Short track#738
Short track speed skating competitions are held on a small ice oval, similar to a hockey rink. The athletes' track is bordered on one side by the rink's boards, and on the other by markers. These markers are placed to form a convex polygon.
Placing these markers is not as simple as it might seem at first glance. The organizers have a set of candidate positions where markers can be placed. According to the rules, they must place exactly markers at some of these positions. The set of placed markers must form a convex polygon. The organizers also want to maximize the ice rink area used, arranging the markers to form a polygon of the largest possible area. Furthermore, there is a belief that if all the other candidate positions lie outside the polygon, the event will be successful. The organizers are eager to satisfy this condition. You need to help the organizers arrange the markers on the rink.
The first line contains the integers and (3 \leq N \leq 20, 3 \leq K \leq 10, K \leq N). Each of the next lines contains two integers, the coordinates of a candidate position. Coordinates do not exceed in absolute value. No three points are collinear.
The first line should contain the area of the selected -gon, rounded to exactly one decimal place (even if zero). The second line should contain the indices of the points forming the -gon in ascending order, separated by spaces. Points are numbered in the order given in the input, starting from .
If multiple valid solutions exist, output the one where the index of the first point is smallest. If these are the same, output the one where the second index is smallest, and so on.
If there is no solution, output -1.
Example 1