Income Taxes (Narrative) (Details) - USD ($) $ in Millions	1 Months Ended	3 Months Ended		12 Months Ended
	Jun. 30, 2021	Jan. 02, 2021	Dec. 28, 2019	Jan. 01, 2022	Jan. 02, 2021	Dec. 28, 2019	Oct. 02, 2021	Sep. 26, 2020	Dec. 29, 2018
Operating Loss Carryforwards [Line Items]
Effective income tax rate				24.10%	20.20%	24.60%
Income tax expense				$ 474	$ 323	$ 321
Out-of-period adjustment - increase tax expense decrease deferred tax asset		$ 39
Pension contributions				20	32	28
Undistributed earnings of foreign subsidiaries				1,000
Amount of unrecognized deferred tax liability on undistributed earnings of foreign subsidiaries				28
Tax benefits of carryforwards		329		363	329
Valuation allowance		192		248	192
Income taxes paid			$ 255	$ 365	281	537
U.S percentage of tax provision				50.00%
Projected additions to unrecognized tax benefits related to ongoing intercompany pricing activity				$ 4
Unrecognized tax benefits that would affect the Company's effective tax rate in future periods				43
Deferred Tax Liabilities, Gross		902		961	902
Deferred tax liabilities		308		507	308
Tax reserves released as a result of finalization of an IRS tax examination							$ 32	$ 32
Deferred Tax Assets, Valuation Allowance		$ 192	$ 146	248	$ 192	$ 146	$ 20		$ 166
Expire in 5 Years or Less
Operating Loss Carryforwards [Line Items]
Tax benefits of carryforwards				23
Expire in 2027 and later
Operating Loss Carryforwards [Line Items]
Tax benefits of carryforwards				75
Do Not Expire
Operating Loss Carryforwards [Line Items]
Tax benefits of carryforwards				265
UNITED KINGDOM
Operating Loss Carryforwards [Line Items]
Income tax expense	$ 23
UNITED KINGDOM | Minimum
Operating Loss Carryforwards [Line Items]
Effective income tax rate	19.00%
UNITED KINGDOM | Maximum
Operating Loss Carryforwards [Line Items]
Effective income tax rate	25.00%
Current liabilities
Operating Loss Carryforwards [Line Items]
Increase in Unrecognized Tax Benefits is Reasonably Possible				$ 16