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: Accepted)

<?php
fscanf(STDIN, "%d %d", $n, $a);
$x = explode(' ', trim(fgets(STDIN)));

for ($i = 0; $i < $n; $i++) {
	$x[$i] -= $a;
}
$sum = array(0 => 0, $x[0] => 1);
for ($i = 1; $i < $n; $i++) {
	$tmp = array();
	foreach ($sum as $k => $v) {
		$tmp[$k + $x[$i]] = $v;
	}
	if (isset($tmp[$x[$i]])) {
		$tmp[$x[$i]]++;
	} else {
		$tmp[$x[$i]] = 1;
	}
	foreach ($tmp as $k => $v) {
		if (isset($sum[$k])) {
			$sum[$k] += $v;
		} else {
			$sum[$k] = $v;
		}
	}
}
echo $sum[0], "\n";