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 PHP (5.6.30) (judge verdict: Time Limit Exceeded)

<?php
/*
    Problem URL : http://arc060.contest.atcoder.jp/tasks/arc060_a

    Score  :
    Result :
    Time   : ms
    Memory : KB
 */

$ans = 0;

fscanf(STDIN, "%d %d", $N, $A);
$x = explode(" ", trim(fgets(STDIN)));
$b = pow(2, $N);
for ($i = 1; $i < $b; $i++) {
    $strB = str_split(str_pad(decbin($i), $N, '0', STR_PAD_LEFT));
    $tmp = 0;
    $kazu = 0;
    for ($j = 0; $j < $N; $j++) {
        $tmp += $strB[$j] * $x[$j];
        $kazu += $strB[$j];
    }

    if ($tmp / $kazu == $A) {
        $ans++;
    }
}

echo $ans . PHP_EOL;