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.