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=list(map(int,input().split()))
X=max(max(x),A)
y=[x[i]-A for i in range(N)]
dp=[[0 for i in range(2*N*X+1)] for j in range(N+1)]
dp[0][N*X]=1
for j in range(1,N+1):
  for k in range(2*N*X+1):
    dp[j][k]=dp[j-1][k]
    if 0<= k-y[j-1] and k-y[j-1]<=2*N*X:
      dp[j][k]+=dp[j-1][k-y[j-1]]
print(dp[N][N*X]-1)