Triangle Containment

You recently discovered there is treasure buried on your farm land. A lot of treasure! You quickly decide to put a fence around the land.

Alas, you have but a single fence post! You will have to drive to town to get more fencing material. But you can't leave the land as open as it is, so you decide to build a makeshift fence to protect some of the treasure while you are gone. You will place the post in the ground and run wire in a straight line from the post to each of two sides of your barn wall, which encloses a triangular area. The ground is very hard: only places that were dug up to bury treasure are soft enough for you to place the fence post quickly.

To figure out the best option, you first calculate the following. For each treasure in your field, suppose you place the fence post at that treasure and complete the fence as described. What is the total value of all treasures enclosed by the fence? The treasure under the post is not considered enclosed, since someone could dig around the post and reach it.

The first line contains two integers $n$ ($1 \le n \le 10^5$) and $x$ ($1 \le x \le 10^9$), where $n$ is the number of treasure points and $x$ places the two corners of the barn wall at $(0,0)$ and $(x,0)$.

Each of the next $n$ lines contains three integers $x$, $y$, and $v$ ($-10^9 \le x \le 10^9$, $1 \le y \le 10^9$, $1 \le v \le 10^9$), giving the location $(x,y)$ and value $v$ of one treasure point. All points are distinct. For each point, the triangle formed with the barn wall does not contain any other treasure point on its boundary.

Output $n$ lines, one for each treasure point in input order. For each point, output a single integer: the total value of all points in the interior of the triangle that the point forms with the barn wall. The value of the point itself is excluded from this sum.