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(lambda x: int(x)-a, input().split()))
k=[[0]*3000 for i in range(60)]
for i in range(3000):
    k[0][i]=0
k[0][x[0]+1500]+=1
k[0][1500]+=1
for i in range(1, n):
    for j in range(3000):
        if 3000>j-x[i]>=0:
            k[i][j]=k[i-1][j-x[i]]+k[i-1][j]
        else:
            k[i][j]=k[i-1][j]
print(k[n-1][1500]-1)