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: Accepted)

import io.{StdIn => in}

object Main extends App {
  val Array(n, a) = in.readLine.split(" ").map(_.toInt)
  val x = in.readLine.split(" ").map(_.toInt).sorted
  val sumMax = math.max(x.max * n, a * n)
  val dp = Array.ofDim[Long](n+1, n+1, sumMax + 1)

  for(i <- 0 to n) dp(i)(0)(0) = 1
  for{
      i <- 1 to n; xi = i - 1
      j <- 1 to n; if j <= i
      k <- 1 to sumMax
    } {
      dp(i)(j)(k) =
        if(k < x(xi)) dp(i-1)(j)(k)
        else dp(i-1)(j)(k) + dp(i-1)(j-1)(k-x(xi))

      // if(k == sumMax) println(i + " " + j + " : " + dp(i)(j).mkString(" "))
    }

  val ans = (1 to n)./:(0L)((acc,j) => {
    // println(n + " " + j +  " " + a*j + " : " + dp(n)(j)(a*j))
    acc + dp(n)(j)(a*j)
  })
  println(ans)
}