For technical reasons, some programming languages (Kotlin, C #) will not be available during round 877. ×

D. Minimum Diameter
time limit per test
1.5 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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 xi, yi (0 ≤ xi, yi ≤ 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.

Examples
Input
5 2
1 2
0 0
2 2
1 1
3 3
Output
5 2
Input
4 1
0 0
0 0
1 1
1 1
Output
3