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Stock-Based Compensation (Details) | 12 Months Ended
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May 30, 2020 USD ($) $ / shares shares | Jun. 01, 2019 USD ($) $ / shares shares | Jun. 02, 2018 USD ($) $ / shares shares
Share-based Compensation Arrangement by Share-based Payment Award |  |  |
Shares Authorized ( in shares) | shares | 5,991,307,000,000 |  |
Stock-based compensation cost not yet recognized | $ 3,200,000 |  |
Weighted-average period over which this amount is expected to be recognized | 1 year 2 months 12 days |  |
Balance at beginning of period (in shares) | shares | 70,145 | 62,957 | 67,335
Cash received during fiscal 2020 from the exercise of stock options | $ 12,000,000 |  |
IRS statutory compensation ceiling | $ 285,000 |  |
Employee stock purchase program |  |  |
Share-based Compensation Arrangement by Share-based Payment Award |  |  |
Capital shares reserved for future issuance | shares | 4,000,000 |  |
Reserved for purchase by plan participants (percentage) | 85.00% |  |
Employee stock option |  |  |
Share-based Compensation Arrangement by Share-based Payment Award |  |  |
Weighted-average period over which this amount is expected to be recognized | 1 year |  |
Intrinsic value of options exercised | $ 5,500,000 | $ 3,300,000 | $ 5,000,000.0
Employee stock option | Director |  |  |
Share-based Compensation Arrangement by Share-based Payment Award |  |  |
Exercisable period (in years) | 1 year |  |
Expiration period (in years) | 10 years |  |
Restricted stock units |  |  |
Share-based Compensation Arrangement by Share-based Payment Award |  |  |
Weighted-average period over which this amount is expected to be recognized | 1 year 2 months 12 days |  |
Conversion ratio to common stock | 1 |  |
Fair value of the shares that vested | $ 5,900,000 |  |
Granted | $ / shares | $ 44.70 | $ 37.81 | $ 35.28
Performance share units |  |  |
Share-based Compensation Arrangement by Share-based Payment Award |  |  |
Weighted-average period over which this amount is expected to be recognized | 1 year 3 months 18 days |  |
Conversion ratio to common stock | 1 |  |
Fair value of the shares that vested | $ 0 |  |
Granted | $ / shares | $ 45.71 | $ 36.37 | $ 31.28
Minimum | Employee stock option |  |  |
Share-based Compensation Arrangement by Share-based Payment Award |  |  |
Exercisable period (in years) | 1 year |  |
Minimum | Restricted stock units |  |  |
Share-based Compensation Arrangement by Share-based Payment Award |  |  |
Exercisable period (in years) | 3 years |  |
Minimum | Performance share units |  |  |
Share-based Compensation Arrangement by Share-based Payment Award |  |  |
Exercisable period (in years) | 3 years |  |
Maximum | Employee stock option |  |  |
Share-based Compensation Arrangement by Share-based Payment Award |  |  |
Exercisable period (in years) | 3 years |  |
Expiration period (in years) | 10 years |  |
Maximum | Executive Equalization Retirement Plan |  |  |
Share-based Compensation Arrangement by Share-based Payment Award |  |  |
Cash awards granted, percentage | 50.00% |  |
Percentage of incentive cash bonus | 100.00% |  |

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