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Segment Information (Net Sales by Geographic Region) (Details) - USD ($)
$ in Thousands
12 Months Ended
Mar. 31, 2019
Mar. 31, 2018
Mar. 31, 2017
Net sales to unaffiliated customers and long-lived assets by geographic region      
Net sales $ 2,788,322 $ 2,566,863 $ 2,221,427
Americas      
Net sales to unaffiliated customers and long-lived assets by geographic region      
Net sales 1,190,216 1,118,324 963,674
EMEA      
Net sales to unaffiliated customers and long-lived assets by geographic region      
Net sales 861,731 820,347 746,898
Asia Pacific      
Net sales to unaffiliated customers and long-lived assets by geographic region      
Net sales $ 736,375 $ 628,192 $ 510,855
Geographic Concentration | Consolidated net sales | United States      
Net sales to unaffiliated customers and long-lived assets by geographic region      
Concentration credit risk by major customer (as a percent) 36.00% 37.00% 37.00%
Geographic Concentration | Consolidated net sales | Germany      
Net sales to unaffiliated customers and long-lived assets by geographic region      
Concentration credit risk by major customer (as a percent) 18.00% 16.00% 17.00%
Geographic Concentration | Consolidated net sales | China      
Net sales to unaffiliated customers and long-lived assets by geographic region      
Concentration credit risk by major customer (as a percent) 10.00%    
Geographic Concentration | Consolidated net sales | Switzerland      
Net sales to unaffiliated customers and long-lived assets by geographic region      
Concentration credit risk by major customer (as a percent) 3.00% 2.00% 2.00%