Contest: Task: Related: TaskB

Score : $300$ points

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?

- $1 \leq N \leq 50$
- $1 \leq A \leq 50$
- $1 \leq x_i \leq 50$
- $N,\,A,\,x_i$ are integers.

- $200$ points will be awarded for passing the test set satisfying $1 \leq N \leq 16$.

The input is given from Standard Input in the following format:

$N$ $A$ $x_1$ $x_2$ $...$ $x_N$

Print the number of ways to select cards such that the average of the written integers is exactly $A$.

4 8 7 9 8 9

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.

3 8 6 6 9

0

8 5 3 6 2 8 7 6 5 9

19

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

8589934591

- The answer may not fit into a $32$-bit integer.