Problem Statement

Takumi is playing a shooting game. He can earn a positive score by hitting the targets that appear with bullets from his gun. A total of $N$ targets appear.
Bullets can only be fired at integer seconds. The $i$-th target appears from $L_i-0.1$ seconds to $R_i+0.1$ seconds (inclusive) after the start of the game, and it is considered hit if a bullet is fired at an integer time $t$ during this period. The score obtained in that case is $P_i$ points.
Each shot from the gun hits one target. Reloading then takes $T$ seconds, and the next bullet can be fired $T$ seconds after the shot.
Note that $T$ seconds is longer than the appearance duration of any target.
Also, a bullet is already loaded at the start of the game.
Output the maximum total score Takumi can obtain.

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $0 \leq L_i < R_i \leq 2 \times 10^5$
• $1 \leq P_i \leq 10^9$
• $\max(R_i - L_i) < T \leq 2 \times 10^5$ $(1 \leq i \leq N)$
• All inputs are integers.

Input

The input is given from standard input in the following format.

$N\ T$
$L_1\ R_1\ P_1$  
$L_2\ R_2\ P_2$  
⋮  
$L_N\ R_N\ P_N$

Output

Output the maximum total score Takumi can obtain on a single line.

Sample

4 5
0 4 10
5 7 20
6 9 30
10 11 50

90

5 2
1 2 1000000000
3 4 1000000000
5 6 1000000000
7 8 1000000000
9 10 1000000000

5000000000

7 8
0 4 10
5 7 20
6 9 30
10 11 50
3 6 50
10 12 70
25 30 100

220