14765번 - Studying For Exams 스페셜 저지다국어

It is exam time! You have, of course, been spending too much time participating in various programming contests and have not done much studying. Now you have N subjects to study for, but only a limited amount of time before the final exams. You have to decide how much time to allocate to studying each subject, so that your average grade over all N subjects is maximized.

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_it ² + b_it + c_i, satisfying the following properties:

• f_i(0) ≥ 0;
• f_i(T) ≤ 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?

The first line of each input contains the integers N (1 ≤ N ≤ 10) and T (1 ≤ T ≤ 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 in a single line the maximum average grade you can obtain. Answers within 0.01 of the correct answer will be accepted.