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>
const int N = 4e6 + 10;
int idx[N], rank[N];
struct Point {
  int x, y;
} A[N], Line[N];
inline double slope(Point a) {
  return double(A[a.x].y - A[a.y].y) / double(A[a.x].x - A[a.y].x);
}
inline long long area(Point A, Point B, Point C) {
  return fabs(1LL * (A.x - C.x) * (B.y - C.y) -
              1LL * (B.x - C.x) * (A.y - C.y));
}
inline int find1(int l, int r, int u, int v, long long s) {
  int res = -1;
  while (l <= r) {
    int mid = (l + r) >> 1;
    if (area(A[idx[mid]], A[u], A[v]) >= s)
      l = mid + 1, res = mid;
    else
      r = mid - 1;
  }
  return res != -1 && area(A[idx[res]], A[u], A[v]) == s ? res : -1;
}
inline int find2(int l, int r, int u, int v, long long s) {
  int res = -1;
  while (l <= r) {
    int mid = (l + r) >> 1;
    if (area(A[idx[mid]], A[u], A[v]) <= s)
      l = mid + 1, res = mid;
    else
      r = mid - 1;
  }
  return res != -1 && area(A[idx[res]], A[u], A[v]) == s ? res : -1;
}
inline int solve(int u, int v, int n, long long s) {
  if (rank[u] > rank[v]) std::swap(u, v);
  int res1 = find1(1, rank[u] - 1, u, v, s);
  if (res1 != -1) return res1;
  int res2 = find2(rank[v] + 1, n, u, v, s);
  if (res2 != -1) return res2;
  std::swap(rank[u], rank[v]), std::swap(idx[rank[u]], idx[rank[v]]);
  return 0;
}
int main() {
  int n, tot = 0;
  long long s;
  std::cin >> n >> s;
  s <<= 1;
  for (int i = 1; i <= n; ++i)
    std::cin >> A[i].x >> A[i].y, idx[i] = i, rank[i] = i;
  std::sort(A + 1, A + n + 1, [&](const Point &a, const Point &b) {
    return a.x < b.x || a.x == b.x && a.y < b.y;
  });
  for (int i = 1; i <= n; ++i)
    for (int j = i + 1; j <= n; ++j) Line[++tot] = Point{i, j};
  std::sort(Line + 1, Line + tot + 1, [&](const Point &a, const Point &b) {
    int x1 = A[a.y].x - A[a.x].x, y1 = A[a.y].y - A[a.x].y;
    int x2 = A[b.y].x - A[b.x].x, y2 = A[b.y].y - A[b.x].y;
    return 1LL * x1 * y2 - 1LL * x2 * y1 > 0;
  });
  for (int i = 1; i <= tot; ++i) {
    int res = solve(Line[i].x, Line[i].y, n, s);
    if (res)
      return printf("Yes\n%d %d\n%d %d\n%d %d\n", (A[Line[i].x]).x,
                    (A[Line[i].x]).y, (A[Line[i].y]).x, (A[Line[i].y]).y,
                    (A[idx[res]]).x, (A[idx[res]]).y),
             0;
  }
  return puts("No"), 0;
}