On April $15,$ Y$2,$ a married couple filed their joint Y$1$ tax return showing gross income of $$120,000.$ Their return was prepared by a professional tax preparer who mistakenly omitted $$45,000$ of income, which the preparer in good faith considered to be nontaxable. No information with regard to this omitted income was disclosed on the return or attached statements. By what date must the IRS assert a notice of deficiency before the statute of limitations expires?

April $15,$ Y$8$

December $31,$ Y$2$

April $15,$ Y$5$

December $31,$ Y$7$