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.

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.

Examples

Input

4 8
7 9 8 9


Output

5


Input

3 8
6 6 9


Output

0


Input

8 5
3 6 2 8 7 6 5 9


Output

19


Input

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


Output

8589934591
n,a=map(int,input().split())
X=[int(i) for i in input().split()]
DP=[[[0 for i in range(50*n+1)] for i in range(n+1)] for i in range(n+1)]
DP[0][0][0]=1
for i in range(1,n+1):
  for j in range(i+1):
    for s in range(50*j+1):
      DP[i][j][s]=DP[i-1][j][s]+DP[i-1][j-1][s-X[i-1]]
ans=0
for j in range(1,n+1):
  ans+=DP[n][j][j*a]
print(ans)