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(input) {
  input = input.split('\n');
  var tmp = input[0].split(' ');

  var N = Number(tmp[0]);
  var A = Number(tmp[1]);

  var x = [0];
  x = x.concat(input[1].split(' ').map(Number));

  var dp = new Array(N + 1);
  for (var i = 0; i <= N; ++i) {
    dp[i] = new Array(N + 1);
    for (var j = 0; j <= N; ++j) {
      dp[i][j] = new Array(A * N + 1).fill(0);
    }
  }

  for (var i = 0; i < N; ++i) dp[i][0][0] = 1;

  for (var i = 1; i <= N; ++i) {
    for (var j = 1; j <= i; ++j) {
      for (var k = 1; k <= A * N; ++k) {
        if (k < x[i]) {
          dp[i][j][k] = dp[i - 1][j][k];
        } else {
          dp[i][j][k] = dp[i - 1][j][k] + dp[i - 1][j - 1][k - x[i]];
        }
      }
    }
  }

  var ans = 0;
  for (var j = 1; j <= N; ++j) {
    ans += dp[N][j][j * A];
  }

  console.log(ans);
}

main(require('fs').readFileSync('/dev/stdin', 'utf8'));