Self Digit Sum

First, let $\oplus_D$ denote a binary operation of two nonnegative integers $a$ and $b$ , such that $a \oplus_D b$ is the sum of the digits of both $a$ and $b$ .

Then, let $z \oplus_D^{n} = (\cdots (((z \oplus_D z) \oplus_D z) \oplus_D \cdots )\oplus_D z$ , where $\oplus_D$ occurs $(n - 1)$ times and $n$ is a positive integer.

How many nonnegative integers $z$ satisfy $z \oplus_D^m = z$ , where $m \geq 2$ is a finite minimum?

Note: $\oplus_D$ may not be associative. If you think there are infinitely many integers, input -1 as your answer.