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,raw_input().split())
x=map(int,raw_input().split())
x.sort()
dp=[[[0]*(n+1) for i in xrange(n*a+1)] for j in xrange(n+1)]
for i in xrange(n+1):
    dp[i][0][0]=1
ans=0
for i in xrange(n):
    for j in xrange(1,n*a+1):
        for k in xrange(1,n+1):
            if i+1<k:break
            if j<x[i]:
                dp[i+1][j][k]=dp[i][j][k]
                continue
            dp[i+1][j][k]=dp[i][j][k]+dp[i][j-x[i]][k-1]
for j in xrange(1,n*a+1):
    for k in xrange(1,n+1):
        if j==a*k:
            ans+=dp[n][j][k]
print(ans)