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Long-Term Obligations - Additional Information (Details) - USD ($)	12 Months Ended
	Jan. 03, 2026	Sep. 26, 2025	Sep. 25, 2025	Dec. 28, 2024	Dec. 29, 2018
Debt Instrument [Line Items]
Long-term debt	$ 372,720,000
Maximum \| The Clouth Group of Companies
Debt Instrument [Line Items]
Effective interest rate, up to	1.70%
Revolving credit facility
Debt Instrument [Line Items]
Long-term debt	$ 366,707,000			$ 278,384,000
Weighted average interest rate for long-term obligations	4.49%			5.27%
Senior Promissory Notes, due 2026 to 2028
Debt Instrument [Line Items]
Long-term debt	$ 4,990,000			$ 6,660,000
Other Borrowings, due 2026 to 2031
Debt Instrument [Line Items]
Other Borrowings, due 2026 to 2031	1,023,000			1,460,000
Amendment To Unsecured Multi-Currency Revolving Credit Facility ("Credit Agreement")
Debt Instrument [Line Items]
Borrowing capacity available under committed portion		$ 750,000,000	$ 400,000,000
Amendment To Unsecured Multi-Currency Revolving Credit Facility ("Credit Agreement") \| Revolving credit facility
Debt Instrument [Line Items]
Uncommitted unsecured additional borrowing capacity	200,000,000
Maximum amount of unrestricted cash	$ 50,000,000
Maximum consolidated leverage ratio	3.75
Maximum consolidated leverage ratio upon material acquisition	4.25
Remaining borrowing capacity	$ 383,175,000
Debt issuance costs, net	$ 3,129,000			$ 993,000
Amendment To Unsecured Multi-Currency Revolving Credit Facility ("Credit Agreement") \| Revolving credit facility \| Minimum \| Revolving Credit Facility
Debt Instrument [Line Items]
Commitment fee percentage	0.15%
Amendment To Unsecured Multi-Currency Revolving Credit Facility ("Credit Agreement") \| Revolving credit facility \| Minimum \| Base Rate
Debt Instrument [Line Items]
Basis spread on variable rate (as a percentage)	0.25%
Amendment To Unsecured Multi-Currency Revolving Credit Facility ("Credit Agreement") \| Revolving credit facility \| Minimum \| Eurocurrency Rate, Term SOFR, Term CORRA, And RFR
Debt Instrument [Line Items]
Basis spread on variable rate (as a percentage)	1.25%
Amendment To Unsecured Multi-Currency Revolving Credit Facility ("Credit Agreement") \| Revolving credit facility \| Maximum \| Revolving Credit Facility
Debt Instrument [Line Items]
Commitment fee percentage	0.35%
Amendment To Unsecured Multi-Currency Revolving Credit Facility ("Credit Agreement") \| Revolving credit facility \| Maximum \| Base Rate
Debt Instrument [Line Items]
Basis spread on variable rate (as a percentage)	1.25%
Amendment To Unsecured Multi-Currency Revolving Credit Facility ("Credit Agreement") \| Revolving credit facility \| Maximum \| Eurocurrency Rate, Term SOFR, Term CORRA, And RFR
Debt Instrument [Line Items]
Basis spread on variable rate (as a percentage)	2.25%
Eighth Amendment To Unsecured Multi-Currency Revolving Credit Facility ("Credit Agreement") \| Revolving credit facility
Debt Instrument [Line Items]
Debt issuance costs, net	$ 2,645,000
Note Purchase Agreement \| Senior Promissory Notes, due 2026 to 2028
Debt Instrument [Line Items]
Principal amount					$ 10,000,000
Fixed interest rate					4.90%
Euro-Denominated Borrowing \| Revolving credit facility
Debt Instrument [Line Items]
Long-term debt	$ 92,707,000