题目描述

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.

输入格式

• Line 1: The integers $N$ and $K$.

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

输出格式

• 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

提示

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.