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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 |  |

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