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>
const int MAXN = 1005;
const int MAXM = 2 * MAXN * MAXN;
int n, k, l;
int x[MAXN], y[MAXN], v[MAXN], dis[MAXN][MAXN];
int tot, d[MAXM], next[MAXM], last[MAXN];
void add(int x, int y) {
  d[++tot] = y;
  next[tot] = last[x];
  last[x] = tot;
}
bool dfs(int x, int k) {
  if (x > n) return 1;
  if (v[x]) return dfs(x + 1, k);
  for (int p = last[x]; p; p = next[p]) k -= !v[d[p]]++;
  if (k >= 0 && dfs(x + 1, k)) return 1;
  v[x] = 1;
  int tmp = k;
  for (int p = last[x]; p; p = next[p]) k += !--v[d[p]];
  if (--k >= 0 && k > tmp && dfs(x + 1, k)) return 1;
  v[x] = 0;
  return 0;
}
bool check(long long mid) {
  l = 0;
  memset(v, 0, sizeof(v));
  memset(last, 0, sizeof(last));
  for (int i = 1; i <= n; i++)
    for (int j = 1; j <= n; j++)
      if (dis[i][j] > mid) add(i, j);
  return dfs(1, k);
}
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 = 1; j <= n; ++j)
      dis[i][j] =
          ((x[i] - x[j]) * (x[i] - x[j])) + ((y[i] - y[j]) * (y[i] - y[j]));
  long long l = 0, r = 1ll << 31;
  while (l < r) {
    int mid = (l + r) / 2;
    if (check(mid))
      r = mid;
    else
      l = mid + 1;
  }
  check(r);
  for (int i = 1; i <= n && k; ++i)
    if (v[i]) printf("%d%s", i, --k ? " " : "\n");
  for (int i = 1; i <= n && k; ++i)
    if (!v[i]) printf("%d%s", i, --k ? " " : "\n");
  return 0;
}