Cayman Corp. incurred $ $140,000$ of basic research and $ $35,000$ of development costs to develop a product for which a patent was granted on January $2,2015.$ Legal fees and other costs associated with registration of the patent totalled $ $50,000.$ On March $31,2020,$ Cayman paid $ $75,000$ for legal fees in a successful defence of the patent. The total amount capitalized for the patent through March $31,2020$ should be

a$.$ $ $265,000.$

b$.$ $ $160,000.$