Problem Statement

yuki-kun has decided to visit a friend's house, which is at distance $L$ from his home.
To reach the friend's house, he must cross the \(N\) intersections between them.
The i-th intersection starts at distance \(X_i\) from his home and has width \(W_i\).
That is, the interval \((X_i,X_i + W_i)\) is an intersection.

The traffic light installed at each intersection alternates between green and red every \(T_i\) units of time.
The light at every intersection turned green at the moment yuki-kun departed.

yuki-kun walks straight ahead at a speed of distance $1$ per unit time.
However, when yuki-kun arrives at distance \(X_i\), just before an intersection, if there is a possibility that he would be inside the intersection while the light is red, he waits at the position of distance \(X_i\) until that possibility disappears.

Find the time elapsed from when yuki-kun leaves his home until he arrives at the friend's house.

Input

\(N\) \(L\)
\(X_1\) \(W_1\) \(T_1\)
\(X_2\) \(W_2\) \(T_2\)
...
\(X_N\) \(W_N\) \(T_N\)

\(1 \le N \le 100\)
\(1 \le L \le 10^5\)
\(1 \le T \le 10^7\)
The intersections are listed in increasing order of distance from his home. Neither his home nor the friend's house lies inside an intersection. That is, the following relation holds.
\(0 \le X_1 \lt X_1+W_1 \le X_2 \lt X_2+W_2 \le ... \le X_N \lt X_N+W_N \le L\)
Also, the duration of a green light is sufficient to cross the intersection. That is, the following relation holds.
\(W_i \le T_i\)

Output

Output on one line the time elapsed from when yuki-kun leaves his home until he arrives at the friend's house.

Sample

1 8
5 2 2

11

3 10
1 2 10
3 4 20
7 3 30

10

4 20
3 2 2
6 3 3
10 2 9
15 3 5

35