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: Time Limit Exceeded)

function zeroPadding(numStr,n){
  var zeros='';
  for(var k=0;k<n;k++){
    zeros = zeros+'0';
  }
  return (zeros + numStr).slice(-n);
}

function main(input){
  var Lines=input.split('\n');
  Lines[0]=Lines[0].split(' ');
  Lines[1]=Lines[1].split(' ');
  var N=parseInt(Lines[0][0]);
  var A=parseInt(Lines[0][1]);
  var x=Lines[1];
  var M=Math.pow(2,N);
  var counter=0;
  for(var i=1;i<M;i++){
    var b=zeroPadding((i.toString(2)),N);
    var B=0;
    var n=b.match(/1/g).length;
    for(var j=0;j<N;j++){
      B += (b[j]==='1')?parseInt(x[j]):0;
    }
    if(A===B/n){
      counter++;
    }
  }
  console.log(counter);
}

main(require('fs').readFileSync('/dev/stdin', 'UTF-8'));