Postretirement Plans - Additional Information (Detail) - USD ($)	3 Months Ended				12 Months Ended
	Jan. 01, 2022	Oct. 09, 2021	Oct. 03, 2020	Oct. 05, 2019	Jan. 01, 2022	Jan. 02, 2021	Dec. 28, 2019
Pension and Other Postretirement Benefits Disclosure [Line Items]
Voluntarily contributions made by an employer					$ 0
Cash contributions						$ 0
Non-cash settlement and curtailment charge						108,800,000
Settlement loss	$ 400,000
Expected pension cost for fiscal 2022	700,000				$ 700,000
Postretirement Benefits, minimum years of service for eligibility					10 years
Postretirement Benefits, minimum age for eligibility					60 years
Expected company contribution	548,000				$ 548,000
Expense under plans					$ 1,306,000	$ 109,823,000	$ 3,234,000
Contribution of pension fund in excess of total contribution					5.00%	5.00%	5.00%
Multiemployer plans, minimum contribution					$ 0
Multi-employer pension plan withdrawal liability	2,100,000	$ 2,100,000			$ 2,100,000
Multiemployer plan withdrawal liability of net present value monthly payments period		20 years
Multiemployer plans transition payments payable		$ 1,200,000
Multiemployer plan withdrawal liability estimate payment period		3 years
Minimum
Pension and Other Postretirement Benefits Disclosure [Line Items]
Retiree medical coverage provided					3 years
Maximum
Pension and Other Postretirement Benefits Disclosure [Line Items]
Retiree medical coverage provided					5 years
Pension plans
Pension and Other Postretirement Benefits Disclosure [Line Items]
Settlement loss					$ (403,000)	$ (104,473,000)
Actual return on plan assets					$ 1,929,000	$ 15,790,000	$ 51,800,000
Expected long-term rate of return and average annual return on plan assets					5.70%	4.97%	5.34%
Contribution of company to company pension plans					$ 271,000	$ 7,871,000	$ 2,771,000
Last Fifteen Years
Pension and Other Postretirement Benefits Disclosure [Line Items]
Expected long-term rate of return and average annual return on plan assets					6.30%
Non Qualified Pension Plans
Pension and Other Postretirement Benefits Disclosure [Line Items]
Expected company contribution	300,000				$ 300,000
Qualified Pension Plans
Pension and Other Postretirement Benefits Disclosure [Line Items]
Contribution of company to company pension plans					0
Postretirement Benefit Plans
Pension and Other Postretirement Benefits Disclosure [Line Items]
Contribution of company to company pension plans					931,000	575,000
Expected company contribution	500,000				500,000
Contributions by participants					453,000	573,000	700,000
Multiemployer Plans
Pension and Other Postretirement Benefits Disclosure [Line Items]
Expense under plans					$ 1,000,000.0	1,200,000	1,100,000
Red Zone
Pension and Other Postretirement Benefits Disclosure [Line Items]
Percentage of funded under multi employer plans					Less than 65 percent
Yellow Zone
Pension and Other Postretirement Benefits Disclosure [Line Items]
Percentage of funded under multi employer plans					Between 65 and less than 80 percent
Green Zone
Pension and Other Postretirement Benefits Disclosure [Line Items]
Percentage of funded under multi employer plans					At least 80 percent
Plan No. 2
Pension and Other Postretirement Benefits Disclosure [Line Items]
Voluntarily contributions made by an employer			$ 7,600,000	$ 2,500,000
Expected long-term rate of return and average annual return on plan assets					5.90%
Plan No. 1
Pension and Other Postretirement Benefits Disclosure [Line Items]
Voluntarily contributions made by an employer						0	0
Required | Pension plans
Pension and Other Postretirement Benefits Disclosure [Line Items]
Contribution of company to company pension plans					$ 271,000	271,000	1,040,000
Required | Non Qualified Pension Plans
Pension and Other Postretirement Benefits Disclosure [Line Items]
Contribution of company to company pension plans					300,000
Required | Plan No. 2
Pension and Other Postretirement Benefits Disclosure [Line Items]
Expected company contribution	0				0
Discretionary | Pension plans
Pension and Other Postretirement Benefits Disclosure [Line Items]
Contribution of company to company pension plans						$ 7,600,000	$ 1,731,000
Discretionary | Plan No. 2
Pension and Other Postretirement Benefits Disclosure [Line Items]
Expected company contribution	$ 1,000,000.0				$ 1,000,000.0