Statistics

It is time to select courses for your last semester of university. There are $N$ courses available, numbered from $1$ through $N$. Course $i$ is worth $v\_i$ units, and you need at least $V$ units to graduate. Because you want more time to train for ACM ICPC, you want to choose a subset of courses that gives exactly $V$ units. Also, you want to choose the least number of courses possible to minimize the amount of time spent walking around campus. You call such a subset a good schedule.

You are having trouble choosing among all possible good schedules, so you turn to statistics for help. For each good schedule, viewing it as a list of the units of its courses, you calculate:

• $a$, the average value.
• $b$, the median value. (In case the list's length is even, use the smaller of the two middle values.)
• $c$, the maximum number of times a single value appears.
• $d$, the difference between the maximum value and the minimum value.

For each of $a$, $b$, $c$, and $d$, find its minimum over all good schedules.

The first line contains two integers, $N$ and $V$: the number of courses and the number of units you need to graduate ($1 \leq N, V \leq 5000$).

The next line contains $N$ integers $v\_1, v\_2, \ldots, v\_N$, the number of units in each of the available courses ($1 \leq v\_i \leq V$).

Print out four space-separated real numbers: the minimum $a$, $b$, $c$, and $d$ over all good schedules, in that order. If there are no good schedules, print a single integer $-1$ instead. Your answer must have an absolute or relative error less than $10^{-6}$.