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 Ruby (2.3.3) (judge verdict: Runtime Error)

N,A = gets.split(/\s/).map {|s|s.to_i}
X_list = gets.split(/\s/).map {|s|s.to_i}

check = true
X_list.each do |x|
  if(x!=A)then
    check = false
    break
  end
end

if(check)then
  puts 2**N-1
  exit
end

cnt = 0
for i in 0..2**N-1 do
  si = i.to_s(2)
  if(si.size < N)then
    si = "0" * (N-si.size) + si
  end
  #p si
  calc = 0
  one_sum = 0
  for i in 0..N-1 do
    calc += X_list[i] * si[i].to_i
    if(si[i].to_i==1)then
      one_sum += 1
    end
  end

  if(one_sum!=0)then
    if(calc.to_f/one_sum.to_f == A.to_f)then
      cnt += 1
      #p si
    end
  end
end

puts cnt
~