Adding Squares

There are $N$ different vertical lines on the plane, $i$-th of which is defined by the equation $x=a_i$ ($0 \le a_i \le W$) and $M$ different horizontal lines, $i$-th of which is defined by the equation $y=b_i$ ($0 \le b_i \le H$). You must add one line of the form $y=k$ ($0 \le k \le H$, $k \neq b_i$ for every $1 \le i \le M$) to the plane. What is the maximum possible number of squares with diff