[USACO14MAR] The Lazy Cow G

``` Bessie的田里有N(1<=N<=100,000)块草地，每块草地的坐标是 (xi, yi) (0<=xi,yi<=1,000,000),上面长着gi(1<=gi<=10,000)个单位的牧草。 Bessie可以向东南西北方向走，一次走一步（一个单位长度）。如她从（0,0）走到（3,2）需要5步。她最多可以一次走k (1<=k<=2,000,000) 步。 现在她想找一个位置，使她从该位置出发可以得到最多单位的牧草(她可以走多次，但每次都从该位置出发)。 输入格式： 第1行：两个整数N和K 第2~N+1行：三个整数gi，xi，yi 输出格式： 第1行：Bessie所能获得的最多单位牧草数 ```

It's a hot summer day, and Bessie the cow is feeling quite lazy. She wants to locate herself at a position in her field so that she can reach as much delicious grass as possible within only a short distance. There are $N$ patches of grass $(1 <= N <= 100,000)$ in Bessie's field. The $ith$ such patch contains $g_i$ units of grass $(1 <= g_i <= 10,000)$ and is located at a distinct point $(x_i, y_i)$ in the field $(0 <= x_i,$ $y_i <= $ $1,000,000)$. Bessie would like to choose a point in the field as her initial location (possibly the same point as a patch of grass, and possibly even a point with non-integer coordinates) so that a maximum amount of grass is within a distance of $K$ steps from this location $(1 <= K <= 2,000,000)$. When Bessie takes a step, she moves 1 unit north, south, east, or west of her current position. For example, to move from $(0,0)$ to $(3,2)$, this requires 5 total steps. Bessie does not need to take integer-sized steps -- for example, 1 total step could be divided up as half a unit north and half a unit east. Please help Bessie determine the maximum amount of grass she can reach, if she chooses the best possible initial location.

* Line 1: The integers $N$ and $K$. * Lines 2..1+N: Line $i+1$ describes the $ith$ patch of grass using 3 integers: $g_i, x_i, y_i.$

* Line 1: The maximum amount of grass Bessie can reach within $K$ steps, if she locates herself at the best possible initial position.

4 3
7 8 6
3 0 0
4 6 0
1 4 2

8

INPUT DETAILS: Bessie is willing to take at most 3 steps from her initial position. There are 4 patches of grass. The first contains 7 units of grass and is located at position $(8,6)$, and so on. OUTPUT DETAILS: By locating herself at $(3,0)$, the grass at positions $(0,0)$, $(6,0)$, and $(4,2)$ is all within $K$ units of distance.