A8384. Minimum Diameter

You are given $n$ points on the plane. You need to delete exactly $k$ of them $(k<n)$ so that the diameter of the set of the remaining $n-k$ points were as small as possible. The diameter of a set of points is the maximum pairwise distance between the points of the set. The diameter of a one point set equals zero.

The first input line contains a pair of integers $n,k$ ( $2<=n<=1000$ , $1<=k<=30$ , $k<n$ ) — the numbers of points on the plane and the number of points to delete, correspondingly.

Next $n$ lines describe the points, one per line. Each description consists of a pair of integers $x_{i},y_{i}$ ( $0<=x_{i},y_{i}<=32000$ ) — the coordinates of the $i$ -th point. The given points can coincide.

Print $k$ different space-separated integers from $1$ to $n$ — the numbers of points to delete. The points are numbered in the order, in which they are given in the input from $1$ to $n$ . You can print the numbers in any order. If there are multiple solutions, print any of them.