A14511. Polygon

You are given a strictly convex polygon with $n$ vertices.

You will make $k$ cuts that meet the following conditions:

- each cut is a segment that connects two different nonadjacent vertices;
- two cuts can intersect only at vertices of the polygon.

Your task is to maximize the area of the smallest region that will be formed by the polygon and those $k$ cuts.

The first line contains two integers $n$ , $k$ ( $3 \le n \le 200$ , $0 \le k \le n-3$ ).

The following $n$ lines describe vertices of the polygon in anticlockwise direction. The $i$ -th line contains two integers $x_i$ , $y_i$ ( $|x_i|, |y_i| \le 10^8$ ) — the coordinates of the $i$ -th vertex.

It is guaranteed that the polygon is convex and that no two adjacent sides are parallel.

Print one integer: the maximum possible area of the smallest region after making $k$ cuts multiplied by $2$ .

In the first example, it's optimal to make cuts between the following pairs of vertices:

- $(-2, -4)$ and $(4, 2)$ ,
- $(-2, -4)$ and $(1, 5)$ ,
- $(-5, -1)$ and $(1, 5)$ ,
- $(-5, 0)$ and $(0, 5)$ .

 Points $(-5, -1)$ , $(1, 5)$ , $(0, 5)$ , $(-5, 0)$ determine the smallest region with double area of $11$ . In the second example, it's optimal to make cuts between the following pairs of vertices:

- $(2, -1)$ and $(0, 2)$ ,
- $(2, -1)$ and $(1, 0)$ ,
- $(-1, 0)$ and $(0, 2)$ .

 Points $(2, -2)$ , $(2, -1)$ , $(-1, 0)$ determine one of the smallest regions with double area of $3$ .