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;
const int N = 1010;
int n, m, len = 0;
int x[N], y[N];
int b[N * N], a[N][N];
int u[N], ot[N][N], hd[N];
bool dfs(const int x, int y) {
  if (x > n) return 1;
  if (u[x] > 0) return dfs(x + 1, y);
  for (int i = 1; i <= hd[x]; ++i) {
    if (u[ot[x][i]] == 0) --y;
    ++u[ot[x][i]];
  }
  if (y >= 0 && dfs(x + 1, y)) return 1;
  int p = y;
  for (int i = 1; i <= hd[x]; ++i) {
    --u[ot[x][i]];
    if (u[ot[x][i]] == 0) ++y;
  }
  ++u[x], --y;
  if (y >= 0 && y > p && dfs(x + 1, y)) return 1;
  --u[x], ++y;
  return 0;
}
bool ok(const int X) {
  memset(hd, 0, sizeof(hd));
  for (int i = 1; i <= n; ++i)
    for (int j = 1; j <= n; ++j)
      if (a[i][j] > X) ot[i][++hd[i]] = j;
  memset(u, 0, sizeof(u));
  return dfs(1, m);
}
int main() {
  scanf("%d%d", &n, &m);
  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)
      a[i][j] = (x[i] - x[j]) * (x[i] - x[j]) + (y[i] - y[j]) * (y[i] - y[j]),
      b[++len] = a[i][j];
  sort(b + 1, b + 1 + len);
  int R = 1, L = 0, mid;
  for (int i = 2; i <= len; ++i)
    if (b[i] != b[R]) b[++R] = b[i];
  while (L + 1 < R) {
    mid = (L + R) >> 1;
    if (ok(b[mid]))
      R = mid;
    else
      L = mid;
  }
  ok(b[R]);
  for (int i = 1; i <= n; ++i)
    if (u[i] > 0) printf("%d ", i), --m;
  for (int i = 1; i <= n; ++i)
    if (m > 0 && u[i] == 0) printf("%d ", i), --m;
  return 0;
}