Problem Statement

There are $N$ points on a two-dimensional plane. The coordinates of the $i\; (1 \leq i \leq N)$-th point are $(X_i,Y_i)$, and the value of the point is $V_i$.

Suppose you specify exactly $1$ square whose every side is parallel to one of the coordinate axes and whose side length is $A$. Output the maximum possible total value of the points inside the square (including its boundary).

Constraints

• $1 \leq N \leq 10^{5}$
• $-10^9 \leq X_i , Y_i \leq 10^9 $
• $-10^9 \leq V_i \leq 10^9 $
• $1 \leq A \leq 10^9 $
• All inputs are integers.

Input

$N$ $A$
$X_1$ $Y_1$ $V_1$
$X_2$ $Y_2$ $V_2$
$\vdots$
$X_N$ $Y_N$ $V_N$

Output

Suppose you specify exactly $1$ square whose every side is parallel to one of the coordinate axes and whose side length is $A$. Output the maximum possible total value of the points inside the square (including its boundary).

Sample

4 3
3 5 9
7 8 25
4 3 18
-1 2 -14

27

3 4
1 0 -2
5 0 3
6 0 -4

3

9 2
0 0 -3
1 0 2
2 0 3
2 0 2
3 0 -3
0 2 -4
1 2 1
2 2 1
3 2 -4

9