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(2)
using namespace std;
const int maxn = 2000;
const int maxe = 2e6;
const int INF = 0x7fffffff;
const int mod = 1e9 + 7;
const double eps = 1e-7;
const double Pi = acos(-1.0);
inline int read_int() {
  char c;
  int ret = 0, sgn = 1;
  do {
    c = getchar();
  } while ((c < '0' || c > '9') && c != '-');
  if (c == '-')
    sgn = -1;
  else
    ret = c - '0';
  while ((c = getchar()) >= '0' && c <= '9') ret = ret * 10 + (c - '0');
  return sgn * ret;
}
inline long long read_ll() {
  char c;
  long long ret = 0, sgn = 1;
  do {
    c = getchar();
  } while ((c < '0' || c > '9') && c != '-');
  if (c == '-')
    sgn = -1;
  else
    ret = c - '0';
  while ((c = getchar()) >= '0' && c <= '9') ret = ret * 10 + (c - '0');
  return sgn * ret;
}
inline long long quick_pow(long long base, long long index, long long p) {
  long long res = 1;
  while (index) {
    if (index & 1) res = res * base % p;
    base = base * base % p;
    index >>= 1;
  }
  return res;
}
struct point {
  point operator-(const point& rhs) const {
    return point(x - rhs.x, y - rhs.y);
  }
  bool operator<(const point& rhs) const {
    return x == rhs.x ? y < rhs.y : x < rhs.x;
  }
  point() {}
  point(int _x, int _y) { x = _x, y = _y; }
  point(int _x, int _y, int _id1, int _id2) {
    x = _x, y = _y, id1 = _id1, id2 = _id2;
  }
  long long dot(const point& rhs) const {
    return 1ll * x * rhs.x + 1ll * y * rhs.y;
  }
  long long det(const point& rhs) const {
    return 1ll * x * rhs.y - 1ll * y * rhs.x;
  }
  int x, y, id1, id2;
};
point a[maxn + 5], arr[maxe + 5];
int n, m, id[maxn + 5], pos[maxn + 5];
inline long long Area(int x, int y, int z) {
  return abs((a[x] - a[y]).det(a[x] - a[z]));
}
long long S;
int main() {
  n = read_int(), S = 2 * read_ll();
  for (int i = 1; i <= n; ++i) a[i].x = read_int(), a[i].y = read_int();
  sort(a + 1, a + 1 + n);
  for (int i = 1; i <= n; ++i)
    for (int j = i + 1; j <= n; ++j) {
      point u = a[j] - a[i];
      u.id1 = i, u.id2 = j;
      arr[++m] = u;
    }
  sort(arr + 1, arr + 1 + m,
       [](const point& a, const point& b) { return a.det(b) > 0; });
  for (int i = 1; i <= n; ++i) id[i] = pos[i] = i;
  for (int i = 1; i <= m; ++i) {
    int x = arr[i].id1, y = arr[i].id2;
    if (pos[x] > pos[y]) swap(x, y);
    int l = 1, r = pos[x] - 1, res = pos[x] - 1;
    while (l <= r) {
      int mid = l + r >> 1;
      long long nowS = Area(id[pos[x]], id[pos[y]], id[mid]);
      if (nowS == S) {
        res = mid;
        break;
      }
      if (nowS > S)
        res = mid, l = mid + 1;
      else
        r = mid - 1;
    }
    if (Area(id[pos[x]], id[pos[y]], id[res]) == S) {
      printf("Yes\n");
      printf("%d %d\n", a[id[pos[x]]].x, a[id[pos[x]]].y);
      printf("%d %d\n", a[id[pos[y]]].x, a[id[pos[y]]].y);
      printf("%d %d\n", a[id[res]].x, a[id[res]].y);
      return 0;
    }
    l = pos[y] + 1, r = n, res = pos[y] + 1;
    while (l <= r) {
      int mid = l + r >> 1;
      long long nowS = Area(id[pos[x]], id[pos[y]], id[mid]);
      if (nowS == S) {
        res = mid;
        break;
      }
      if (nowS > S)
        res = mid, r = mid - 1;
      else
        l = mid + 1;
    }
    if (Area(id[pos[x]], id[pos[y]], id[res]) == S) {
      printf("Yes\n");
      printf("%d %d\n", a[id[pos[x]]].x, a[id[pos[x]]].y);
      printf("%d %d\n", a[id[pos[y]]].x, a[id[pos[y]]].y);
      printf("%d %d\n", a[id[res]].x, a[id[res]].y);
      return 0;
    }
    swap(pos[x], pos[y]);
    swap(id[pos[x]], id[pos[y]]);
  }
  printf("No\n");
  return 0;
}