Stockholders' Equity and Noncontrolling Interests - Schedule of Accumulated Other Comprehensive Loss and Related Tax Effects (Detail) - USD ($) $ in Millions	12 Months Ended
	Oct. 02, 2020	Sep. 27, 2019	Sep. 28, 2018
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward]
Balance at beginning of period	$ 1,777.6	$ 1,588.7	$ 1,521.9
Balance at end of period	2,084.8	1,777.6	1,588.7
Net Unrealized Gains (Losses) Defined Benefit Pension and Post-Retirement Benefit Plans
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward]
Balance at beginning of period	(61.7)	(35.2)	(44.1)
Other comprehensive earnings (loss) before reclassifications	14.4	(32.3)	9.0
Amounts reclassified out of other comprehensive earnings (loss)	3.2	1.5	1.7
Tax benefit (expense)	(2.8)	4.3	(1.8)
Balance at end of period	(46.9)	(61.7)	(35.2)
Net Unrealized Gains (Losses) Cash Flow Hedging Instruments
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward]
Balance at beginning of period	2.1	0.0	0.0
Other comprehensive earnings (loss) before reclassifications	(0.3)	3.0	(0.9)
Amounts reclassified out of other comprehensive earnings (loss)	(2.6)	(0.2)	0.9
Tax benefit (expense)	0.7	(0.7)	0.0
Balance at end of period	(0.1)	2.1	0.0
Cumulative Translation Adjustment
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward]
Balance at beginning of period	(42.5)	(30.1)	(24.7)
Other comprehensive earnings (loss) before reclassifications	3.8	(12.4)	(5.4)
Amounts reclassified out of other comprehensive earnings (loss)	0.0	0.0	0.0
Tax benefit (expense)	0.0	0.0	0.0
Balance at end of period	(38.7)	(42.5)	(30.1)
Accumulated  Other Comprehensive Loss
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward]
Balance at beginning of period	(102.1)	(65.3)	(68.8)
Other comprehensive earnings (loss) before reclassifications	17.9	(41.7)	2.7
Amounts reclassified out of other comprehensive earnings (loss)	0.6	1.3	2.6
Tax benefit (expense)	(2.1)	3.6	(1.8)
Balance at end of period	$ (85.7)	$ (102.1)	$ (65.3)