Statistics

You are choosing 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. You also want to choose the fewest courses possible, so you spend less time walking around campus. Such a subset is called a good schedule.

You want to pick among all good schedules with the help of some statistics. For each good schedule, view it as a list of the units of its courses and calculate the following values.

• $a$: the average value.
• $b$: the median value. If the list has an even length, 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 course ($1 \leq v_i \leq V$).

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