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Nature of Operations and Summary of Significant Accounting Policies - Additional Information (Details)
 3 Months Ended 12 Months Ended
Jan. 01, 2022
USD ($)
Jan. 02, 2021
USD ($)
Jan. 01, 2022
USD ($)
segment
Jan. 02, 2021
USD ($)
Dec. 28, 2019
USD ($)
Nature of Operations [Line Items]          
Number of reportable segments | segment     3    
Revenue recognized from contract liabilities     $ 33,128,000 $ 30,426,000  
Revenue, remaining performance obligation, amount $ 37,905,000   $ 37,905,000    
Maturity period for bank acceptance     6 months    
Due from bankers acceptances drafts 8,049,000 $ 9,445,000 $ 8,049,000 9,445,000  
Finite and indefinite lived intangible assets acquired     63,228,000    
Impairment of intangible assets, finite-and definite lived   1,861,000 804,000 1,861,000 $ 2,336,000
Definite-lived intangible assets 170,420,000 136,538,000 $ 170,420,000 136,538,000  
Weighted average useful life of acquired intangible assets     13 years    
Amortization expense of acquired intangible assets     $ 20,869,000 19,125,000 20,154,000
Estimated Future Amortization Expense [Abstract]          
2022 20,994,000   20,994,000    
2023 18,725,000   18,725,000    
2024 17,830,000   17,830,000    
2025 15,754,000   15,754,000    
2026 15,119,000   15,119,000    
Thereafter $ 81,998,000   81,998,000    
Goodwill impairment loss     0 0  
Acquisition related costs     $ 3,655,000 485,000 843,000
Joint Venture with an Italian Company          
Nature of Operations [Line Items]          
Remaining ownership interest with an option to purchase 50.00%   50.00%    
Italian Company | Joint Venture with an Italian Company          
Nature of Operations [Line Items]          
Ownership interest 50.00%   50.00%    
Tradenames          
Nature of Operations [Line Items]          
Indefinite-lived intangible assets $ 28,923,000 24,427,000 $ 28,923,000 24,427,000  
Product technology          
Nature of Operations [Line Items]          
Impairment of intangible assets, finite-and definite lived 499,000   499,000    
Definite-lived intangible assets 29,645,000 23,451,000 29,645,000 23,451,000  
Tradenames          
Nature of Operations [Line Items]          
Definite-lived intangible assets 3,649,000 2,799,000 3,649,000 2,799,000  
Wood Processing          
Nature of Operations [Line Items]          
Impairment of intangible assets, finite-and definite lived       1,861,000 $ 2,336,000
Definite-lived intangible assets $ 443,000   $ 443,000    
Scenario, Adjustment | Madill | Tradenames          
Nature of Operations [Line Items]          
Indefinite-lived intangible assets   (1,300,000)   (1,300,000)  
Scenario, Adjustment | Tradenames | Madill          
Nature of Operations [Line Items]          
Definite-lived intangible assets   $ 1,300,000   $ 1,300,000