Darts Game

Darts is a fun game. The game in this problem is a bit different.

The board can be considered as an infinite 2-dimensional plane, and you have already shot $N$ darts. Each dart is at a point $(X, Y)$ and has a score $S$. Several darts can be at the exact same location, even with different scores. A score can be negative.

After shooting all the darts, you must draw a square on the plane. The side length of the square must be $L$, and the point $(0, 0)$ must be exactly at the center of the square. You can rotate the square in any direction you want. You can rotate it only once, before considering any darts.

You get the score of every dart that is inside the square or on its boundary. Given the location and score of each dart and the value of $L$, find the maximum score you can get. The square is allowed to contain no darts.

Your program will be tested on one or more test cases. The first line contains an integer $T$ ($1 \le T \le 100$), the number of test cases.

Each test case starts with a line containing two integers $N$ ($1 \le N \le 10^5$) and $L$ ($1 \le L \le 10^5$), separated by a space. Then $N$ lines follow. Each line contains three integers $X$, $Y$, $S$, separated by spaces. This means there is a dart at $(X, Y)$ that gives score $S$. All values satisfy $-10^5 \le X, Y, S \le 10^5$.

For each test case, print one line with the maximum score you can get by drawing the square.

The figure shows the first test case. No placement of the square includes the point with score 100, but if you rotate the square slightly, it no longer includes the point with score -101.