Problem: 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

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int n, k;
int x[1010], y[1010];
int d[1000010], cnt;
int dis[1010][1010];
vector<int> G[1010];
int del[1010];
int ans[31];
bool dfs(int x, int s) {
  if (x > n) {
    int t = k - s;
    int p = 0;
    for (int i = 1; i <= n; i++) {
      if (del[i])
        ans[++p] = i;
      else if (t)
        ans[++p] = i, t--;
    }
    return true;
  }
  if (del[x]) {
    if (dfs(x + 1, s)) return true;
    return false;
  }
  int ns = s;
  for (int i = 0; i < (int)G[x].size(); i++) {
    if (!del[G[x][i]]) ns++;
    del[G[x][i]]++;
  }
  bool res = false;
  if (ns <= k) res = dfs(x + 1, ns);
  for (int i = 0; i < (int)G[x].size(); i++) del[G[x][i]]--;
  if (res) return true;
  if ((int)G[x].size() == 1) return false;
  if (s < k && s + 1 < ns) {
    del[x]++;
    res = dfs(x + 1, s + 1);
    del[x]--;
    if (res) return true;
  }
  return false;
}
int main() {
  scanf("%d%d", &n, &k);
  for (int i = 1; i <= n; i++) scanf("%d%d", x + i, y + i);
  for (int i = 1; i < n; i++) {
    for (int j = i + 1; j <= n; j++) {
      dis[i][j] = (x[i] - x[j]) * (x[i] - x[j]) + (y[i] - y[j]) * (y[i] - y[j]);
      d[++cnt] = dis[i][j];
    }
  }
  sort(d, d + cnt + 1);
  int l = 0, r = unique(d, d + cnt + 1) - d - 1;
  while (l <= r) {
    int mid = (l + r) >> 1;
    for (int i = 1; i <= n; i++) G[i].clear();
    for (int i = 1; i < n; i++) {
      for (int j = i + 1; j <= n; j++) {
        if (dis[i][j] > d[mid]) {
          G[i].push_back(j);
          G[j].push_back(i);
        }
      }
    }
    if (dfs(1, 0))
      r = mid - 1;
    else
      l = mid + 1;
  }
  for (int i = 1; i <= k; i++) printf("%d ", ans[i]);
  return 0;
}