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>
int chkmax(T &a, T b) {
  if (b > a) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T>
int chkmin(T &a, T b) {
  if (b < a) {
    a = b;
    return 1;
  }
  return 0;
}
template <class iterator>
void output(iterator begin, iterator end, ostream &out = cerr) {
  while (begin != end) {
    out << (*begin) << " ";
    begin++;
  }
  out << '\n';
}
template <class T>
void output(T x, ostream &out = cerr) {
  output(x.begin(), x.end(), out);
}
struct vect {
  long long x, y;
  vect() : x(0), y(0) {}
  vect(long long _x, long long _y) : x(_x), y(_y) {}
};
vect operator+(vect a, vect b) { return vect(a.x + b.x, a.y + b.y); }
vect operator-(vect a, vect b) { return vect(a.x - b.x, a.y - b.y); }
long long operator*(vect a, vect b) { return a.x * b.x + a.y * b.y; }
long long operator/(vect a, vect b) { return a.x * b.y - a.y * b.x; }
bool operator==(vect a, vect b) { return a.x == b.x && a.y == b.y; }
bool operator!=(vect a, vect b) { return !(a == b); }
istream &operator>>(istream &is, vect &p) {
  is >> p.x >> p.y;
  return is;
}
ostream &operator<<(ostream &os, vect &p) {
  os << p.x << " " << p.y;
  return os;
}
int half_plane(vect p) { return (p.y < 0 || (p.y == 0 && p.x < 0)); }
bool operator<(vect a, vect b) {
  int pa = half_plane(a), pb = half_plane(b);
  if (pa < pb) return 1;
  if (pa > pb) return 0;
  if (a / b == 0) {
    return (a * a < b * b);
  }
  return a / b > 0;
}
bool same_dir(vect a, vect b) { return !(a < b) && !(b < a); }
long long norm(vect a) { return a * a; }
vect rotatem90(vect a) { return vect(a.y, -a.x); }
struct line {
  long double A, B, C;
  line() {}
  line(vect v1, vect v2) {
    A = v1.y - v2.y;
    B = v2.x - v1.x;
    C = -(long double)v1.x * A - (long double)v1.y * B;
    long double nrm = sqrt(A * A + B * B);
    A /= nrm;
    B /= nrm;
    C /= nrm;
  }
  long double get(vect v) {
    return (A * (long double)v.x + B * (long double)v.y + C);
  }
};
ostream &operator<<(ostream &os, line &l) {
  os << l.A << " " << l.B << " " << l.C;
  return os;
}
bool operator<(line a, line b) {
  return rotatem90(vect(a.A, a.B)) < rotatem90(vect(b.A, b.B));
}
bool ycmp(vect a, vect b) { return make_pair(a.y, a.x) < make_pair(b.y, b.x); }
bool pycmp(pair<vect, int> a, pair<vect, int> b) {
  return ycmp(a.first, b.first);
}
struct event {
  line l;
  int i, j;
};
const long double EPS = 1e-9;
int n;
long double S;
vector<vect> a, _a;
vector<int> p;
vector<event> ev;
vector<pair<vect, int> > vp;
bool operator<(event e1, event e2) {
  return (a[e1.j] - a[e1.i]) < (a[e2.j] - a[e2.i]);
}
void my_swap(int i, int j) {
  int pi = p[i];
  int pj = p[j];
  swap(a[pi], a[pj]);
  p[i] = pj;
  p[j] = pi;
}
long double length(vect v) { return sqrt(norm(v)); }
signed main() {
  cin >> n >> S;
  a.resize(n);
  for (int i = 0; i < n; ++i) {
    cin >> a[i];
    vp.push_back({a[i], i});
  }
  _a = a;
  ev.reserve(n * n);
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < n; ++j) {
      if (i != j && half_plane(a[j] - a[i]) == 0) {
        ev.push_back({line(a[i], a[j]), i, j});
      }
    }
  }
  p.resize(n);
  iota(p.begin(), p.end(), 0);
  sort(ev.begin(), ev.end());
  sort(vp.begin(), vp.end(), pycmp);
  for (int i = 0; i < n; ++i) {
    a[i] = vp[i].first;
    p[vp[i].second] = i;
  }
  for (int i = 0; i < ev.size(); ++i) {
    long double h = 2 * S / length(_a[ev[i].i] - _a[ev[i].j]);
    int l = 0, r = n - 1;
    while (r > l) {
      int mid = (l + r) >> 1;
      long double cur_h = ev[i].l.get(a[mid + 1]);
      if (cur_h > h + EPS)
        r = mid;
      else
        l = mid + 1;
    }
    long double cur_h = ev[i].l.get(a[l]);
    if (abs(h - cur_h) < EPS) {
      cout << "Yes" << '\n';
      cout << _a[ev[i].i] << '\n';
      cout << _a[ev[i].j] << '\n';
      cout << a[l] << '\n';
      return 0;
    }
    h = -2 * S / length(_a[ev[i].i] - _a[ev[i].j]);
    l = 0, r = n - 1;
    while (r > l) {
      int mid = (l + r) >> 1;
      long double cur_h = ev[i].l.get(a[mid + 1]);
      if (cur_h > h + EPS)
        r = mid;
      else
        l = mid + 1;
    }
    cur_h = ev[i].l.get(a[l]);
    if (abs(h - cur_h) < EPS) {
      cout << "Yes" << '\n';
      cout << _a[ev[i].i] << '\n';
      cout << _a[ev[i].j] << '\n';
      cout << a[l] << '\n';
      return 0;
    }
    my_swap(ev[i].i, ev[i].j);
  }
  cout << "No" << '\n';
}