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)

class Main {
  import java.{ util => ju }

  import scala.annotation._
  import scala.collection._
  import scala.collection.{ mutable => mu }
  import scala.collection.JavaConverters._
  import scala.math._
  val sc = new ju.Scanner(System.in)

  def solveC() {
    val br = new java.io.BufferedReader(new java.io.InputStreamReader(System.in))
    val n = br.readLine().toInt
    val x = br.readLine().split(" ").map { _.toInt }
    val l = br.readLine().toInt
    val q = br.readLine().toInt

    val days = Array.ofDim[Int](n, n)
    for (i <- 0 until n - 1) {
      var result = 0
      for (j <- i + 1 until n) {
        val move = x(j) - x(j - 1)
        if (move <= result) {
          days(i)(j) = days(i)(j - 1)
          result -= move
        } else {
          result = l
          days(i)(j) = days(i)(j - 1) + 1
          result -= move
        }
      }
    }

    for (i <- 0 until q) {
      val fromTo = br.readLine().split(" ").map(_.toInt)
      val from = fromTo.min - 1
      val to = fromTo.max - 1
      println(days(from)(to))
    }

    br.close()
  }

  def solveA() {
    val n = sc.nextInt()
    val a = sc.nextInt()
    val nums = Array.fill[Int](n)(sc.nextInt())
    var nowCount = 0
    var total = 0l
    for (i <- 1 to n) {
      nowCount = i
      calc(0, 0, 0)
    }

    def calc(count: Int, index: Int, sum: Int) {
      if (count == nowCount) {
        if (count * a == sum) {
          total += 1
        }
      } else {
        if (index < n) {
          calc(count + 1, index + 1, sum + nums(index))
          calc(count, index + 1, sum)
        }
      }
    }

    println(total)

  }
}

object Main {
  def main(args: Array[String]): Unit = {
    val app = new Main()
    app.solveA()
    //    app.solveC()

  }
}