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Goodwill and Other Long-Lived Assets - Additional Information (Detail) - USD ($) | 3 Months Ended | 12 Months Ended
--- | --- | ---
Feb. 28, 2021 | May 31, 2023 | May 31, 2022 | May 31, 2021
Goodwill And Other Intangible Assets [Line Items] |  |  |  |  |  |
Goodwill |  |  | $ 414,820,000 |  | $ 401,469,000 | $ 351,056,000
Amortization expense |  |  | $ 18,221,000 |  | 14,937,000 | 12,257,000
Number of plans |  |  | two |  |  |
Assets held for sale |  |  | $ 3,381,000 |  | 20,318,000 |
Impairment of long-lived assets |  |  | 2,596,000 |  | 3,076,000 | 13,739,000
Operating lease assets |  |  | 99,967,000 |  | 98,769,000 |
Other |  |  |  |  |  |
Goodwill And Other Intangible Assets [Line Items] |  |  |  |  |  |
Goodwill |  |  | 0 |  | 0 |
Impairment charge of long-lived assets |  |  |  |  |  | 11,810,000
Impairment of goodwill |  |  | 198,290,000 |  | 198,290,000 |
Cryogenics |  |  |  |  |  |
Goodwill And Other Intangible Assets [Line Items] |  |  |  |  |  |
Impairment charge of long-lived assets |  |  |  |  |  | 3,662,000
Impairment of long-lived assets |  |  |  |  |  | 4,333,000
Jefferson |  |  |  |  |  |
Goodwill And Other Intangible Assets [Line Items] |  |  |  |  |  |
Impairment of long-lived assets |  |  |  |  |  | 1,423,000
Superior Tools |  |  |  |  |  |
Goodwill And Other Intangible Assets [Line Items] |  |  |  |  |  |
Impairment of long-lived assets |  |  |  |  |  | 506,000
Building Products |  |  |  |  |  |
Goodwill And Other Intangible Assets [Line Items] |  |  |  |  |  |
Goodwill | [1] |  | 65,213,000 |  | 65,408,000 | 72,273,000
Impairment charge of long-lived assets |  |  | 484,000 |  |  | 1,423,000
Fixed Assets |  |  |  |  |  |
Goodwill And Other Intangible Assets [Line Items] |  |  |  |  |  |
Assets held for sale |  |  | 2,623,000 |  |  |
Impairment charge of long-lived assets |  |  | 2,112,000 |  |  |
Production Equipment Member | Twinsburg | Samuel Joint Ventures Facility |  |  |  |  |  |
Goodwill And Other Intangible Assets [Line Items] |  |  |  |  |  |
Impairment charge of long-lived assets |  | $ 3,076,000 |  |  |  |
Fair Value, Nonrecurring |  |  |  |  |  |
Goodwill And Other Intangible Assets [Line Items] |  |  |  |  |  |
Fair market value of assets |  |  | 2,693,000 |  | 700,000 |
Fair Value, Nonrecurring | Fair Value, Inputs, Level 2 |  |  |  |  |  |
Goodwill And Other Intangible Assets [Line Items] |  |  |  |  |  |
Fair market value of assets |  |  | 2,693,000 |  | $ 700,000 |
Long Lived Assets Held And Used | Jefferson |  |  |  |  |  |
Goodwill And Other Intangible Assets [Line Items] |  |  |  |  |  |
Carrying value long-lived assets |  |  |  |  |  | 1,823,000
Long Lived Assets Held And Used | Jefferson | Building Products Facility |  |  |  |  |  |
Goodwill And Other Intangible Assets [Line Items] |  |  |  |  |  |
Impairment of non cash charge |  |  | 484,000 |  |  |
Long Lived Assets Held And Used | Fair Value, Inputs, Level 2 | Cryogenics |  |  |  |  |  |
Goodwill And Other Intangible Assets [Line Items] |  |  |  |  |  |
Fair market value of assets |  |  |  |  |  | 9,193,000
Carrying value long-lived assets |  |  |  |  |  | 13,526,000
Long Lived Assets Held And Used | Fair Value, Nonrecurring |  |  |  |  |  |
Goodwill And Other Intangible Assets [Line Items] |  |  |  |  |  |
Fair market value of assets | [2] |  | 70,000 |  |  |
Impairment charge of long-lived assets |  |  |  |  |  | 1,441,000
Fixed asset net book value |  |  |  |  |  | 7,375,000
Intangible assets with net book value |  |  |  |  |  | 2,374,000
Long Lived Assets Held And Used | Fair Value, Nonrecurring | Jefferson |  |  |  |  |  |
Goodwill And Other Intangible Assets [Line Items] |  |  |  |  |  |
Fair market value of assets |  |  |  |  |  | 400,000
Long Lived Assets Held And Used | Fair Value, Nonrecurring | Fair Value, Inputs, Level 2 |  |  |  |  |  |
Goodwill And Other Intangible Assets [Line Items] |  |  |  |  |  |
Fair market value of assets |  |  | $ 70,000 | [2] |  | 5,934,000
Long Lived Assets Held And Used | Fair Value, Nonrecurring | Fair Value, Inputs, Level 3 |  |  |  |  |  |
Goodwill And Other Intangible Assets [Line Items] |  |  |  |  |  |
Impairment charge of long-lived assets |  |  |  |  |  | $ 2,374,000
Minimum |  |  |  |  |  |
Goodwill And Other Intangible Assets [Line Items] |  |  |  |  |  |
Definite-lived intangible assets, estimated useful lives |  |  | 10 years |  |  |
Maximum |  |  |  |  |  |
Goodwill And Other Intangible Assets [Line Items] |  |  |  |  |  |
Definite-lived intangible assets, estimated useful lives |  |  | 20 years |  |  |
[1] | In connection with the realignment of the our legacy Pressure Cylinders business, as discussed further in “Note P - Segment Data”, the goodwill of our legacy Pressure Cylinders business unit was allocated to the new reporting units on a relative fair value basis.
[2] | Comprised of certain assets associated with a capital project at our Building Products facility in Jefferson, Ohio which were written down to their estimated salvage value of $70. These assets continue to be held and used. Refer to “Note E – Goodwill and Other Long-Lived Assets” for additional information.

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