [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Percent of performance award to be granted		50.00%
Tranche Two and Three [Member] \| Performance-Based Award [Member] \| Minimum [Member] \| Fiscal 2019 Long Term Incentive Plan Award [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Percent of performance award to be granted				50.00%
Tranche Two and Three [Member] \| Performance-Based Award [Member] \| Maximum [Member] \| Fiscal 2021 Long Term Incentive Plan Award [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Percent of performance award to be granted	200.00%
Shares may be awarded	316,176
Tranche Two and Three [Member] \| Performance-Based Award [Member] \| Maximum [Member] \| Fiscal 2020 Long Term Incentive Plan Award [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Percent of performance award to be granted		200.00%
Tranche Two and Three [Member] \| Performance-Based Award [Member] \| Maximum [Member] \| Fiscal 2019 Long Term Incentive Plan Award [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Percent of performance award to be granted				200.00%