Segment Information - Operating Segments (Details) - USD ($) $ in Thousands	12 Months Ended
	Jan. 02, 2022	Jan. 03, 2021	Dec. 29, 2019
Segment Reporting Information [Line Items]
Net sales	$ 1,200,398	$ 1,103,262	$ 1,343,029
Depreciation and amortization	46,345	45,920	44,932
Operating Segments | AMS
Segment Reporting Information [Line Items]
Net sales	651,216	593,418	757,112
AOI	85,014	89,097	120,921
Depreciation and amortization	17,963	17,164	15,884
Operating Segments | EAAA
Segment Reporting Information [Line Items]
Net sales	549,182	509,844	585,917
AOI	37,268	21,403	28,832
Depreciation and amortization	$ 28,382	$ 28,756	$ 29,048