How to make last row of each table's part unfinished in latex longtable?

Question

I have a table that automatically stretched over several pages by longtable package.

\begin{longtable}{| l | l |}
 \hline
 A & B \\ \hline
 \endfirsthead
 \multicolumn{3}{l}{Table \thetable{} -- finishing} \\ \hline
 \endhead
 a1 & b1 \\ \hline
 a1 & b2 \\ \hline
 ........
\end{longtable}

Suppose that table was broken (automatically) between first and second rows. Than we have this output:

-------
|A | B|
-------
|a1|b1|
-------
<page break>
Table 1 -- finishing.
-------
|a2|b2|
-------

I want the following effect:

-------
|A | B|
-------
|a1|b1|

<page break>
Table 1 -- finishing.
-------
|a2|b2|
-------

I.e. last row of the table's first part should be unfinished (without \hline).

In general case i have a table with multiple rows with \hline after each row. What i want is to "erase" last \hline of table's first part. Or that \hline of all table's parts except the last one.

Answer 1

I'm not sure I get it... Isn't the ----- in

|a1|b1|
-------
<page break>

is due to the \hline at

 a1 & b1 \\ \hline

??

So the problem is that the \hline appears both at the end of the first part of the table and at the start of the second part?