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
def makelist2(n,m):
    return[[0 for k in range(m)]for i in range(n)]

n,a = map(int,input().split())
x = list(map(int,input().split()))
X = max(x)
X = max(X,a)
b=[]
for i in range(n):
    b.append(x[i]-a)


dp =makelist2(n+1,2*n*X+1)
dp[0][n*X] = 1
for j in range(n+1):
    for t in range(2*n*X+1):
        if j>=1 and (t-b[j-1] < 0 or t-b[j-1]>2*n*X):
            dp[j][t] = dp[j-1][t]
        elif j>= 1:
            dp[j][t] = dp[j-1][t] + dp[j-1][t-b[j-1]]
print(dp[n][n*X]-1)