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;
using ll = long long;
using ull = unsigned long long;
using uint = unsigned int;
using ld = long double;
using vi = vector<int>;
using pii = pair<int, int>;
using vvi = vector<vi>;
using vii = vector<pii>;
template <typename T>
int sign(const T& t) {
  return (t > 0) - (t < 0);
}
template <typename T>
bool remax(T& a, T b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <typename T>
bool remin(T& a, T b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <typename T>
T gcd(T a, T b) {
  return b ? gcd(b, a % b) : a;
}
template <typename T>
T lcm(T a, T b) {
  return a * (b / gcd(a, b));
}
template <typename T>
std::ostream& operator<<(std::ostream& os, const std::vector<T>& vec) {
  os << "{ ";
  bool first = true;
  for (const auto& it : vec) {
    if (!first) {
      os << ", ";
    }
    os << it;
    first = false;
  }
  os << " }";
  return os;
}
template <typename T>
std::ostream& operator<<(std::ostream& os, const std::set<T>& s) {
  os << "{ ";
  bool first = true;
  for (const auto& it : s) {
    if (!first) {
      os << ", ";
    }
    os << it;
    first = false;
  }
  os << " }";
  return os;
}
template <typename K, typename V>
std::ostream& operator<<(std::ostream& os, const std::map<K, V>& m) {
  os << "{"
     << "\n";
  for (const auto& it : m) {
    os << " " << it.first << " -> " << it.second << "\n";
  }
  os << "}"
     << "\n";
  return os;
}
double get_time() { return static_cast<double>(clock()) / CLOCKS_PER_SEC; }
uint32_t mrand_32t() {
  static std::random_device rd;
  static std::mt19937 rng(rd());
  return rng();
}
uint64_t mrand_64t() {
  static std::random_device rd;
  static std::mt19937_64 rng(rd());
  return rng();
}
struct pnt {
  ll x, y;
  pnt() = default;
  pnt(ll x, ll y) : x(x), y(y) {}
  bool read() {
    if (!(cin >> x >> y)) {
      return 0;
    }
    return 1;
  }
  ll operator%(const pnt& p) const { return x * p.y - y * p.x; }
  bool operator<(const pnt& p) const {
    return make_pair(x, y) < make_pair(p.x, p.y);
  }
  pnt operator-(const pnt& p) const { return pnt(x - p.x, y - p.y); }
  void print() const { cout << x << " " << y << endl; }
};
int n;
ll S;
vector<pnt> ps;
bool read() {
  if (!(cin >> n)) {
    return 0;
  }
  cin >> S;
  ps.resize(n);
  for (int i = int(0); i < int(n); ++i) {
    assert(ps[i].read());
  }
  return 1;
}
struct seg {
  int i, j;
  pnt vec() const { return ps[j] - ps[i]; }
  bool operator<(const seg& s) const { return vec() % s.vec() > 0; }
};
void solve() {
  S *= 2;
  vector<seg> segs;
  for (int i = int(0); i < int(n); ++i)
    for (int j = int(0); j < int(n); ++j) {
      if (ps[i] < ps[j]) {
        segs.push_back(seg{i, j});
      }
    }
  sort(begin(segs), end(segs));
  assert(int((segs).size()) == n * (n - 1) / 2);
  if (false) cerr << "segs:" << endl;
  for (const auto& s : segs) {
    if (false) cerr << s.i << " " << s.j << endl;
  }
  if (false) cerr << endl;
  vi order(n);
  iota(begin(order), end(order), 0);
  const auto vec0 = segs[0].vec();
  sort(begin(order), end(order), [&](int k1, int k2) -> bool {
    const auto vec1 = ps[k1] - ps[segs[0].i];
    const auto vec2 = ps[k2] - ps[segs[0].i];
    const auto val1 = vec0 % vec1;
    const auto val2 = vec0 % vec2;
    if (val1 == val2) {
      return ps[k1] < ps[k2];
    }
    return val1 < val2;
  });
  vi pos(n, -1);
  for (int i = int(0); i < int(n); ++i) {
    pos[order[i]] = i;
  }
  const auto check = [&](int i, int j, int k) -> bool {
    ll area = (ps[j] - ps[i]) % (ps[k] - ps[i]);
    area = abs(area);
    if (area == S) {
      cout << "Yes" << endl;
      ps[i].print();
      ps[j].print();
      ps[k].print();
      return 1;
    }
    return 0;
  };
  for (const auto& s : segs) {
    ;
    ;
    const auto vec = s.vec();
    const auto area = [&](int k) -> ll { return vec % (ps[k] - ps[s.i]); };
    const auto find_last = [&](const ll upper) -> int {
      int L = -1;
      int R = n;
      while (L != R - 1) {
        int M = (L + R) / 2;
        if (area(order[M]) < upper) {
          L = M;
        } else {
          R = M;
        }
      }
      return L;
    };
    int left = find_last(-S + 1);
    if (left > -1) {
      if (check(s.i, s.j, order[left])) {
        return;
      }
    }
    int right = find_last(S + 1);
    if (right > -1) {
      if (check(s.i, s.j, order[right])) {
        return;
      }
    }
    assert(pos[s.j] == pos[s.i] + 1);
    swap(order[pos[s.i]], order[pos[s.j]]);
    swap(pos[s.i], pos[s.j]);
  }
  cout << "No" << endl;
}
int main() {
  cin.tie(nullptr);
  ios_base::sync_with_stdio(false);
  cout.tie(nullptr);
  cout.precision(12);
  cout << fixed;
  while (read()) {
    solve();
  }
  return 0;
}