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: Accepted)

function Main(s) {
  s[0] = s[0].split(" ").map(a => parseInt(a));
  var n = s[0][0];
  var a = s[0][1];
  var x = s[1].split(" ").map(a => parseInt(a));
  var b = Array(2).fill(0).map(a => Array(n + 1).fill(0).map(a => Array(50 * n + 1).fill(0)));
  var ans = 0;
  b[0][0][0] = 1;
  for(var i = 1; i <= n; i++){
    b[i&1][0][0] = 1;
    for(var j = 1; j <= i; j++){
      for(var k = 0; k <= j * 50; k++){
        b[i&1][j][k] = b[(i+1)&1][j][k];
        if(k >= x[i-1])b[i&1][j][k] += b[(i+1)&1][j-1][k-x[i-1]];
      }
    }
  }
  for(var j = 1; j <= n; j++){
    ans += b[n&1][j][j*a];
  }
  console.log(ans);
}
Main(require("fs").readFileSync("/dev/stdin", "utf8").split("\n"));