$1.$ Lenore, Inc. declared a cash dividend of $$130,000$ in $2023$ when the following stocks were outstanding:

Common stock $30,000$ shares, $$5$ par value $$150,000$

Preferred stock, $6\%,5,000$ shares, $$100$ par value $$500,000$

No dividends were declared or paid during the prior two years.

a$.$ Compute the amount of dividends that would be paid to each stockholder group if the preferred stock is noncumulative.

b$.$ Compute the amount of dividends that would be paid to each stockholder group if the preferred stock is cumulative