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Repurchases of Common Shares (Details) $ / shares in Units, $ in Thousands	12 Months Ended
	Mar. 31, 2019 USD ($) shares	Mar. 31, 2018 USD ($) shares	Mar. 31, 2017 USD ($) shares	May 03, 2019 $ / shares	Mar. 31, 2019 £ / shares	Mar. 31, 2019 $ / shares	Mar. 31, 2019 EUR (€) shares	Mar. 31, 2018 £ / shares shares	Aug. 09, 2016 USD ($)
Debt Securities, Available-for-sale [Line Items]
Preferred Stock, Shares Authorized							50,000,000	100,000
Preferred Stock, Par or Stated Value Per Share | (per share)					£ 0.001	$ 0.001		£ 0.10
Stock Repurchase Program, Authorized Amount | $									$ 300,000
Stock Repurchased During Period, Shares	651,093	664,963
Ordinary Stock Repurchases Not Including Shares Withheld for Taxes | $	$ 72,082	$ 58,939
Share-based Compensation Arrangement by Share-based Payment Award, Options, Exercises in Period	112,356	127,903	168,906
Payments Related to Tax Withholding for Share-based Compensation | $	$ 8,262	$ 7,014	$ 7,034
Common Stock, Par or Stated Value Per Share | (per share)				$ 0.001		$ 75.00		£ 0.10
Value (EUROS) Ordinary Shares Deferred | €							€ 25,000
Deferred Ordinary Shares							25,000
Euro Member Countries, Euro
Debt Securities, Available-for-sale [Line Items]
Par Value (Euros) of Deferred Ordinary Shares | €							€ 1.00

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Deferred Ordinary Shares

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Ordinary Stock Repurchases Not Including Shares Withheld for Taxes

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Par Value (Euros) of Deferred Ordinary Shares

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Value (EUROS) Ordinary Shares Deferred

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Face amount or stated value per share of common stock.

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-SubTopic 10
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Amount of cash outflow to satisfy an employee's income tax withholding obligation as part of a net-share settlement of a share-based award.

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Face amount or stated value per share of preferred stock nonredeemable or redeemable solely at the option of the issuer.

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The maximum number of nonredeemable preferred shares (or preferred stock redeemable solely at the option of the issuer) permitted to be issued by an entity's charter and bylaws.

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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.

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For net-share settlement of share-based awards when the employer settles employees' income tax withholding obligations, this element represents the number of shares the employees use to repay the employer.

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Amount of stock repurchase plan authorized.

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Number of shares that have been repurchased during the period and have not been retired and are not held in treasury. Some state laws may govern the circumstances under which an entity may acquire its own stock and prescribe the accounting treatment therefore. This element is used when state law does not recognize treasury stock.

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