Problem Statement

On a number line, there are ~N~ fish swimming.

Fish ~i~ , which has a weight of ~W_i~ , is at the coordinate ~X_i~ at time ~0~ and moves at a speed of ~V_i~ in the positive direction.

Takahashi will choose an arbitrary real number ~t~ greater than or equal to ~0~ and do the following action at time ~t~ just once.
Action: Choose an arbitrary real number ~x~ . Catch all fish whose coordinates are between ~x~ and ~x+A~ , inclusive.

Find the maximum total weight of fish that he can catch.

Constraints

• ~1 \leq N \leq 2000~
• ~1 \leq A \leq 10^4~
• ~1 \leq W_i\leq 10^4~
• ~0 \leq X_i\leq 10^4~
• ~1 \leq V_i\leq 10^4~
• All values in the input are integers.

Input

The input is given from Standard Input in the following format:

~N~ ~A~

~W_1~ ~X_1~ ~V_1~

~W_2~ ~X_2~ ~V_2~

~\vdots~

~W_N~ ~X_N~ ~V_N~

Output

Print the answer.

Sample Input 1

3 10
100 0 100
1 10 30
10 20 10

Sample Output 1

111

At time ~0.25~ , fish ~1~ , ~2~ , and ~3~ are at the coordinates ~25~ , ~17.5~ , and ~22.5~ , respectively. Thus, the action done at this time with ~x=16~ catches all the fish.

Sample Input 2

3 10
100 100 100
1 10 30
10 20 10

Sample Output 2

100

One optimal choice is to do the action at time ~0~ with ~x=100~ .

Sample Input 3

4 10
1000 100 10
100 99 1
10 0 100
1 1 1

Sample Output 3

1110

One optimal choice is to do the action at time ~1~ with ~x=100~ .