Problem: There is a strange peculiarity: if you connect the cities of Rostov, Taganrog and Shakhty, peculiarly, you get a triangle

«Unbelievable But True»

Students from many different parts of Russia and abroad come to Summer Informatics School. You marked the hometowns of the SIS participants on a map.

Now you decided to prepare an interesting infographic based on this map. The first thing you chose to do is to find three cities on this map, such that they form a triangle with area S.

Input

The first line of input contains two integers n and S (3 ≤ n ≤ 2000, 1 ≤ S ≤ 2 ⋅ 10^{18}) — the number of cities on the map and the area of the triangle to be found.

The next n lines contain descriptions of the cities, one per line. Each city is described by its integer coordinates x_i, y_i (-10^9 ≤ x_i, y_i ≤ 10^9). 

It is guaranteed that all cities are located at distinct points. It is also guaranteed that no three cities lie on the same line.

Output

If the solution doesn't exist — print «No».

Otherwise, print «Yes», followed by three pairs of coordinates (x, y) — the locations of the three cities, which form the triangle of area S.

Examples

Input

3 7
0 0
3 0
0 4


Output

No


Input

4 3
0 0
2 0
1 2
1 3


Output

Yes
0 0
1 3
2 0

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
typedef long long Di;
typedef double D;
int DEFAULT_PREC = 6;
const D EPS = 1e-9, PI = acos((D)-1.0);
const Di INF = 1010101010101010101ll;
inline int cmp(double a) { return a > EPS ? 1 : a >= -EPS ? 0 : -1; }
inline int cmp(long double a) { return a > EPS ? 1 : a >= -EPS ? 0 : -1; }
inline int cmp(int a) { return a > 0 ? 1 : !a ? 0 : -1; }
inline int cmp(long long a) { return a > 0 ? 1 : !a ? 0 : -1; }
template <class T>
inline int cmp(T a, T b) {
  return cmp(a - b);
}
template <class T>
T sqr(T x) {
  return x * x;
}
inline void inputnum(double &p) { scanf("%lf", &p); }
inline void inputnum(long double &p) {
  double tmp;
  scanf("%lf", &tmp);
  p = tmp;
}
inline void inputnum(int &p) { scanf("%d", &p); }
inline void inputnum(long long &p) { scanf("%lld", &p); }
inline void outputnum(const double &p, int prec = DEFAULT_PREC) {
  printf("%.*f", prec, p);
}
inline void outputnum(const long double &p, int prec = DEFAULT_PREC) {
  printf("%.*f", prec, (double)p);
}
inline void outputnum(const int &p, int prec = DEFAULT_PREC) {
  printf("%d", p);
  if (prec)
    for (printf("."); prec--; printf("0"))
      ;
}
inline void outputnum(const long long &p, int prec = DEFAULT_PREC) {
  printf("%lld", p);
  if (prec)
    for (printf("."); prec--; printf("0"))
      ;
}
D safeacos(D x) {
  if (x <= -1) return PI;
  if (x >= 1) return 0;
  return acos(x);
}
class Point {
 public:
  Di x, y;
  Point() {}
  Point(Di x, Di y) : x(x), y(y) {}
  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*(Di b) const { return Point(x * b, y * b); }
  Point operator/(Di b) const { return Point(x / b, y / b); }
  Point &operator+=(const Point &b) { return *this = *this + b; }
  Point &operator-=(const Point &b) { return *this = *this - b; }
  Point &operator*=(Di b) { return *this = *this * b; }
  Point &operator/=(Di b) { return *this = *this / b; }
  bool operator<(const Point &b) const {
    return cmp(x, b.x) == 0 ? cmp(y, b.y) < 0 : cmp(x, b.x) < 0;
  }
  bool operator>(const Point &b) const { return b < *this; }
  bool operator==(const Point &b) const {
    return cmp(x, b.x) == 0 && cmp(y, b.y) == 0;
  }
  bool operator<=(const Point &b) const { return !(*this > b); }
  bool operator>=(const Point &b) const { return !(*this < b); }
  bool operator!=(const Point &b) const { return !(*this == b); }
  Di len2() const { return x * x + y * y; }
  D len() const { return sqrt(len2()); }
  void read() {
    inputnum(x);
    inputnum(y);
  }
  void write(int prec = DEFAULT_PREC) const {
    printf("(");
    outputnum(x, prec);
    printf(",");
    outputnum(y, prec);
    printf(") ");
  }
  void writeln(int prec = DEFAULT_PREC) const {
    write(prec);
    printf("\n");
  }
  Point unit() const { return *this / len(); }
  Point &tounit() { return *this = *this / len(); }
  Point normal() const { return Point(-y, x); }
  Point symmetry(const Point &b) const { return b + b - *this; }
  D angle() const { return atan2(y, x); }
  Point rotate(const Point &b) const {
    return Point(x * b.x - y * b.y, x * b.y + y * b.x);
  }
  Point rotate(double b) const { return rotate(Point(cos(b), sin(b))); }
  Point &torotate(const Point &b) { return *this = rotate(b); }
  Point &torotate(double b) { return *this = rotate(b); }
};
Point operator*(Di b, const Point &a) { return Point(a.x * b, a.y * b); }
Point middle(const Point &a, const Point &b) { return (a + b) / 2; }
Di dot(const Point &a, const Point &b) { return a.x * b.x + a.y * b.y; }
Di det(const Point &a, const Point &b) { return a.x * b.y - a.y * b.x; }
bool in_triangle(const Point &a, const Point &b, const Point &c,
                 const Point &p) {
  return cmp(abs(det(a - p, b - p)) + abs(det(b - p, c - p)) +
                 abs(det(c - p, a - p)),
             abs(det(a - b, c - b))) == 0;
}
bool convex_tetragon(const Point &a, const Point &b, const Point &c,
                     const Point &d) {
  Di s[4] = {abs(det(a - b, a - c)), abs(det(b - c, b - d)),
             abs(det(c - d, c - a)), abs(det(d - a, d - b))};
  return cmp(s[0] + s[1] + s[2], s[3]) != 0 &&
         cmp(s[1] + s[2] + s[3], s[0]) != 0 &&
         cmp(s[2] + s[3] + s[0], s[1]) != 0 &&
         cmp(s[3] + s[0] + s[1], s[2]) != 0;
}
const int MAXN = 2020;
const int MAXM = 4040404;
int n;
long long S;
pair<Point, int> a[MAXN];
pair<Point, pair<int, double> > b[MAXM];
int pos[MAXN];
int bn = 0;
bool cmp_angle(const pair<Point, pair<int, double> > &a,
               const pair<Point, pair<int, double> > &b) {
  return a.second.second < b.second.second;
}
Point nowvec;
bool cmp_nowvec(const pair<Point, int> &a, const pair<Point, int> &b) {
  return det(nowvec, a.first) < det(nowvec, b.first);
}
void found(int p1, int p2, int p3) {
  printf("Yes\n");
  printf("%d %d\n", (int)a[p1].first.x, (int)a[p1].first.y);
  printf("%d %d\n", (int)a[p2].first.x, (int)a[p2].first.y);
  printf("%d %d\n", (int)a[p3].first.x, (int)a[p3].first.y);
  exit(0);
}
int rr() { return (rand() & 32767) << 15 ^ (rand() & 32767); }
int main() {
  scanf("%d", &n);
  scanf("%I64d", &S);
  S *= 2;
  for (int i = 1; i <= n; i++) {
    a[i].first.read();
    a[i].second = i;
  }
  for (int i = 1; i <= n; i++)
    for (int j = 1; j < i; j++) {
      b[++bn] =
          make_pair(a[i].first - a[j].first,
                    make_pair(i * MAXN + j, (a[i].first - a[j].first).angle()));
      b[++bn] =
          make_pair(a[j].first - a[i].first,
                    make_pair(j * MAXN + i, (a[j].first - a[i].first).angle()));
    }
  sort(b + 1, b + bn + 1, cmp_angle);
  b[0] = b[bn];
  nowvec = b[0].first + b[1].first;
  sort(a + 1, a + n + 1, cmp_nowvec);
  for (int i = 1; i <= n; i++) {
    pos[a[i].second] = i;
  }
  for (int i = 1; i <= bn; i++) {
    if (i > 1) {
      int x = b[i - 1].second.first / MAXN;
      int y = b[i - 1].second.first % MAXN;
      swap(a[pos[x]], a[pos[y]]);
      swap(pos[x], pos[y]);
    }
    int l = 1, r = n;
    Point nowp = a[pos[b[i].second.first % MAXN]].first;
    while (l < r) {
      int m = (l + r) / 2;
      long long mv = det(b[i].first, a[m].first - nowp);
      if (mv < S)
        l = m + 1;
      else if (mv > S)
        r = m - 1;
      else
        found(m, pos[b[i].second.first / MAXN], pos[b[i].second.first % MAXN]);
    }
    if (det(b[i].first, a[r].first - nowp) == S)
      found(r, pos[b[i].second.first / MAXN], pos[b[i].second.first % MAXN]);
  }
  printf("No\n");
  return 0;
}