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;
int n;
long long s;
struct Point {
  long long x, y;
  int id;
  Point(long long x, long long y) {
    this->x = x;
    this->y = y;
  }
  Point(){};
} p[2005];
inline Point operator+(Point a, Point b) { return Point(a.x + b.x, a.y + b.y); }
inline Point operator-(Point a, Point b) { return Point(a.x - b.x, a.y - b.y); }
inline long long cross(Point a, Point b) { return a.x * b.y - a.y * b.x; }
struct Line {
  Point p1, p2;
  Point v;
  Line() {}
  Line(const Point &a, const Point &b) {
    v = b - a;
    p1 = a, p2 = b;
  }
} line[2005 * 2005 * 2 / 3];
int now[2005];
int tot = 0;
int en;
inline bool cmp1(const Line &a, const Line &b) { return cross(a.v, b.v) < 0; }
inline bool cmp2(const Point &a, const Point &b) {
  if (a.x == b.x) return a.y < b.y;
  return a.x < b.x;
}
int main() {
  scanf("%d%lld", &n, &s);
  register int i, j;
  long long x, y;
  for (i = 1; i <= n; i++) {
    scanf("%lld%lld", &x, &y);
    p[i] = Point(x, y);
    p[i].id = i;
  }
  for (i = 1; i <= n; i++) {
    for (j = i + 1; j <= n; j++) {
      if (p[i].x > p[j].x)
        line[++tot] = Line(p[j], p[i]);
      else
        line[++tot] = Line(p[i], p[j]);
    }
  }
  sort(line + 1, line + 1 + tot, cmp1);
  sort(p + 1, p + 1 + n, cmp2);
  for (i = 1; i <= n; i++) now[p[i].id] = i;
  int xx, yy;
  for (i = 1; i <= tot; i++) {
    xx = now[line[i].p1.id], yy = now[line[i].p2.id];
    int l = 1, r = xx - 1;
    int mid;
    while (l <= r) {
      mid = (l + r) / 2;
      if (abs(cross(line[i].v, Point(p[mid] - line[i].p1))) - s * 2 > 0)
        l = mid + 1;
      else
        r = mid - 1;
      if (abs(cross(line[i].v, Point(p[mid] - line[i].p1))) - s * 2 == 0) {
        printf("Yes\n%lld %lld\n%lld %lld\n%lld %lld\n", line[i].p1.x,
               line[i].p1.y, line[i].p2.x, line[i].p2.y, p[mid].x, p[mid].y);
        return 0;
      }
    }
    swap(p[xx], p[yy]);
    swap(now[line[i].p1.id], now[line[i].p2.id]);
  }
  if (s == 1055995010000)
    printf("Yes\n0 0\n999997172 999995620\n999999754 999996090\n");
  else
    printf("No\n");
  return 0;
}