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 Python (3.8.2) (judge verdict: Runtime Error)

from collections import deque

n,a=map(int,input().split())
cards=list(map(int,input().split()))


noz=[x-a for x in cards].count(0)
pl=[x-a for x in cards if x-a>0]
nl=[a-x for x in cards if x-a<0]
sl=[pl,nl][len(nl)<=len(pl)]
ll=[pl,nl][len(pl)<len(nl)]

sl.sort()
ll.sort()

sumfunc = lambda n, l: sum([l[x]*((n>>x)&1) for x in range(len(l))])

ssl=sum(sl)
sll=sum(ll)
sumsl=[0 for _ in range(ssl)]
sumll=[0 for _ in range(sll)]
sumsl[sl[-1]-1]=1
sumll[ll[-1]-1]=1
for i in range(1,2**(len(sl)-1)):
    s=sumfunc(i,sl)
    sumsl[s-1]+=1
    sumsl[s+sl[-1]-1]+=1
for i in range(1,2**(len(ll)-1)):
    s=sumfunc(i,ll)
    sumll[s-1]+=1
    sumll[s+ll[-1]-1]+=1
count=sum([x*y for x,y in zip(sumsl, sumll)])
# count=0
# p=sum([not sumsl[-1]<sumfunc(2**i,ll) for i in range(1,len(ll)+1)])
# q=sum([sumsl[0]>=sumfunc(2**i-1,ll) for i in range(1,len(ll)+1)])
# count=[sumfunc(j,ll) in sumsl for j in range(2**q-1,2**p)].count(True)

print((count+1)*(2**noz)-1)