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?

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.

Constraints

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

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.

见题面 Input 部分

见题面 Output 部分