Problem: You are given n points with integer coordinates on the plane. Points are given in a way such that there is no triangle, formed by any three of these n points, which area exceeds S.

Alyona tried to construct a triangle with integer coordinates, which contains all n points and which area doesn't exceed 4S, but, by obvious reason, had no success in that. Please help Alyona construct such triangle. Please note that vertices of resulting triangle are not necessarily chosen from n given points.

Input

In the first line of the input two integers n and S (3 ≤ n ≤ 5000, 1 ≤ S ≤ 1018) are given — the number of points given and the upper bound value of any triangle's area, formed by any three of given n points.

The next n lines describes given points: ith of them consists of two integers xi and yi ( - 108 ≤ xi, yi ≤ 108) — coordinates of ith point.

It is guaranteed that there is at least one triple of points not lying on the same line.

Output

Print the coordinates of three points — vertices of a triangle which contains all n points and which area doesn't exceed 4S.

Coordinates of every triangle's vertex should be printed on a separate line, every coordinate pair should be separated by a single space. Coordinates should be an integers not exceeding 109 by absolute value.

It is guaranteed that there is at least one desired triangle. If there is more than one answer, print any of them.

Example

Input

4 1
0 0
1 0
0 1
1 1


Output

-1 0
2 0
0 2

Note

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Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const double eps = 1e-8;
const double PI = acos(-1.0);
int sgn(double x) {
  if (fabs(x) < eps) return 0;
  return x < 0 ? -1 : 1;
}
struct Point {
  double x, y;
  Point(double x = 0, double y = 0) : x(x), y(y) {}
  void scan() {
    double _x, _y;
    scanf("%lf%lf", &_x, &_y);
    x = _x, y = _y;
  }
  void print() { printf("%.11f %.11f\n", x, y); }
  bool operator==(const Point &b) const {
    return sgn(x - b.x) == 0 && sgn(y - b.y) == 0;
  }
  bool operator<(const Point &b) const {
    return sgn(x - b.x) == 0 ? sgn(y - b.y) < 0 : x < b.x;
  }
  Point operator+(const Point &b) const { return Point(x + b.x, y + b.y); }
  Point operator-(const Point &b) const { return Point(x - b.x, y - b.y); }
  Point operator*(const double &b) const { return Point(x * b, y * b); }
  Point operator/(const double &b) const { return Point(x / b, y / b); }
  double operator^(const Point &b) const { return x * b.y - y * b.x; }
  double operator*(const Point &b) const { return x * b.x + y * b.y; }
  double len() { return hypot(x, y); }
  double len2() { return x * x + y * y; }
  double dis(Point b) { return hypot(x - b.x, y - b.y); }
  int quad() {
    int _x = sgn(x), _y = sgn(y);
    if (_x > 0 && _y >= 0) return 1;
    if (_x <= 0 && _y > 0) return 2;
    if (_x < 0 && _y <= 0) return 3;
    if (_x >= 0 && _y < 0) return 4;
  }
  double rad(Point a, Point b) {
    Point p = *this;
    return fabs(atan2(fabs((a - p) ^ (b - p)), (a - p) * (b - p)));
  }
  Point trunc(double r) {
    double l = len();
    if (!sgn(l)) return *this;
    r /= l;
    return Point(x * r, y * r);
  }
  Point rotleft() { return Point(-y, x); }
  Point rotright() { return Point(y, -x); }
  Point rotate(Point p, double angle) {
    Point v = (*this) - p;
    double c = cos(angle), s = sin(angle);
    return Point(p.x + v.x * c - v.y * s, p.y + v.x * s + v.y * c);
  }
};
struct Line {
  Point s, e;
  Line() {}
  Line(Point s, Point e) : s(s), e(e) {}
  void scan() {
    s.scan();
    e.scan();
  }
  void print() {
    s.print();
    e.print();
  }
  bool operator==(const Line &b) const { return s == b.s && e == b.e; }
  Line(Point p, double angle) {
    s = p;
    if (sgn(angle - PI / 2) == 0) {
      e = (s + Point(0, 1));
    } else {
      e = (s + Point(1, tan(angle)));
    }
  }
  Line(double a, double b, double c) {
    if (sgn(a) == 0) {
      s = Point(0, -c / b);
      e = Point(1, -c / b);
    } else if (sgn(b) == 0) {
      s = Point(-c / a, 0);
      e = Point(-c / a, 1);
    } else {
      s = Point(0, -c / b);
      e = Point(1, (-c - a) / b);
    }
  }
  void adjust() {
    if (e < s) swap(s, e);
  }
  double length() { return s.dis(e); }
  double getAngle() {
    double k = atan2(e.y - s.y, e.x - s.x);
    if (sgn(k) < 0) k += PI;
    if (sgn(k - PI) == 0) k -= PI;
    return k;
  }
  int relationPoint(Point p) {
    int c = sgn((p - s) ^ (e - s));
    if (c < 0) return 1;
    if (c > 0) return 2;
    return 3;
  }
  bool pointOnSeg(Point p) {
    return sgn((p - s) ^ (e - s)) == 0 && sgn((p - s) * (p - e)) <= 0;
  }
  bool parallel(Line b) { return sgn((e - s) ^ (b.e - b.s)) == 0; }
  int segCrossSeg(Line b) {
    int d1 = sgn((e - s) ^ (b.s - s));
    int d2 = sgn((e - s) ^ (b.e - s));
    int d3 = sgn((b.e - b.s) ^ (s - b.s));
    int d4 = sgn((b.e - b.s) ^ (e - b.s));
    if ((d1 ^ d2) == -2 && (d3 ^ d4) == -2) return 2;
    return ((d1 == 0 && sgn((b.s - s) * (b.s - e)) <= 0) ||
            (d2 == 0 && sgn((b.e - s) * (b.e - e)) <= 0) ||
            (d3 == 0 && sgn((s - b.s) * (s - b.e)) <= 0) ||
            (d4 == 0 && sgn((e - b.s) * (e - b.e)) <= 0));
  }
  int lineCrossSeg(Line b) {
    int d1 = sgn((e - s) ^ (b.s - s));
    int d2 = sgn((e - s) ^ (b.e - s));
    if ((d1 ^ d2) == -2) return 2;
    return (d1 == 0 || d2 == 0);
  }
  int lineCrossLine(Line b) {
    if ((*this).parallel(b)) return b.relationPoint(s) == 3;
    return 2;
  }
  Point crossPoint(Line b) {
    double a1 = (b.e - b.s) ^ (s - b.s);
    double a2 = (b.e - b.s) ^ (e - b.s);
    return Point((s.x * a2 - e.x * a1) / (a2 - a1),
                 (s.y * a2 - e.y * a1) / (a2 - a1));
  }
  double disPointToLine(Point p) { return fabs((p - s) ^ (e - s)) / length(); }
  double disPointToSeg(Point p) {
    if (sgn((p - s) * (e - s)) < 0 || sgn((p - e) * (s - e)) < 0)
      return min(p.dis(s), p.dis(e));
    return disPointToLine(p);
  }
  double disSegToSeg(Line b) {
    return min(min(disPointToSeg(b.s), disPointToSeg(b.e)),
               min(b.disPointToSeg(s), b.disPointToSeg(e)));
  }
  Point lineProg(Point p) {
    return s + (((e - s) * ((e - s) * (p - s))) / ((e - s).len2()));
  }
  Point symmetryPoint(Point p) {
    Point q = lineProg(p);
    return Point(q.x * 2 - p.x, q.y * 2 - p.y);
  }
};
struct Polygon {
  vector<Point> p;
  Polygon() { p.clear(); }
  Polygon(int n) {
    p.clear();
    p.resize(n);
  }
  int sze() { return p.size(); }
  Point &operator[](int x) { return p[(x + sze()) % sze()]; }
  void add(Point q) { p.push_back(q); }
  void scan(int n = -1) {
    if (n == -1) scanf("%d", &n);
    p.resize(n);
    for (int i = 0; i < n; ++i) p[i].scan();
  }
  vector<Line> getline() {
    vector<Line> l(sze());
    for (int i = 0; i < sze(); ++i) {
      int j = (i + 1) % sze();
      l[i] = Line(p[i], p[j]);
    }
    return l;
  }
  struct cmpNorm {
    Point p;
    cmpNorm(Point p) : p(p) {}
    bool operator()(Point a, Point b) {
      int d = sgn((a - p) ^ (b - p));
      if (d == 0) {
        return sgn(a.dis(p) - b.dis(p) < 0);
      } else {
        return d > 0;
      }
    }
  };
  void norm() {
    Point mi = *p.begin();
    for (int i = 1; i < sze(); ++i) mi = min(mi, p[i]);
    sort(p.begin(), p.end(), cmpNorm(mi));
  }
  void norm(Point mi) { sort(p.begin(), p.end(), cmpNorm(mi)); }
  void convexHull(int opt = 1) {
    sort(p.begin(), p.end());
    Polygon res;
    res.p.resize(sze() * 2);
    int top = 0;
    for (int i = 0; i < sze(); ++i) {
      while (top > 1 && sgn((res.p[top - 1] - res.p[top - 2]) ^
                            (p[i] - res.p[top - 2])) < opt)
        --top;
      res[top++] = p[i];
    }
    int k = top;
    for (int i = sze() - 2; i >= 0; --i) {
      while (top > k && sgn((res.p[top - 1] - res.p[top - 2]) ^
                            (p[i] - res.p[top - 2])) < opt)
        --top;
      res[top++] = p[i];
    }
    if (sze() > 1) --top;
    res.p.resize(top);
    p = res.p;
  }
  double getCircumference() {
    double res = 0;
    for (int i = 0; i < sze(); ++i) {
      int j = (i + 1) % sze();
      res += p[i].dis(p[j]);
    }
    return res;
  }
  double getArea() {
    double res = 0;
    for (int i = 0; i < sze(); ++i) {
      int j = (i + 1) % sze();
      res += (p[i] ^ p[j]);
    }
    return res / 2;
  }
  bool getDir() { return sgn(getArea()) > 0; }
  Point getBarycenter() {
    Point res(0, 0);
    double area = 0;
    for (int i = 1; i < sze() - 1; ++i) {
      double tmp = (p[i] - p[0]) ^ (p[i + 1] - p[0]);
      if (sgn(tmp) == 0) continue;
      area += tmp;
      res.x += (p[0].x + p[i].x + p[i + 1].x) * tmp;
      res.y += (p[0].y + p[i].y + p[i + 1].y) * tmp;
    }
    if (sgn(area)) res = res / (area * 3);
    return res;
  }
  bool isConvex() {
    bool s[3] = {0, 0};
    for (int i = 0; i < sze(); ++i) {
      int j = (i + 1) % sze();
      int k = (j + 1) % sze();
      s[sgn((p[j] - p[i]) ^ (p[k] - p[i])) + 1] = true;
      if (s[0] && s[2]) return false;
    }
    return true;
  }
  int pointInConvex(Point q) {
    int l = 1, r = sze() - 2;
    while (r - l >= 0) {
      int mid = (l + r) >> 1;
      int a1 = sgn((p[mid] - p[0]) ^ (q - p[0]));
      int a2 = sgn((p[mid + 1] - p[0]) ^ (q - p[0]));
      if (a1 >= 0 && a2 <= 0) {
        int a3 = sgn((q - p[mid]) ^ (q - p[mid + 1]));
        if (a3 < 0)
          return -1;
        else if (a1 || a2 || a3)
          return 0;
        return 1;
      } else if (a1 < 0) {
        r = mid - 1;
      } else {
        l = mid + 1;
      }
    }
    return -1;
  }
  int relationPoint(Point q) {
    for (int i = 0; i < sze(); ++i) {
      if (p[i] == q) return 3;
    }
    vector<Line> l(getline());
    for (int i = 0; i < (int)l.size(); ++i) {
      if (l[i].pointOnSeg(q)) return 2;
    }
    int cnt = 0;
    for (int i = 0; i < sze(); ++i) {
      int j = (i + 1) % sze();
      int k = sgn((q - p[j]) ^ (p[i] - p[j]));
      int u = sgn(p[i].y - q.y);
      int v = sgn(p[j].y - q.y);
      if (k > 0 && u < 0 && v >= 0) cnt++;
      if (k < 0 && v < 0 && u >= 0) cnt--;
    }
    return cnt != 0;
  }
  Polygon convexCut(Line u) {
    Polygon res;
    for (int i = 0; i < sze(); ++i) {
      int j = (i + 1) % sze();
      int d1 = sgn((u.e - u.s) ^ (p[i] - u.s));
      int d2 = sgn((u.e - u.s) ^ (p[j] - u.s));
      if (d1 >= 0) res.add(p[i]);
      if (d1 * d2 < 0) res.add(u.crossPoint(Line(p[i], p[j])));
    }
    return res;
  }
  bool ConvexPolygonDisjoint(Polygon &b) {
    for (int i = 0; i < sze(); ++i)
      if (b.pointInConvex(p[i]) >= 0) return true;
    for (int i = 0; i < b.sze(); i++)
      if (pointInConvex(b[i]) >= 0) return true;
    for (int i = 0; i < sze(); i++)
      for (int j = 0; j < b.sze(); j++) {
        int _i = (i + 1) % sze();
        int _j = (j + 1) % sze();
        if (Line(p[i], p[_i]).segCrossSeg(Line(b[j], b[_j]))) return true;
      }
    return false;
  }
  Polygon convexInnerTriangle() {
    if (sze() < 3) return Polygon();
    Polygon res(3);
    double ans = 0;
    for (int i = 0, j, k; i < sze(); ++i) {
      j = (i + 1) % sze();
      k = (j + 1) % sze();
      while ((j != k) && (k != i)) {
        while (sgn(((p[j] - p[i]) ^ (p[(k + 1) % sze()] - p[i])) -
                   ((p[j] - p[i]) ^ (p[k] - p[i]))) > 0)
          k = (k + 1) % sze();
        double tmp = (p[j] - p[i]) ^ (p[k] - p[i]);
        if (tmp > ans) {
          res[0] = p[i];
          res[1] = p[j];
          res[2] = p[k];
          ans = tmp;
        }
        j = (j + 1) % sze();
      }
    }
    return res;
  }
};
int main() {
  int n;
  double S;
  while (scanf("%d%lf", &n, &S) != EOF) {
    Polygon po;
    po.scan(n);
    po.convexHull();
    Polygon tri = po.convexInnerTriangle();
    Polygon res;
    for (int i = 0; i < 3; ++i) {
      int j = (i + 1) % 3;
      int k = (j + 1) % 3;
      res.add(tri[i] + tri[j] - tri[k]);
    }
    for (int i = 0; i < 3; ++i) printf("%.0f %.0f\n", res[i].x, res[i].y);
  }
  return 0;
}