Colliding Balls

There are $n$ red balls kept on the positive $X$ axis, and $m$ blue balls kept on the positive $Y$ axis. You are given the positions of the balls. For each $i$ from $1$ to $n$, the $i$-th red ball has the coordinates $(x_i, 0)$, where $x_i$ is a positive integer. For each $i$ from $1$ to $m$, the $i$-th blue ball has the coordinates $(0, y_i)$, where $ y_i$ is a positive integer. It is given tha