Codeforces Round 732 (Div. 1) |
---|

Finished |

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

data structures

dp

*3500

No tag edit access

The problem statement has recently been changed. View the changes.

×
E2. AquaMoon and Time Stop (hard version)

time limit per test

7 secondsmemory limit per test

1024 megabytesinput

standard inputoutput

standard outputNote 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

The first line contains a single integer $$$n$$$ ($$$1\le n\le 2 \cdot 10^5$$$) — 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

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

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Apr/15/2024 13:44:48 (g1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|