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 Pascal (FPC 2.6.2) (judge verdict: Accepted)

var
	n,a,i,j,x,L,R:Longint;
	dp:array[0..50,0..5000]of int64;
begin
	read(n,a);
	dp[0,n*a]:=1;
	for i:=1 to n do begin
		for j:=0 to 5000 do dp[i,j]:=dp[i-1,j];
		read(x);
		x:=a-x;
		L:=-x;
		if L<0 then L:=0;
		R:=5000-x;
		if R>5000 then R:=5000;
		for j:=L to R do begin
			inc(dp[i,j+x],dp[i-1,j]);
		end;
	end;
	writeln(dp[n,n*a]-1);
end.