There are $$$n$$$ water refill points on the UNSW campus. Alice challenged Bob with finding a triangle with vertices at three of these points with an area of exactly $$$S$$$.
Not good with geometry (or knowing where is where on campus), Bob came to you for help! Bob wants to know whether such a triangle can be found, and if so, what are the coordinates of the vertices of one such triangle?
The first line of input contains two integers $$$n$$$ and $$$S$$$ ($$$3\leq n\leq 4000$$$, $$$1\leq S\leq 2\cdot 10^18$$$), the number of water refill points and the area of the triangle to be found respectively.
The next $$$n$$$ lines contain the description of the points, one per line. The $$$i$$$-th of these lines contains two integers $$$x_i$$$ and $$$y_i$$$ ($$$-10^9 \leq x_i, y_i \leq 10^9$$$), the coordinate of the $$$i$$$-th point.
It is guaranteed that all points are located at distinct coordinates. It is also guaranteed that no three points lie on the same line.
If the solution doesn't exist print NO.
Otherwise, print YES, followed by three pairs of coordinates $$$x\text{ }y$$$, each on a separate line, which are the coordinates of the three points which form the triangle of area S.
The word can be printed in any case, and the points of a triangle can be printed in any order.
3 7 0 0 3 0 0 4
NO
4 3 0 0 2 0 1 2 1 3
YES 0 0 1 3 2 0
