On its $2019$ balance sheet, Barngrover Books showed $$510$ million of retained earnings, and exactly that same amount was shown the following year in $2020.$ Assuming that no earnings restatements were issued, which of the following statements is CORRECT?

a$.$ Dividends could have been paid in $2020,$ but they would have had to equal the earnings for the year.

b$.$ The company must have paid out half of its earnings as dividends.

c$.$ The company must have had zero net income in $2020.$

d$.$ If the company lost money in $2020,$ they must have paid dividends.

e$.$ The company must have paid no dividends in $2020.$