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) requires 5 total steps. Bessie does not need to take integer-sized steps.

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.

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

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