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 (3.4.3) (judge verdict: Accepted)


line1=input().split()
n=int(line1[0])
a=int(line1[1])
nums=input().split()
for i in range(n):
    nums[i]=int(nums[i])-a

works={}

works[0]=1
s=0
for x in nums:

    if x>=0:
        for i in range(50*(n+1),-50*(n+1), -1):
            try:
                works[i]+=works[i-x]
            except:
                try:
                    works[i]=works[i-x]
                except:
                    pass
    else:
        for i in range (-50*(n+1),50*(n+1)):
            try:
                works[i+x]+=works[i]
            except:
                try:
                    works[i+x]=works[i]
                except:
                    pass

print (works[0]-1)