Self-Replicating Numbers

Misha likes playing with numbers. A few days ago he found that $9376^2 = 87909376$, and the last four digits of the square are $9376$ again. Misha calls a number like this self-replicating.

Misha knows bases other than ten, so he also wants the self-replicating numbers of base 2 and base 16. Given a base $b$ and a length $n$, find every self-replicating number that has $n$ digits in base $b$.

A number $x$ is an $n$-digit self-replicating number in base $b$ when both of the following hold.

• Written in base $b$ without leading zeros, $x$ has exactly $n$ digits. The value $0$ counts as the one-digit string 0.
• The last $n$ digits of $x^2$ in base $b$ are the base $b$ representation of $x$, that is, $x^2 \equiv x \pmod{b^n}$.

The first line contains the base $b$ and the length $n$, separated by a single space. ($2 \le b \le 36$, $1 \le n \le 2000$)

On the first line print $K$, the number of $n$-digit self-replicating numbers in base $b$. On each of the next $K$ lines print one such number in base $b$, ordered from the smallest value to the largest.

When $b > 10$, use the uppercase letters A to Z for the digit values $10$ to $35$. If no number qualifies, print only $0$ on the first line.