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;
const int Imx = 2147483647;
const long long Lbig = 2e18;
const int mod = 1e9 + 7;
struct fastio {
  char s[100000];
  int it, len;
  fastio() { it = len = 0; }
  inline char get() {
    if (it < len) return s[it++];
    it = 0;
    len = fread(s, 1, 100000, stdin);
    if (len == 0)
      return EOF;
    else
      return s[it++];
  }
  bool notend() {
    char c = get();
    while (c == ' ' || c == '\n') c = get();
    if (it > 0) it--;
    return c != EOF;
  }
} _buff;
inline long long getnum() {
  long long r = 0;
  bool ng = 0;
  char c;
  c = _buff.get();
  while (c != '-' && (c < '0' || c > '9')) c = _buff.get();
  if (c == '-') ng = 1, c = _buff.get();
  while (c >= '0' && c <= '9') r = r * 10 + c - '0', c = _buff.get();
  return ng ? -r : r;
}
template <class T>
inline void putnum(T x) {
  if (x < 0) putchar('-'), x = -x;
  register short a[20] = {}, sz = 0;
  while (x) a[sz++] = x % 10, x /= 10;
  if (sz == 0) putchar('0');
  for (int i = sz - 1; i >= 0; i--) putchar('0' + a[i]);
}
inline char getreal() {
  char c = _buff.get();
  while (c <= 32) c = _buff.get();
  return c;
}
long long qpow(long long x, long long k) {
  return k == 0 ? 1
                : 1ll * qpow(1ll * x * x % mod, k >> 1) * (k & 1 ? x : 1) % mod;
}
long long Cx, Cy;
const double eps = 1e-10;
const double pi = acos(-1);
inline bool is0(double x) { return x < eps && x > -eps; }
inline double modp(double x) { return x < 0 ? x + 2 * pi : x; }
struct point {
  int x, y;
  double rad;
  point(int X = 0, int Y = 0) {
    x = X;
    y = Y;
  }
  point operator+(const point &t) const { return point(x + t.x, y + t.y); }
  point operator-(const point &t) const { return point(x - t.x, y - t.y); }
  long long det(const point &t) const { return 1ll * x * t.y - 1ll * y * t.x; }
  long long dot(const point &t) const { return 1ll * x * t.x + 1ll * y * t.y; }
  bool operator<(const point &t) const {
    if (det(t) != 0)
      return det(t) > 0;
    else
      return (point(Cx, Cy).dot(*this) > 0) > (point(Cx, Cy).dot(t) > 0);
  }
  void out() { cout << x << " " << y << endl; }
};
bool cmp_init(point x, point y) {
  return make_pair(x.y, x.x) < make_pair(y.y, y.x);
}
const int maxn = 2011;
int n;
long long S;
point a[maxn];
set<pair<point, int> > st;
void del_gap(int x) {
  if (x >= 0 && x + 1 < n) st.erase(make_pair(a[x + 1] - a[x], x));
}
void add_gap(int x) {
  if (x >= 0 && x + 1 < n) st.insert(make_pair(a[x + 1] - a[x], x));
}
void query(int x, point p, long long s) {
  int l = 0, r = n - 1;
  while (l <= r) {
    int m = l + r >> 1;
    long long curs = p.det(a[m] - a[x]);
    if (curs == s) {
      puts("Yes");
      a[x].out();
      a[x + 1].out();
      a[m].out();
      exit(0);
    } else if (curs < s)
      l = m + 1;
    else
      r = m - 1;
  }
}
void SWAP(int x) {
  del_gap(x - 1);
  del_gap(x);
  del_gap(x + 1);
  query(x, a[x + 1] - a[x], -2 * S);
  query(x, a[x + 1] - a[x], 2 * S);
  swap(a[x], a[x + 1]);
  add_gap(x - 1);
  add_gap(x);
  add_gap(x + 1);
}
void solve() {
  bool pre = 0;
  int ti = 0;
  while (true) {
    Cx = st.begin()->first.x;
    Cy = st.begin()->first.y;
    int x = st.begin()->second;
    SWAP(x);
    if (pre && !(point(Cx, Cy) < point(1, 0))) break;
    pre = point(Cx, Cy) < point(1, 0);
    if (pre) break;
  }
  puts("No");
}
int main() {
  n = getnum(), S = getnum();
  for (int i = 0; i < n; i++) a[i].x = getnum(), a[i].y = getnum();
  sort(a, a + n, cmp_init);
  Cx = 1;
  Cy = 0;
  for (int i = 0; i < n; i++) add_gap(i);
  solve();
  return 0;
}