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: Wrong Answer)

object Main extends App {
  val scan = new java.util.Scanner(System.in)
  val n = scan.next().toInt
  val a = scan.next().toDouble
  val xs = (1 to n).toArray.map(_ => scan.next().toInt)
  val memo = Array.fill(n+1, n+1,2501)(-1)
  memo(0)(0)(0) = 0
  for (i<-1 to n; j<-0 to n; k<-0 to 2500) {
    if (memo(i-1)(j)(k) != -1) { 
      if (memo(i)(j)(k) == -1) memo(i)(j)(k) = 0
      memo(i)(j)(k) = memo(i-1)(j)(k)
    }
    if ((k-xs(i-1)>=0 && j-1>=0 && memo(i-1)(j-1)(k-xs(i-1)) != -1)) {
      if (memo(i)(j)(k) == -1) memo(i)(j)(k) = 0
      memo(i)(j)(k) += 1
    } 
  }

  println((for (j<-1 to n; k<-0 to 2500; if memo(n)(j)(k) != -1 && k%j==0 && k/j==a) yield memo(n)(j)(k)).sum)
}