Problem X
Studying For Exams

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As a seasoned programming contest competitor, you recognize immediately that you can determine the optimal allocation with a computer program. Of course, you have decided to ignore the amount of time you spend solving this problem (i.e. procrastinating).

You have a total of $T$ hours that you can split among different subjects. For each subject $i$, the expected grade with $t$ hours of studying is given by the function $f_i(t)=a_i{t}^2+b_{i}t+c_i$, satisfying the following properties:

• $f_i(0)\ge 0$;

• $f_i(T)\le 100$;

• $a_i<0$;

• $f_i(t)$ is a non-decreasing function in the interval $[0,T]$.

You may allocate any fraction of an hour to a subject, not just whole hours. What is the maximum average grade you can obtain over all $n$ subjects?

Input

The first line of each input contains the integers $N$ ($1\le N\le 10$) and $T$ ($1\le T\le 240$) separated by a space. This is followed by $N$ lines, each containing the three parameters $a_i$, $b_i$, and $c_i$ describing the function $f_i(t)$. The three parameters are separated by a space, and are given as real numbers with $4$ decimal places. Their absolute values are no more than $100$.

Output

Output in a single line the maximum average grade you can obtain. Answers within $0.01$ of the correct answer will be accepted.

2 96
-0.0080 1.5417 25.0000
-0.0080 1.5417 25.0000

80.5696000000

3 34
-0.0657 4.4706 23.0000
-0.0562 3.8235 34.0000
-0.0493 3.3529 42.0000

70.0731488027