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 JavaScript (node.js v5.12) (judge verdict: Wrong Answer)

function Main(input) {
  input = input.split("\n");
  tmp1 = input[0].split(" ");
  var n = parseInt(tmp1[0]);
  var a = parseInt(tmp1[1]);
  tmp= input[1].split(" ");
  x=new Array(n);
  var sum2=0;
  for(i=0;i<tmp.length;i++){
    x[i]=parseInt(tmp[i]);
  }
  var s=0;
  for(i=0;i<n;i++){
    sum2=sum2+x[i];
  }
  var b = new Array(sum2+1);
  for(var y = 0; y < sum2+1; y++) {
    b[y] = new Array(n+1).fill(0);
  }
  b[0][0]=1;
  for(j=0;j<n;j++){
    for(i=sum2;i>=0;i--){
      for(k=0;k<n+1;k++){
        if(b[i][k]>=1){
          b[i+x[j]][k+1]=b[i+x[j]][k+1]+b[i][k];
        }
      }
    }
  }
  for(i=1;i<=n && i*a<sum2;i++){
      s=s+b[i*a][i];
  }


  console.log('%s', s);
}
Main(require("fs").readFileSync("/dev/stdin", "utf8"));