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.

Input

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.

Output

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.