Summary of Significant Accounting Policies - Changes in the Carrying Amount of Goodwill (Details) - USD ($) $ in Thousands	12 Months Ended
	Jan. 03, 2026	Dec. 28, 2024	Dec. 30, 2023
Goodwill [Line Items]
Goodwill, Impaired, Accumulated Impairment Loss	$ 0
Goodwill [Roll Forward]
Balance beginning of period	1,744,246	$ 1,704,273
Goodwill, Acquired During Period	13,312	60,932
Measurement period adjustments to goodwill acquired in prior year	2,131	328
Exchange effect and other	(39,960)	21,287
Balance end of period	1,799,649	1,744,246	$ 1,704,273
Accumulated other comprehensive loss	(141,864)	(269,390)	(223,198)
Other Comprehensive Income (Loss), Net of Tax	127,526	(46,192)	55,274
Other Comprehensive Income (Loss), before Reclassifications, Net of Tax	(143,945)	21,582
Accumulated Foreign Currency Adjustment Attributable to Parent
Goodwill [Roll Forward]
Other Comprehensive Income (Loss), Net of Tax	143,643	(67,765)
Other Comprehensive Income (Loss), before Reclassifications, Net of Tax	(143,643)	67,765
Accumulated Defined Benefit Plans Adjustment Attributable to Parent
Goodwill [Roll Forward]
Other Comprehensive Income (Loss), Net of Tax	(1,829)	31,179
Other Comprehensive Income (Loss), before Reclassifications, Net of Tax	(2,125)	28,585
Accumulated Gain (Loss), Net, Cash Flow Hedge, Parent | Interest Rate Swap
Goodwill [Roll Forward]
Other Comprehensive Income (Loss), Net of Tax	(14,288)	(9,606)
Other Comprehensive Income (Loss), before Reclassifications, Net of Tax	(2,427)	(17,598)
Commercial Foodservice Equipment Group
Goodwill [Roll Forward]
Balance beginning of period	1,312,085	1,307,136
Goodwill, Acquired During Period	0	14,187
Measurement period adjustments to goodwill acquired in prior year	(985)	271
Exchange effect and other	13,768	9,509
Balance end of period	1,297,332	1,312,085	1,307,136
Food Processing Group
Goodwill [Roll Forward]
Balance beginning of period	432,161	397,137
Goodwill, Acquired During Period	13,312	46,745
Measurement period adjustments to goodwill acquired in prior year	3,116	57
Exchange effect and other	(53,728)	11,778
Balance end of period	$ 502,317	$ 432,161	$ 397,137