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;
struct point {
  long long x, y;
  bool operator<(const point &p) const { return x != p.x ? x < p.x : y < p.y; }
} w[2010];
struct Vec {
  long long x, y;
  int a, b;
  bool operator<(const Vec &p) const { return y * p.x < p.y * x; }
} P[2200100];
int n, cnt, Num[3010], ord[3010];
long long S;
long long get(point a, point b, point c) {
  return a.x * b.y + b.x * c.y + c.x * a.y - a.y * b.x - b.y * c.x - c.y * a.x;
}
void Print(point a) { printf("%lld %lld\n", a.x, a.y); }
bool Go1(int x, int y, int st, int ed) {
  int b = st, e = ed, mid;
  while (b <= e) {
    mid = (b + e) >> 1;
    long long t = get(w[x], w[y], w[Num[mid]]);
    if (t < 0) t = -t;
    if (t == S * 2) {
      puts("Yes");
      Print(w[x]);
      Print(w[y]);
      Print(w[Num[mid]]);
      return true;
    }
    if (t < S * 2)
      e = mid - 1;
    else
      b = mid + 1;
  }
  return false;
}
bool Go2(int x, int y, int st, int ed) {
  int b = st, e = ed, mid;
  while (b <= e) {
    mid = (b + e) >> 1;
    long long t = get(w[x], w[y], w[Num[mid]]);
    if (t < 0) t = -t;
    if (t == S * 2) {
      puts("Yes");
      Print(w[x]);
      Print(w[y]);
      Print(w[Num[mid]]);
      return true;
    }
    if (t > S * 2)
      e = mid - 1;
    else
      b = mid + 1;
  }
  return false;
}
int main() {
  int i, j;
  scanf("%d%lld", &n, &S);
  for (i = 1; i <= n; i++) {
    scanf("%lld%lld", &w[i].x, &w[i].y);
  }
  sort(w + 1, w + n + 1);
  cnt = 0;
  for (i = 1; i <= n; i++) {
    for (j = i + 1; j <= n; j++) {
      P[cnt].x = w[j].x - w[i].x;
      P[cnt].y = w[j].y - w[i].y;
      P[cnt].a = i, P[cnt].b = j;
      cnt++;
    }
  }
  sort(P, P + cnt);
  for (i = 1; i <= n; i++) Num[i] = ord[i] = i;
  for (i = cnt - 1; i >= 0; i--) {
    int a = P[i].a, b = P[i].b;
    swap(Num[ord[a]], Num[ord[b]]);
    swap(ord[a], ord[b]);
    if (Go1(a, b, 1, min(ord[a], ord[b]))) return 0;
    if (Go2(a, b, max(ord[a], ord[b]), n)) return 0;
  }
  puts("No");
}