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## Greedy Students GRDSTD SOLUTION Code Chef

Rafid is teaching his students plane geometry. Today they are talking about convex polygons. A convex polygon is a simple non-degenerate polygon such that each of its internal angles is strictly smaller than 180∘.

Rafid drew N points (numbered 1 through N) on a blackboard (a two-dimensional plane) and told each student to choose some of the points and connect them to obtain a convex polygon. For each valid i, the coordinates of the i-th point are (Xi,Yi).

*Greedy Students Solution *

There are K students (numbered 1 through K). To prevent the students from choosing the same polygon over and over, Rafid told them that they have to choose polygons one by one in the order from student 1 to student K and each student has to choose a set of points which was not chosen by any earlier student. *Greedy Students solution . *That means they have to choose K different sets of points, resulting in K different polygons. As a result, some students may end up unable to choose any polygon.

To encourage the students, Rafid announced that each student will receive a number of candies proportional to the area of this student’s polygon. The students are very greedy, so the first student will choose the polygon with the largest area, the second student will choose the polygon with the largest area which does not use the same set of points as the first student’s polygon, and so on.

For each student, help Rafid find the area of the polygon chosen by this student or determine that this student cannot choose a polygon anymore. Note that while there may be many ways in which the students could choose their polygons, their areas are uniquely determined.

*Greedy Students GRDSTD Solution*Input

The first line of the input contains two space-separated integers N and K.

N lines follow. For each valid i, the i-th of these lines contains two space-separated integers Xi and Yi.

Output

Print a single line containing K space-separated integers A1,A2,…,AK. For each valid i, Ai should be twice the area of a polygon chosen by the i-th student, or −1 if all possible polygons have already been chosen by students before the i-th student.

Constraints

3≤N≤120

1≤K≤106

|Xi|,|Yi|≤106 for each valid i

the points (X1,Y1),(X2,Y2),…,(XN,YN) are pairwise distinct

Subtasks

Subtask #1 (5 points):

K=2

it is possible to form at least K convex polygons

Subtask #2 (15 points): K≤1,000

Subtask #3 (80 points): original constraints

Example Input

5 15

0 0

10 0

10 10

0 10

5 5

Example Output

200 100 100 100 100 50 50 50 50 -1 -1 -1 -1 -1 -1

Explanation

The following figure describes the points and some polygons.

*Greedy Students GRDSTD Solution*- The first student chooses the largest polygon ABCD with area 100.Greedy Students Solution
- The next four students choose the triangles ABC, BCD, CDA and DAB, each with area 50. Note that for example, the polygon AECB is not convex because it has one internal angle equal to 180∘.
- The next four students choose the triangles AEB, BEC, CED and DEA, each with area 25.Greedy Students Solution
- There are no more polygons the students can choose, so the remaining six students are left without a polygon.

### January Long Challenge 2021

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