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())
m=list(map(lambda x:int(x)-a,input().split()))
x=max(abs(max(m)),abs(min(m)))*n
dp=[[0for _ in range(2*x+1)]for i in range(n)]
dp[0][0+x]+=1
dp[0][m[0]+x]+=1
for i in range(1,n):
  y=m[i]
  for j in range(2*x+1):
    if 0<=j+y and j+y<2*x+1:
      dp[i][j+y]+=dp[i-1][j]
    dp[i][j]+=dp[i-1][j]
  #print(y,dp[i])
print(max(0,dp[n-1][0+x]-1))