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>
#pragma GCC optimize("O3")
using namespace std;
const double pi = 3.141592653589793238462643383279;
const double log23 = 1.58496250072115618145373894394781;
const double eps = 1e-8;
const long long INF = 1e18 + 239;
const long long prost = 239;
const int two = 2;
const int th = 3;
const long long MOD = 1e9 + 7;
const long long MOD2 = MOD * MOD;
const int BIG = 1e9 + 239;
const int alf = 26;
const int dx[4] = {-1, 0, 1, 0};
const int dy[4] = {0, 1, 0, -1};
const int dxo[8] = {-1, -1, -1, 0, 1, 1, 1, 0};
const int dyo[8] = {-1, 0, 1, 1, 1, 0, -1, -1};
const int dig = 10;
const string str_alf = "abcdefghijklmnopqrstuvwxyz";
const string str_alf_big = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
const int day[12] = {31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31};
const int digarr[10] = {6, 2, 5, 5, 4, 5, 6, 3, 7, 6};
const int bt = 31;
const int fr = 4;
template <typename T>
inline T gcd(T a, T b) {
  return a ? gcd(b % a, a) : b;
}
template <typename T>
inline T lcm(T a, T b) {
  return (a / gcd(a, b)) * b;
}
inline bool is_down(char x) { return ('a' <= x && x <= 'z'); }
inline bool is_upper(char x) { return ('A' <= x && x <= 'Z'); }
inline bool is_digit(char x) { return ('0' <= x && x <= '9'); }
inline int power(long long a, int b) {
  long long res = 1;
  while (b > 0) {
    if (b & 1) res = (res * a) % MOD;
    a = (a * a) % MOD;
    b >>= 1;
  }
  return res;
}
mt19937 rnd(239);
const int M = 2 * 1e5 + 239;
const int N = 2 * 1e3 + 239;
const int L = 19;
const int T = (1 << 20);
const int B = trunc(sqrt(M)) + 1;
const int X = 2e6 + 239;
int n, x[N], y[N], cur, id[N], pos[N];
long long s;
tuple<int, int> ask[X];
long long gett(int i, int j, int h) {
  long long vx1 = x[j] - x[i];
  long long vy1 = y[j] - y[i];
  long long vx2 = x[h] - x[i];
  long long vy2 = y[h] - y[i];
  long long sq = (vx1 * vy2 - vx2 * vy1);
  return abs(sq);
}
void answer(int i, int j, int h) {
  cout << "Yes\n";
  cout << x[i] << " " << y[i] << "\n";
  cout << x[j] << " " << y[j] << "\n";
  cout << x[h] << " " << y[h] << "\n";
  exit(0);
}
void reinit(int &x, int &y) {
  if (y < 0) {
    y = -y;
    x = -x;
    return;
  }
  if (y == 0) {
    if (x < 0) {
      y = -y;
      x = -x;
    }
  }
}
inline bool cmp(tuple<int, int> a, tuple<int, int> b) {
  int vx1 = x[get<1>(a)] - x[get<0>(a)];
  int vy1 = y[get<1>(a)] - y[get<0>(a)];
  int vx2 = x[get<1>(b)] - x[get<0>(b)];
  int vy2 = y[get<1>(b)] - y[get<0>(b)];
  reinit(vx1, vy1);
  reinit(vx2, vy2);
  if ((long long)vx2 * (long long)vy1 == (long long)vx1 * (long long)vy2)
    return (a < b);
  return ((long long)vx2 * (long long)vy1 < (long long)vx1 * (long long)vy2);
}
inline void change(int i, int j) {
  swap(id[pos[i]], id[pos[j]]);
  swap(pos[i], pos[j]);
}
int main() {
  ios_base::sync_with_stdio(0);
  cin >> n >> s;
  s *= 2LL;
  cur = 0;
  for (int i = 0; i < n; i++) cin >> x[i] >> y[i];
  for (int i = 0; i < n; i++)
    for (int j = i + 1; j < n; j++) {
      ask[cur] = make_tuple(i, j);
      cur++;
    }
  sort(ask, ask + cur, cmp);
  vector<tuple<int, int, int> > al;
  for (int i = 0; i < n; i++) al.push_back(make_tuple(y[i], x[i], i));
  sort(al.begin(), al.end());
  for (int i = 0; i < n; i++) id[i] = get<2>(al[i]);
  for (int i = 0; i < n; i++) pos[id[i]] = i;
  int xq, yq, l, r;
  for (int i = 0; i < cur; i++) {
    xq = get<0>(ask[i]);
    yq = get<1>(ask[i]);
    l = -1;
    r = pos[xq];
    while (r - l > 1) {
      int h = (l + r) / 2;
      if (gett(xq, yq, id[h]) > s)
        l = h;
      else
        r = h;
    }
    for (int u = l - 1; u <= l + 1; u++)
      if (0 <= u && u < n && gett(xq, yq, id[u]) == s) answer(xq, yq, id[u]);
    l = pos[xq];
    r = n;
    while (r - l > 1) {
      int h = (l + r) / 2;
      if (gett(xq, yq, id[h]) < s)
        l = h;
      else
        r = h;
    }
    for (int u = l - 1; u <= l + 1; u++)
      if (0 <= u && u < n && gett(xq, yq, id[u]) == s) answer(xq, yq, id[u]);
    change(xq, yq);
  }
  cout << "No\n";
  return 0;
}