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 kMaxN = 1005;
struct Edge {
  int to, nxt;
} e[kMaxN * kMaxN * 2];
int n, k, x[kMaxN], y[kMaxN], head[kMaxN], vis[kMaxN], dis[kMaxN][kMaxN], ecnt;
inline void AddEdge(int u, int v) {
  e[++ecnt] = (Edge){v, head[u]};
  head[u] = ecnt;
}
void InitEdge(int mid) {
  memset(head, 0x00, sizeof head);
  memset(vis, 0x00, sizeof vis);
  ecnt = 0;
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < n; ++j) {
      if (dis[i][j] > mid) AddEdge(i, j);
    }
  }
}
bool Dfs(int now, int k) {
  if (now >= n) return true;
  if (vis[now]) return Dfs(now + 1, k);
  for (int i = head[now]; i; i = e[i].nxt) {
    k -= !vis[e[i].to];
    ++vis[e[i].to];
  }
  if (k >= 0 && Dfs(now + 1, k)) return true;
  vis[now] = true;
  int x = k;
  for (int i = head[now]; i; i = e[i].nxt) {
    --vis[e[i].to];
    k += !vis[e[i].to];
  }
  --k;
  if (k > x && k >= 0 && Dfs(now + 1, k)) return true;
  vis[now] = false;
  return false;
}
int main() {
  scanf("%d%d", &n, &k);
  int l = 0, r = 0, ans = 0;
  for (int i = 0; i < n; ++i) {
    scanf("%d%d", x + i, y + i);
    for (int j = 0; j < i; ++j) {
      dis[i][j] = dis[j][i] =
          (x[i] - x[j]) * (x[i] - x[j]) + (y[i] - y[j]) * (y[i] - y[j]);
      r = max(r, dis[i][j]);
    }
  }
  while (l <= r) {
    int mid = (l + r) >> 1;
    InitEdge(mid);
    if (Dfs(0, k)) {
      ans = mid;
      r = mid - 1;
    } else
      l = mid + 1;
  }
  InitEdge(ans);
  Dfs(0, k);
  for (int i = 0; i < n; ++i) {
    if (vis[i]) printf("%d%c", i + 1, " \n"[!--k]);
  }
  for (int i = 0; i < n; ++i) {
    if (!vis[i] && k) printf("%d%c", i + 1, " \n"[!--k]);
  }
  return 0;
}