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;
template <class T>
void _R(T &x) {
  cin >> x;
}
void _R(int &x) { scanf("%d", &x); }
void _R(long long &x) { scanf("%lld", &x); }
void _R(double &x) { scanf("%lf", &x); }
void _R(char &x) { scanf(" %c", &x); }
void _R(char *x) { scanf("%s", x); }
void R() {}
template <class T, class... U>
void R(T &head, U &...tail) {
  _R(head);
  R(tail...);
}
template <class T>
void _W(const T &x) {
  cout << x;
}
void _W(const int &x) { printf("%d", x); }
void _W(const long long &x) { printf("%lld", x); }
void _W(const double &x) { printf("%.16f", x); }
void _W(const char &x) { putchar(x); }
void _W(const char *x) { printf("%s", x); }
template <class T, class U>
void _W(const pair<T, U> &x) {
  _W(x.first);
  putchar(' ');
  _W(x.second);
}
template <class T>
void _W(const vector<T> &x) {
  for (auto i = x.begin(); i != x.end(); _W(*i++))
    if (i != x.cbegin()) putchar(' ');
}
void W() {}
template <class T, class... U>
void W(const T &head, const U &...tail) {
  _W(head);
  putchar(sizeof...(tail) ? ' ' : '\n');
  W(tail...);
}
int MOD = 1e9 + 7;
void ADD(long long &x, long long v) {
  x = (x + v) % MOD;
  if (x < 0) x += MOD;
}
const int SIZE = 1e6 + 10;
const double EPS = 1e-12;
const double PI = acos(-1);
int n;
long long AA;
struct Point {
  long long x, y;
  int id;
  Point(long long x = 0, long long y = 0, int id = -1) : x(x), y(y), id(id) {}
  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 long long v) const { return Point(x * v, y * v); }
  long long operator*(const Point &b) const { return x * b.y - y * b.x; }
  long long operator^(const Point &b) const { return x * b.x + y * b.y; }
  bool operator<(const Point &b) const {
    return y > b.y || (y == b.y && x < b.x);
  }
  double angle() const { return atan2(y, x); }
  double dis() const { return sqrt(x * x + y * y); }
  void scan() { R(x, y); }
  void print() { W(x, y); }
} p[2000], p2[2000];
struct Line {
  long long a, b, c;
  int id1, id2;
  Line() {}
  Line(int _id1, int _id2) : id1(_id1), id2(_id2) {
    Point v = p[id2] - p[id1];
    a = v.y, b = -v.x, c = 2 * AA + p[id1].x * v.y - p[id1].y * v.x;
    if (make_pair(a, b) < make_pair(0LL, 0LL)) {
      a = -a;
      b = -b;
      c = -c;
    }
  }
  long long get(const Point &x) { return a * x.x + b * x.y - c; }
  bool operator<(const Line &line2) const {
    return Point(a, b) * Point(line2.a, line2.b) < 0;
  }
} line[4000000];
int ln, pos[2000];
bool haha(int id1, int id2, Line &lin) {
  if (lin.get(p[id1]) <= lin.get(p[id2])) {
    int x = pos[id1];
    int y = pos[id2];
    swap(p2[x], p2[y]);
    pos[id1] = y;
    pos[id2] = x;
    return 1;
  }
  return 0;
}
struct CHANGE {
  int id1, id2;
  CHANGE() {}
  CHANGE(int id1, int id2) : id1(id1), id2(id2) {}
  bool operator<(const CHANGE &b) const {
    Point v1 = p[id1] - p[id2];
    Point v2 = p[b.id1] - p[b.id2];
    return v1 * v2 < 0;
  }
} over[2000000];
int over_n;
int main() {
  R(n, AA);
  for (int i = 0; i < (n); ++i) {
    p[i].scan();
    p2[i] = p[i];
    p2[i].id = i;
  }
  for (int i = 0; i < (n); ++i)
    for (int j = 0; j < (n); ++j) {
      if (i == j) continue;
      line[ln++] = Line(i, j);
    }
  sort(line, line + ln);
  sort(p2, p2 + n);
  for (int i = 0; i < (n); ++i) {
    pos[p2[i].id] = i;
  }
  for (int i = 0; i < (n); ++i) {
    for (int j = (i + 1); j < (n); ++j) {
      if (p[i] < p[j]) {
        over[over_n++] = CHANGE(i, j);
      } else {
        over[over_n++] = CHANGE(j, i);
      }
    }
  }
  sort(over, over + over_n);
  int over_it = 0;
  for (int i = 0; i < (ln); ++i) {
    while (over_it < over_n &&
           haha(over[over_it].id1, over[over_it].id2, line[i]))
      over_it++;
    int ll = 0, rr = n - 1;
    while (ll <= rr) {
      int mm = (ll + rr) / 2;
      long long v = line[i].get(p2[mm]);
      if (v == 0) {
        W("Yes");
        p[line[i].id1].print();
        p[line[i].id2].print();
        p2[mm].print();
        return 0;
      } else if (v < 0) {
        rr = mm - 1;
      } else {
        ll = mm + 1;
      }
    }
  }
  W("No");
  return 0;
}