Large Triangle

Description:

Input:

The first line of input contains two integers $$$n$$$ and $$$S$$$ ($$$3 \le n \le 2000$$$, $$$1 \le S \le 2 \cdot 10^{18}$$$) — 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 $$$x_i$$$, $$$y_i$$$ ($$$-10^9 \le x_i, y_i \le 10^9$$$).

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 $$$S$$$.

Sample Input:

3 7
0 0
3 0
0 4

Sample Output:

No

Sample Input:

4 3
0 0
2 0
1 2
1 3

Sample Output:

Yes
0 0
1 3
2 0