Problem:
Score : 300 points

Problem Statement

Tak has N cards. On the i-th (1 \leq i \leq N) card is written an integer x_i.
He is selecting one or more cards from these N cards, so that the average of the integers written on the selected cards is exactly A.
In how many ways can he make his selection?

Constraints

1 \leq N \leq 50

1 \leq A \leq 50

1 \leq x_i \leq 50

N,\,A,\,x_i are integers.

Partial Score

200 points will be awarded for passing the test set satisfying 1 \leq N \leq 16.

Input

The input is given from Standard Input in the following format:

N A
x_1 x_2 ... x_N

Output

Print the number of ways to select cards such that the average of the written integers is exactly A.

Sample Input 1

4 8
7 9 8 9

Sample Output 1

5

The following are the 5 ways to select cards such that the average is 8:

Select the 3-rd card.

Select the 1-st and 2-nd cards.

Select the 1-st and 4-th cards.

Select the 1-st, 2-nd and 3-rd cards.

Select the 1-st, 3-rd and 4-th cards.

Sample Input 2

3 8
6 6 9

Sample Output 2

0

Sample Input 3

8 5
3 6 2 8 7 6 5 9

Sample Output 3

19

Sample Input 4

33 3
3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

Sample Output 4

8589934591

The answer may not fit into a 32-bit integer.

Solution in Scala (2.11.7) (judge verdict: Time Limit Exceeded)

import scala.io.Source

object Main extends App {
    val xs = Source.stdin.getLines()
    val Array(n, a) = xs.next().split(' ').map(_.toInt)
    val ds = xs.next().split(' ').map(_.toInt)
    
    println(solve(n, a, ds))
    
    def solve(n: Int, a: Int, ds: Seq[Int]): String = {
        var c = 0
        
        powerset(ds).foreach { dss =>
            val avg = if (dss.length > 0) {
                if (dss.sum % dss.length == 0) {
                    dss.sum / dss.length
                } else {
                    -1
                }
            } else {
                -1
            }
            c = c + (if (avg == a) 1 else 0)
        }
        
        c.toString
    }
    
    def powerset[T](xss: Seq[T]): Seq[Seq[T]] = {
        xss match {
            case Nil =>
                Seq(Seq.empty[T])
            case x +: xs =>
                val qs = powerset(xs)
                val rs = for (ps <- qs) yield x +: ps
                rs ++: qs
        }
    }
}