Related Parties (Details) $ in Thousands		3 Months Ended	12 Months Ended
	Apr. 30, 2019 USD ($) state restaurant	Mar. 29, 2020 USD ($)	Jan. 03, 2021 USD ($) yr shares Rate	Dec. 29, 2019 USD ($) shares	Dec. 30, 2018 USD ($)	Jan. 01, 2017
Related Party Transaction [Line Items]
Preferred Stock, Shares Issued | shares			100	100
Franchise Term | yr			20
Board of directors, number of members			2
Franchise Agreement, Term			20 years
Restaurant rent expense			$ 118,444	$ 107,147	$ 81,409
Related Party Transaction, Accounts Payable			$ 27,596	45,780
Franchise Agreement, Number Of States | state	16
Franchise Agreement, Number Of Additional States | state	4
Franchise Agreement, Remodeling Expense	$ 3,000
Settlement, Approval of Restaurant Development		$ 1,900
Related Party, Burger King Corporate [Member]
Related Party Transaction [Line Items]
Sale of Stock, Percentage of Ownership after Transaction | Rate			15.20%
Related Party Transaction, Royalty Fee Rate | Rate			4.50%
Royalty Expense			$ 67,200	62,000	50,500
Related Party Transaction, Advertising Fee Rate | Rate			4.00%
Advertising Expense			$ 59,300	$ 56,700	47,000
Leases, Number of Leased Restaurants			232	248		244
Restaurant rent expense			$ 25,900	$ 27,400	$ 27,200
Related Party Transaction, Accounts Payable			14,700	$ 11,500
Franchise Agreement, Number Of Restaurant To be Removed Additional | restaurant	500
Affiliated Entity [Member]
Related Party Transaction [Line Items]
Franchise Fees, Initial, Net			$ 50
Popeyes Franchises [Member]
Related Party Transaction [Line Items]
Right Of First Refusal, Number Of Franchises | restaurant	80
Right of First Refusal, Term	6 years
Property Leases Identical to BKC's Lease with Third Party [Member] | Affiliated Entity [Member]
Related Party Transaction [Line Items]
Leases, Number of Leased Restaurants			101
Series B Preferred Stock [Member]
Related Party Transaction [Line Items]
Preferred Stock, Shares Issued | shares			100
Popeyes Franchises [Member]
Related Party Transaction [Line Items]
Related Party Transaction, Royalty Fee Rate | Rate			5.00%
Right of First Refusal, Number of States | shares			2