All submissions for this problem are available.###Read problems statements [Mandarin](http://www.codechef.com/download/translated/LTM67TST/mandarin/DLINE.pdf) , [Bengali](http://www.codechef.com/download/translated/LTM67TST/bengali/DLINE.pdf) , [Hindi](http://www.codechef.com/download/translated/LTM67TST/hindi/DLINE.pdf) , [Russian](http://www.codechef.com/download/translated/LTM67TST/russian/DLINE.pdf) and [Vietnamese](http://www.codechef.com/download/translated/LTM67TST/vietnamese/DLINE.pdf) as well. There is an infinite sheet of paper and a pen. At any time, the pen may be placed above a point $(x, y)$ on the paper or touching it at a point $(x, y)$; in both cases, we call the point $(x, y)$ the *position* of the pen. The initial position of the pen is $(0, 0)$. You may perform the following types of actions: - move the pen down until it touches the paper - lift the pen (if it was touching the paper); after this action, the pen is not touching the paper - move the pen from its current position $(x, y)$ to $(x-1, y)$ or $(x+1, y)$ - move the pen from its current position $(0, y)$ to $(0, y+1)$ Actions of the first two types take no time, an action of the third type takes $1$ second and an action of the fourth type takes $1$ second. Each action may be performed any number of times. You may only move the pen for at most $P$ seconds in total. Whenever the pen is moved from $(x_1, y_1)$ to $(x_2, y_2)$ while touching the paper, it draws a line segment between these points (inclusive). Drawing over a line segment repeatedly is allowed. You are given $N$ *special* line segments; each of them is parallel with the $x$-axis. A special line segment is *fully drawn* if each point belonging to it also belongs to some drawn line segment. Your goal is to fully draw as many special line segments as possible in $P$ seconds. How many can you fully draw? ### Input - The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows. - The first line of each test case contains two space-separated integers $N$ and $P$. - Each of the next $N$ lines contains three space-separated integers $y$, $s$ and $e$ denoting a special line segment between points $(s, y)$ and $(e, y)$ (including these points). ### Output For each test case, print a single line containing one integer — the maximum number of special segments you can fully draw. ### Constraints - $1 \le T \le 15$ - $1 \le N \le 1,000$ - $0 \le s \le e \le 10^6$ - $0 \le P \le 10^6$ - $0 \le y \le 2,000$ - the special line segments do not touch or intersect ### Subtasks **Subtask #1 (10 points):** $1 \le N \le 10$ **Subtask #2 (90 points):** original constraints ### Example Input ``` 4 1 2 0 1 2 3 13 1 1 2 3 1 3 1 3 4 3 14 1 1 2 3 1 3 1 3 4 4 10 1 3 4 1 1 2 2 1 2 2 3 4 ``` ### Example Output ``` 1 2 3 3 ``` ### Explanation
|Tags||arpa, dynamic-programming, ltime67|
|Time Limit:||1 sec|
|Source Limit:||50000 Bytes|
|Languages:||C, CPP14, JAVA, PYTH, PYTH 3.6, PYPY, CS2, PAS fpc, PAS gpc, RUBY, PHP, GO, NODEJS, HASK, rust, SCALA, swift, D, PERL, FORT, WSPC, ADA, CAML, ICK, BF, ASM, CLPS, PRLG, ICON, SCM qobi, PIKE, ST, NICE, LUA, BASH, NEM, LISP sbcl, LISP clisp, SCM guile, JS, ERL, TCL, kotlin, PERL6, TEXT, SCM chicken, PYP3, CLOJ, COB, FS|
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