You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in c++17.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```cpp
<your code here>
```

Execution time limit: 3.0 seconds
Memory limit: 1024.0 MB

# Problem
Note that the differences between easy and hard versions are the constraints on $$$n$$$ and the time limit. You can make hacks only if both versions are solved.

AquaMoon knew through foresight that some ghosts wanted to curse tourists on a pedestrian street. But unfortunately, this time, these ghosts were hiding in a barrier, and she couldn't enter this barrier in a short time and destroy them. Therefore, all that can be done is to save any unfortunate person on the street from the ghosts.

The pedestrian street can be represented as a one-dimensional coordinate system. There is one person hanging out on the pedestrian street. At the time $$$0$$$ he is at coordinate $$$x$$$, moving with a speed of $$$1$$$ unit per second. In particular, at time $$$i$$$ the person will be at coordinate $$$x+i$$$.

The ghosts are going to cast $$$n$$$ curses on the street. The $$$i$$$-th curse will last from time $$$tl_i-1+10^{-18}$$$ to time $$$tr_i+1-10^{-18}$$$ (exclusively) and will kill people with coordinates from $$$l_i-1+10^{-18}$$$ to $$$r_i+1-10^{-18}$$$ (exclusively). Formally that means, that the person, whose coordinate is between $$$(l_i-1+10^{-18},r_i+1-10^{-18})$$$ in the time range $$$(tl_i-1+10^{-18},tr_i+1-10^{-18})$$$ will die.

To save the person on the street, AquaMoon can stop time at any moment $$$t$$$, and then move the person from his current coordinate $$$x$$$ to any coordinate $$$y$$$ ($$$t$$$, $$$x$$$ and $$$y$$$ are not necessarily integers). The movement costs AquaMoon $$$|x-y|$$$ energy. The movement is continuous, so if there exists some cursed area between points $$$x$$$ and $$$y$$$ at time $$$t$$$, the person will die too.

AquaMoon wants to know what is the minimum amount of energy she needs to spend in order to save the person on the street from all $$$n$$$ curses. But she is not good at programming. As her friend, can you help her?

## Input Format
The first line contains a single integer $$$n$$$ ($$$1\le n\le 2000$$$) — the number of curses.

The next line contains a single integer $$$x$$$ ($$$1\le x\le 10^6$$$) — the initial coordinate of the person.

The following $$$n$$$ lines contain four integers $$$tl_i$$$, $$$tr_i$$$, $$$l_i$$$, $$$r_i$$$ each ($$$1\le tl_i\le tr_i\le 10^6$$$, $$$1\le l_i\le r_i\le 10^6$$$).

## Output Format
Print a single integer — the minimum energy which AquaMoon needs to spent, rounded up to the nearest integer (in case there are two nearest integers you should round the answer to the highest of them).

## Examples
```input
2
1
1 2 1 2
2 3 2 3
```
```output
2
```
-----
```input
3
4
1 4 1 2
1 4 4 15
6 7 1 4
```
```output
8
```
-----
```input
4
3
1 5 1 1
4 10 1 4
1 2 3 13
1 10 7 19
```
```output
14
```
-----
```input
7
5
78 96 76 91
6 16 18 37
53 63 40 56
83 88 21 38
72 75 17 24
63 63 53 60
34 46 60 60
```
```output
20
```

Now solve the problem and return the code.