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Employee Benefit Plans (Tables) - Defined Benefit Pension Plans | 12 Months Ended
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Dec. 31, 2021
Expected Benefit Payments | ​
​ | ​ | ​ | ​
Years ending December 31, |  | Amount
​ | ​ | (In thousands)
2022 | ​ | $ | 3,689
2023 | ​ |  | 3,647
2024 | ​ |  | 3,570
2025 | ​ |  | 3,493
2026 | ​ |  | 3,435
Next 5 years | ​ |  | 15,885
Funded Status of Defined Benefit Plans | ​
​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | December 31,
​ |  | 2020 |  | 2021
​ | ​ | (In thousands)
Change in projected benefit obligations (PBO): | ​ | ​ | ​ | ​ | ​ | ​
Benefit obligations at beginning of the year | ​ | $ | 50,350 | ​ | $ | 52,873
Interest cost | ​ |  | 1,483 | ​ |  | 947
Actuarial losses | ​ |  | 4,353 | ​ |  | 295
Change in currency exchange rates | ​ |  | 307 | ​ |  | (73)
Benefits paid | ​ |  | (3,620) | ​ |  | (3,675)
Benefit obligations at end of the year | ​ |  | 52,873 | ​ |  | 50,367
​ | ​ | ​ | ​ | ​ | ​ | ​
Change in plan assets: | ​ |  |  | ​ |  |
Fair value of plan assets at beginning of the year | ​ |  | 46,313 | ​ |  | 50,260
Actual return on plan assets | ​ |  | 5,308 | ​ |  | 226
Employer contributions | ​ |  | 1,841 | ​ |  | 1,169
Change in currency exchange rates | ​ |  | 418 | ​ |  | (40)
Benefits paid | ​ |  | (3,620) | ​ |  | (3,675)
Fair value of plan assets at end of year | ​ |  | 50,260 | ​ |  | 47,940
Funded status | ​ | $ | (2,613) | ​ | $ | (2,427)
​ | ​ | ​ | ​ | ​ | ​ | ​
Amounts recognized in the balance sheet: | ​ |  |  | ​ |  |
Noncurrent pension asset | ​ | $ | 3,881 | ​ | $ | 1,356
Accrued pension costs: | ​ |  |  | ​ |  | ​
Current | ​ |  | (102) | ​ |  | (61)
Noncurrent | ​ |  | (6,392) | ​ |  | (3,722)
Total | ​ |  | (2,613) | ​ |  | (2,427)
​ | ​ | ​ | ​ | ​ | ​ | ​
Accumulated other comprehensive loss - actuarial losses, net | ​ |  | 28,209 | ​ |  | 28,265
Total | ​ | $ | 25,596 | ​ | $ | 25,838
​ | ​ | ​ | ​ | ​ | ​ | ​
Accumulated benefit obligations (ABO) | ​ | $ | 52,873 | ​ | $ | 50,367
Changes in Other Comprehensive Income (Loss) | ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ |  | Years ended December 31,
​ |  | 2019 |  | 2020 |  | 2021
​ | ​ | (In thousands)
Changes in plan assets and benefit obligations recognized in other comprehensive income: | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Net actuarial gain (loss) arising during the year | ​ | $ | 1,330 | ​ | $ | (934) | ​ | $ | 1,618
Amortization of unrecognized net actuarial gain (loss) | ​ |  | 1,584 | ​ |  | 1,412 | ​ |  | (1,562)
Total | ​ | $ | 2,914 | ​ | $ | 478 | ​ | $ | 56
Components of Net Periodic Defined Benefit Cost (Income) | ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | Years ended December 31,
​ |  | 2019 |  | 2020 |  | 2021
​ | ​ | (In thousands)
Net periodic pension cost: |  | ​ |  |  | ​ |  |  | ​ |
Interest cost on PBO | ​ | $ | 1,884 | ​ | $ | 1,483 | ​ | $ | 947
Expected return on plan assets | ​ |  | (1,899) | ​ |  | (1,850) | ​ |  | (1,603)
Recognized actuarial losses | ​ |  | 1,584 | ​ |  | 1,412 | ​ |  | 1,562
Total | ​ | $ | 1,569 | ​ | $ | 1,045 | ​ | $ | 906
Information Concerning Defined Benefit Pension Plans (Including Certain Plans for Which ABO Exceeds Fair Value of Plan Assets) | ​
​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | December 31,
​ |  | 2020 |  | 2021
​ | ​ | (In thousands)
PBO at end of the year: | ​ | ​ | ​ | ​ | ​ | ​
U.S. plan | ​ | $ | 43,754 | ​ | $ | 40,254
U.K. plan | ​ |  | 9,119 | ​ |  | 10,113
Total | ​ | $ | 52,873 | ​ | $ | 50,367
Fair value of plan assets at end of the year: | ​ | ​ | ​ | ​ | ​ | ​
U.S. plan | ​ | $ | 37,260 | ​ | $ | 36,471
U.K. plan | ​ |  | 13,000 | ​ |  | 11,469
Total | ​ | $ | 50,260 | ​ | $ | 47,940
​ | ​ | ​ | ​ | ​ | ​ | ​
Plans for which the ABO exceeds plan assets (only our U.S. plan): | ​ | ​ | ​ | ​ | ​ | ​
PBO | ​ | $ | 43,754 | ​ | $ | 40,254
ABO | ​ |  | 43,754 | ​ |  | 40,254
Fair value of plan assets | ​ |  | 37,260 | ​ |  | 36,471
Summary of Assumptions Used to Determine Net Benefit Obligation | ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | Years ended December 31,
Rate |  | 2019 |  | 2020 |  | 2021 |
Discount rate |  | 3.9 | % | 2.9 | % | 2.1 | %
Long-term rate of return on plan assets |  | 4.7 | % | 4.2 | % | 3.3 | %
Schedule of composition of our pension plan assets by fair value level | ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | Fair Value Measurements
​ | ​ | ​ | ​ | ​ | Quoted prices | ​ | Significant other | ​ | Significant | ​ | ​ | ​
​ | ​ | ​ | ​ | ​ | in active | ​ | observable | ​ | unobservable | ​ | Assets measured
​ |  | Total |  | markets (Level 1) |  | inputs (Level 2) |  | inputs (Level 3) |  | at NAV
​ | ​ | (In thousands)
December 31, 2020: |  | ​ |  |  | ​ |  |  | ​ |  |  | ​ |  |  | ​ |
U.S. |  | ​ |  |  | ​ |  |  | ​ |  |  | ​ |  |  | ​ |
Equities | ​ | $ | 14,636 | ​ | $ | 2,158 | ​ | $ | — | ​ | $ | 538 | ​ | $ | 11,940
Fixed income | ​ |  | 18,747 | ​ |  | 18,747 | ​ |  | — | ​ |  | — | ​ |  | —
Cash and other | ​ |  | 3,877 | ​ |  | 3,052 | ​ |  | — | ​ |  | — | ​ |  | 825
U.K. - Other | ​ |  | 13,000 | ​ |  | 13,000 | ​ |  | — | ​ |  | — | ​ |  | —
Total | ​ | $ | 50,260 | ​ | $ | 36,957 | ​ | $ | — | ​ | $ | 538 | ​ | $ | 12,765
​ ​ ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | Fair Value Measurements
​ | ​ | ​ | ​ | ​ | Quoted prices | ​ | Significant other | ​ | Significant | ​ | ​ | ​
​ | ​ | ​ | ​ | ​ | in active | ​ | observable | ​ | unobservable | ​ | Assets measured
​ |  | Total |  | markets (Level 1) |  | inputs (Level 2) |  | inputs (Level 3) |  | at NAV
​ | ​ | (In thousands)
December 31, 2021: | ​ | ​ |  | ​ | ​ |  | ​ | ​ |  | ​ | ​ |  | ​ | ​ |
U.S. | ​ | ​ |  | ​ | ​ |  | ​ | ​ |  | ​ | ​ |  | ​ | ​ |
Equities | ​ | $ | 12,951 | ​ | $ | 831 | ​ | $ | — | ​ | $ | 108 | ​ | $ | 12,012
Fixed income | ​ | ​ | 21,299 | ​ | ​ | — | ​ | ​ | — | ​ | ​ | — | ​ | ​ | 21,299
Cash and other | ​ | ​ | 2,221 | ​ | ​ | 1,352 | ​ | ​ | — | ​ | ​ | — | ​ | ​ | 869
U.K. - Other | ​ | ​ | 11,469 | ​ | ​ | 1,324 | ​ | ​ | — | ​ | ​ | 10,145 | ​ | ​ | —
Total | ​ | $ | 47,940 | ​ | $ | 3,507 | ​ | $ | — | ​ | $ | 10,253 | ​ | $ | 34,180

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- Definition Tabular disclosure of the major categories of plan assets of pension plans and/or other employee benefit plans. This information may include, but is not limited to, the target allocation of plan assets, the fair value of each major category of plan assets, and the level within the fair value hierarchy in which the fair value measurements fall. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 715 -SubTopic 20 -Section 50 -Paragraph 1 -Subparagraph (d)(5) -URI http://asc.fasb.org/extlink&oid=123447040&loc=d3e1928-114920 + Details
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- Definition Tabular disclosure of the changes in plan assets and benefit obligations recognized in other comprehensive income (loss) during the period. + References No definition available. + Details
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- Definition Tabular disclosure of benefits expected to be paid by pension plans and/or other employee benefit plans in each of the next five fiscal years and in the aggregate for the five fiscal years thereafter. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 715 -SubTopic 20 -Section 50 -Paragraph 1 -Subparagraph (f) -URI http://asc.fasb.org/extlink&oid=123447040&loc=d3e1928-114920 + Details
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