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-----
4 8
7 9 8 9

-----Sample Output-----
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.

见题面

见题面