12. Under the notation of problem 10, find $s$ and $j_{1}, \cdots, j_{s}$, such that
$1 \bmod 3=j_{1} \bmod 21 \cup \cdots \cup j_{s} \bmod 21$.
In general, let $a \mid b$, and $j$ be a given integer, find $s$ and $j_{1}, \cdots, j_{s}$, such that
$j \bmod a=j_{1} \bmod b \cup \cdots \cup j_{s} \bmod b$.
Explain the meaning of this problem.
12. $s=7, j_{i}=1+(i-1) 3,1 \leqslant i \leqslant 7$. Generally,
$$s=b / a, \quad j_{i}=j+(i-1) a, \quad 1 \leqslant i \leqslant b / a$$