Digit Extrema!

Let $A_N$ denote the set of digit sums of $N$ -digit numbers. Let $B_N$ be the set of the digit sums of elements of $A_N$ . Let $b_N$ be the largest element of $B_N$ . Let $a_N$ be the largest element of $A_N$ which gives $b_N$ as a digit sum. Find $a_{10}$

For example, $A_1={1, 2, 3, 4, 5,\ldots, 9}$ , and $B_1={1,2,3,4,5,\ldots,9}$ . Thus, $b_1=9$ , an d $a_1=9$