Sticks and Carrots

Rabbits have overrun Georgia and they eat every carrot they find. Hershel Greene grows expensive carrots, so he ringed his farm with security gates. A gate is a pillar, and anything that crosses the line between two neighbouring pillars gets a stick thrown at it and falls unconscious. The farmers protect the animals and never kill them.

The positions of the $G$ pillars are given in clockwise order. The convex polygon they enclose is the farm as it stands now.

Insects ruined part of the crop, so Hershel wants to sell a few pillars and shrink the farm. The upkeep is proportional to the area. He may sell any pillars he likes, and the pillars that remain keep their original clockwise order and form the boundary of the new farm. He is not giving up the farm, so at least 3 pillars must remain.

The gates shut down every day at noon and Hershel leaves the farm at 12:30. During that half hour he walks from carrot to carrot in straight lines only, and he never steps outside the farm. Every remaining carrot has to lie inside the new farm, and never on its boundary. The boundary is the line between two neighbouring pillars, and for the rest of the day the gates run again and nobody can come near that line, so a carrot sitting on it cannot be harvested.

Over all ways of choosing the pillars to keep, find the smallest area the farm can have.

The first line contains the number of test cases $T$ ($1 \le T \le 5$).

The first line of each test case contains the number of pillars $G$ and the number of carrots $C$, separated by a space ($3 \le G \le 300$, $1 \le C \le 50$).

The next $G$ lines contain the coordinates $x$ and $y$ of one pillar, listed clockwise. The $x$ axis points right and the $y$ axis points up. The pillar positions are distinct, and joining them in the given order traces the boundary of a convex polygon. Three consecutive pillars may be collinear.

The next $C$ lines contain the coordinates $x$ and $y$ of one carrot. The carrot positions are distinct and every one of them lies strictly inside the polygon enclosed by all $G$ pillars. No carrot sits on the boundary.

All coordinates are integers whose absolute value is at most 10000.

For each test case, print the smallest possible area of the farm on its own line, with exactly two digits after the decimal point. Every coordinate is an integer, so the area is always a multiple of 0.5 and the last two digits are 00 or 50.