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 maxN = 2000, mld = 1000000000;
pair<int, int> coords[maxN], pairs[maxN * maxN];
int ind[maxN], T[maxN];
bool dbg;
inline int dy(int a, int b) { return coords[b].second - coords[a].second; }
inline int dx(int a, int b) { return coords[b].first - coords[a].first; }
long long surf(int a, int b, int c) {
  return abs(1LL * dy(a, b) * dx(a, c) - 1LL * dy(a, c) * dx(a, b));
}
bool cmp1(const int& a, const int& b) {
  if (coords[a].first != coords[b].first)
    return coords[a].first < coords[b].first;
  return coords[a].second > coords[b].second;
}
bool cmp2(const pair<int, int>& p1, const pair<int, int>& p2) {
  long long dx1 = dx(p1.first, p1.second);
  long long dx2 = dx(p2.first, p2.second);
  long long dy1 = dy(p1.first, p1.second);
  long long dy2 = dy(p2.first, p2.second);
  long long s = dy1 * dx2 - dy2 * dx1;
  if (s != 0) return s < 0;
  return coords[p1.first].first < coords[p2.first].first;
}
void print(int i) {
  printf("%d %d\n", coords[i].first - mld, coords[i].second - mld);
}
void bins(int end, long long target, int i1, int i2) {
  int begin = 0;
  while (end - begin > 1) {
    int middle = (begin + end) / 2;
    int i = T[middle];
    surf(i1, i2, i) < target ? end = middle : begin = middle;
  }
  if (surf(i1, i2, T[begin]) != target) return;
  printf("Yes\n");
  print(i1);
  print(i2);
  print(T[begin]);
  exit(0);
}
int main() {
  int n;
  long long s;
  scanf("%d%lld", &n, &s);
  s *= 2;
  for (int(i) = (0); (i) < (n); (i)++) {
    scanf("%d%d", &coords[i].first, &coords[i].second);
    coords[i].first += mld, coords[i].second += mld;
    T[i] = i;
  }
  sort(T, T + n, cmp1);
  for (int(i) = (0); (i) < (n); (i)++) ind[T[i]] = i;
  int c = 0;
  for (int(i) = (0); (i) < (n); (i)++)
    for (int(j) = (i + 1); (j) < (n); (j)++)
      pairs[c++] =
          coords[i].first < coords[j].first ? make_pair(i, j) : make_pair(j, i);
  sort(pairs, pairs + c, cmp2);
  for (int(i) = (0); (i) < (c); (i)++) {
    int a = pairs[i].first, b = pairs[i].second;
    int i1 = ind[a], i2 = ind[b];
    swap(T[i1], T[i2]);
    swap(ind[a], ind[b]);
    int j = min(i1, i2);
    bins(j, s, a, b);
    dbg = false;
  }
  printf("No\n");
  return 0;
}