There are $n$ gas stations located at positions $x_1, x_2, \ldots, x_n$ on a straight line.
- Each station $i$ has $f_i$ liters of fuel available.
- Each station $i$ has a "threshold" $r_i$. You can only use station $i$ if your **initial fuel capacity** $V$ satisfies $V \le r_i$.
You want to travel from position $0$ to position $H$.
- Traveling 1 unit of distance consumes 1 liter of fuel.
- You choose an initial fuel amount $V$. You start at position $0$ with $V$ liters of fuel.
- When you arrive at a station $i$, if $V \le r_i$, you can refuel. Refueling adds $f_i$ to your current fuel.
- Your fuel tank has unlimited capacity (you can hold more than $V$ fuel after refueling).
- You cannot move if your fuel becomes negative.
Find the **minimum** initial fuel $V$ required to travel from $0$ to $H$.
#### Input
- The first line contains an integer $n$ ($1 \leq n \leq 10^5$) and an integer $H$ ($1 \leq H \leq 10^9$).
- The next $n$ lines each contain three integers $x_i, f_i, r_i$ ($0 < x_i < H$, $1 \le f_i, r_i \le 10^9$).
#### Output
- Output a single integer, the minimum $V$.
#### Subtasks
- **Subtask 1 (20%):** $H \le 10^4$.
- **Subtask 2 (30%):** $n \le 10^4$.
- **Subtask 3 (50%):** No additional constraints ($n \le 10^5, H \le 10^9$).
#### Example
Input:
```
2 10
3 5 6
7 2 4
```
Output:
```
3
```
