Copy and Paste

Chef has binary string $A$ of length $N$. He constructs a new binary string $B$ by concatenating $M$ copies of $A$ together. For example, if $A = \texttt{"10010"}$, $M = 3$, then $B = \texttt{"100101001010010"}$. Chef calls an index $i$ $(1 \le i \le N \cdot M)$ *good* if: - $pref_i = suf_{i + 1}$. Here, $pref_j = B_1 + B_2 + \ldots + B_j$ and $suf_j = B_{j} + B_{j + 1} + \ldots + B_{N \cdot M}$