Income Taxes (Details 5) - USD ($) $ / shares in Units, $ in Thousands	12 Months Ended
Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019
Income Tax Holiday [Line Items]
Income taxes paid globally, net of refunds	$ 58,324	$ 60,427	$ 59,003
Singapore and China
Income Tax Holiday [Line Items]
Tax benefits	$ 3,219	$ 1,065	$ 2,718
Tax benefits (in dollars per share)	$ 0.06	$ 0.02	$ 0.05

The amount of income taxes from which a reporting entity is exempt or for which it will receive a reduction in income taxes as a result of the income tax holiday granted by the taxing jurisdiction.

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section S99
-Paragraph 2
-Subparagraph (SAB Topic 11.C)
-URI http://asc.fasb.org/extlink&oid=122134291&loc=d3e330215-122817

+ Details

Name:	us-gaap_IncomeTaxHolidayAggregateDollarAmount
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Per share amount effect of the income tax benefit resulting from the income tax holidays granted by taxing jurisdictions.

+ References

+ Details

Name:	us-gaap_IncomeTaxHolidayIncomeTaxBenefitsPerShare
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	duration

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

No definition available.

+ Details

Name:	us-gaap_IncomeTaxHolidayLineItems
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

The amount of cash paid during the current period to foreign, federal, state, and local authorities as taxes on income, net of any cash received during the current period as refunds for the overpayment of taxes.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 50
-Paragraph 2
-URI http://asc.fasb.org/extlink&oid=123431023&loc=d3e4297-108586

+ Details

Name:	us-gaap_IncomeTaxesPaidNet
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Details

Name:	us-gaap_IncomeTaxAuthorityAxis=b_SingaporeandChinaMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: