Short track
Short track speed skating competitions take place 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 arranged to form a convex polygon.
Placing these markers is more complex than it might initially appear. The organizers have N potential positions for placing markers. According to the rules, they need to place exactly K markers at some of these positions. Importantly, the selected markers must form a convex polygon. Additionally, the organizers aim to maximize the rink's area usage by arranging the markers to create the largest possible polygon. There is also a belief that if all other candidate positions lie outside this polygon, the event will be successful. The organizers are keen to ensure everything goes smoothly, so meeting this condition is crucial. Your task is to assist the organizers in placing the markers on the rink.
Input
The first line contains the integers N and K (3 ≤ N ≤ 20, 3 ≤ K ≤ 10, K ≤ N). The next N lines each contain two integers, representing the coordinates of the candidate positions. These coordinates do not exceed 10000 in absolute value. No three points are collinear.
Output
The first line should display the area of the identified K-gon, rounded to exactly one decimal place (even if it is zero). The second line should list the indices of the points that form the K-gon, sorted in ascending order. Points are numbered based on their order in the input, starting from one. If multiple correct solutions exist, choose the one where the first point's index is smallest. If the first points are the same, choose the one where the second point's index is smallest, and so on.
If no solution is possible, output -1.