Segment Information - Operating Segments (Details) - USD ($) $ in Thousands	12 Months Ended
	Jan. 01, 2023	Jan. 02, 2022	Jan. 03, 2021
Segment Reporting Information [Line Items]
Net sales	$ 1,297,919	$ 1,200,398	$ 1,103,262
Depreciation and amortization	40,337	46,345	45,920
Operating Segments | AMS
Segment Reporting Information [Line Items]
Net sales	753,740	651,216	593,418
AOI	102,370	85,014	89,097
Depreciation and amortization	16,827	17,963	17,164
Operating Segments | EAAA
Segment Reporting Information [Line Items]
Net sales	544,179	549,182	509,844
AOI	30,058	37,268	21,403
Depreciation and amortization	$ 23,510	$ 28,382	$ 28,756