Revenge of the ants 2

A circular rail has circumference $L$. Gyeonggeun split the rail into $L$ equal parts and numbered the points from $0$ to $L-1$ in the clockwise direction. He picked some of those points and placed $N$ ants that walk clockwise and $M$ ants that walk counterclockwise. No point holds two or more ants.

Every ant on the rail moves a distance of 1 per second. The rail is narrow enough that only one ant fits across it, so when two ants moving in opposite directions meet at a point, both reverse direction at that instant. An ant is a point with no size, so two ants collide only when their positions become exactly equal.

Gyeonggeun tells all the ants apart. Write a program that finds the minimum number of seconds until every ant is back at its starting point and moving in its starting direction.

The first line has the circumference $L$ of the rail, the number $N$ of ants that walk clockwise, and the number $M$ of ants that walk counterclockwise, separated by spaces. ($1 \le L \le 10^{12}$, $1 \le N$, $1 \le M$, $N + M \le 10^6$)

The second line has the $N$ points that hold the clockwise ants, separated by spaces.

The third line has the $M$ points that hold the counterclockwise ants, separated by spaces.

Every point is an integer between $0$ and $L-1$, and the $N + M$ given points are distinct. The points are not necessarily sorted.

Print the minimum time in seconds until every ant is back at its starting point and moving in its starting direction.

In the first example the two ants collide at 0.5 seconds and at 1.5 seconds, and at 2 seconds the state matches the start.