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()))

dp=[[[0]*(a*n+1) for i in range(n+1)] for i in range(n+1)]
dp[0][0][0]=1
#dp[i番目のカード][選んだ枚数][数の合計]=何組あるか
for i in range(n):
    for j in range(n):
        for k in range(a*n+1):
            if k+x[i]<=a*n:
                #i番目を入れる場合
                dp[i+1][j+1][k+x[i]]+=dp[i][j][k]
            #いれない場合
            dp[i+1][j][k]+=dp[i][j][k]
ans=0
cnt=0
#print(*dp,sep='\n')
for i in dp[-1]:
    ans+=i[cnt*a]
    cnt+=1
print(ans-1)