Fair Value Measurements - Schedule of Fair Value Debt Instruments (Details) - USD ($) $ in Thousands	Jan. 02, 2021	Oct. 03, 2020
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Long-term debt, fair value	$ 548,517	$ 516,440
Tranche B term loan
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Long-term debt, fair value	169,204	169,940
Senior Unsecured Note
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Long-term debt, fair value	379,313	346,500
Carrying Value
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Long-term debt, fair value	517,945	519,095
Carrying Value | Tranche B term loan
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Long-term debt, fair value	167,945	169,095
Carrying Value | Senior Unsecured Note
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Long-term debt, fair value	350,000	350,000
Level 1
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Long-term debt, fair value	0	0
Level 1 | Tranche B term loan
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Long-term debt, fair value	0	0
Level 1 | Senior Unsecured Note
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Long-term debt, fair value	0	0
Level 2
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Long-term debt, fair value	548,517	516,440
Level 2 | Tranche B term loan
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Long-term debt, fair value	169,204	169,940
Level 2 | Senior Unsecured Note
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Long-term debt, fair value	379,313	346,500
Level 3
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Long-term debt, fair value	0	0
Level 3 | Tranche B term loan
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Long-term debt, fair value	0	0
Level 3 | Senior Unsecured Note
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Long-term debt, fair value	$ 0	$ 0