Reportable Segments - Revenue by Contract Type (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2022	Jan. 01, 2022	Jan. 02, 2021
Segment Reporting, Revenue Reconciling Item [Line Items]
Gross revenues	$ 786,778	$ 706,706	$ 659,296
INF
Segment Reporting, Revenue Reconciling Item [Line Items]
Gross revenues	395,878	383,725	352,965
BTS
Segment Reporting, Revenue Reconciling Item [Line Items]
Gross revenues	232,577	185,995	157,432
GEO
Segment Reporting, Revenue Reconciling Item [Line Items]
Gross revenues	158,323	136,986	148,899
Cost-reimbursable contracts
Segment Reporting, Revenue Reconciling Item [Line Items]
Gross revenues	693,442	637,265	609,346
Cost-reimbursable contracts | INF
Segment Reporting, Revenue Reconciling Item [Line Items]
Gross revenues	379,818	367,310	337,580
Cost-reimbursable contracts | BTS
Segment Reporting, Revenue Reconciling Item [Line Items]
Gross revenues	155,632	133,272	123,135
Cost-reimbursable contracts | GEO
Segment Reporting, Revenue Reconciling Item [Line Items]
Gross revenues	157,992	136,683	148,631
Fixed-unit price contracts
Segment Reporting, Revenue Reconciling Item [Line Items]
Gross revenues	93,336	69,441	49,950
Fixed-unit price contracts | INF
Segment Reporting, Revenue Reconciling Item [Line Items]
Gross revenues	16,060	16,415	15,385
Fixed-unit price contracts | BTS
Segment Reporting, Revenue Reconciling Item [Line Items]
Gross revenues	76,945	52,723	34,297
Fixed-unit price contracts | GEO
Segment Reporting, Revenue Reconciling Item [Line Items]
Gross revenues	$ 331	$ 303	$ 268