You are given n points on the plane. You need to delete exactly k of them (k \lt 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 \le n \le 1000, 1 \le k \le 30, k \lt 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 xi,yi (0 \le xi,yi \le 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.