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 = [int(i) for i in input().split()]

table = [[[0]*(N*A+1) for i in range(N+1)] for j in range(N+1)]
table[0][0][0] = 1

for j in range(1,N+1):
  for k in range(j+1):
    for s in range(N*A+1):
      c = x[j-1]
      if s-c<0:
        table[j][k][s] = table[j-1][k][s]
      elif s-c>=0 and k>=1:
        table[j][k][s] = table[j-1][k][s] + table[j-1][k-1][s-c]
      
ans = 0
for i in range(1,N+1):
  ans += table[N][i][i*A]
print(ans)