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;
pair<long long, long long> ps[2002];
int id[2002], pos[2002];
pair<int, int> line[4000006];
int main() {
  int n;
  cin >> n;
  long long s;
  cin >> s;
  s <<= 1;
  for (int i = 1; i <= n; ++i) cin >> ps[i].first >> ps[i].second;
  sort(ps + 1, ps + 1 + n);
  int m = 0;
  for (int i = 1; i <= n; ++i)
    for (int j = i + 1; j <= n; ++j) line[++m] = make_pair(i, j);
  sort(line + 1, line + 1 + m,
       [&](const pair<int, int> &a, const pair<int, int> &b) -> bool {
         return (ps[a.first].second - ps[a.second].second) *
                    (ps[b.first].first - ps[b.second].first) <
                (ps[b.first].second - ps[b.second].second) *
                    (ps[a.first].first - ps[a.second].first);
       });
  for (int i = 1; i <= n; ++i) id[i] = i;
  sort(id + 1, id + 1 + n,
       [&](const int &a, const int &b) { return ps[a] < ps[b]; });
  for (int i = 1; i <= n; ++i) pos[id[i]] = i;
  for (int i = 1; i <= m; ++i) {
    auto l = line[i];
    auto getarea = [&](const pair<long long, long long> &a,
                       const pair<long long, long long> &b,
                       const pair<long long, long long> &c) -> long long {
      return abs(a.first * b.second + b.first * c.second + c.first * a.second -
                 a.second * b.first - b.second * c.first - c.second * a.first);
    };
    assert(abs(pos[l.first] - pos[l.second]) == 1);
    int L = 1, R = min(pos[l.first], pos[l.second]) - 1;
    while (R >= L) {
      int M = (L + R) >> 1;
      long long area = getarea(ps[id[M]], ps[l.first], ps[l.second]);
      if (area == s) {
        cout << "Yes" << endl;
        cout << ps[id[M]].first << " " << ps[id[M]].second << endl;
        cout << ps[l.first].first << " " << ps[l.first].second << endl;
        cout << ps[l.second].first << " " << ps[l.second].second << endl;
        exit(0);
      }
      if (area < s)
        R = M - 1;
      else
        L = M + 1;
    }
    L = max(pos[l.first], pos[l.second]) + 1, R = n;
    while (R >= L) {
      int M = (L + R) >> 1;
      long long area = getarea(ps[id[M]], ps[l.first], ps[l.second]);
      if (area == s) {
        cout << "Yes" << endl;
        cout << ps[id[M]].first << " " << ps[id[M]].second << endl;
        cout << ps[l.first].first << " " << ps[l.first].second << endl;
        cout << ps[l.second].first << " " << ps[l.second].second << endl;
        exit(0);
      }
      if (area < s)
        L = M + 1;
      else
        R = M - 1;
    }
    tie(pos[l.first], pos[l.second], id[pos[l.first]], id[pos[l.second]]) =
        make_tuple(pos[l.second], pos[l.first], l.second, l.first);
  }
  cout << "No" << endl;
}