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 = list(map(int, input().split()))
x = list(map(int, input().split()))
y = [ele-a for ele in x]
m = n*max(a, max(x))
dp = [[0 for _ in range(2*m+1)]for _ in range(n+1)]
dp[0][m] = 1
for j in range(1, n+1):
  for t in range(2*m+1):
    if t-y[j-1]<0 or 2*m<t-y[j-1]:
      dp[j][t] = dp[j-1][t]
    elif 0<=t-y[j-1]<=2*m:
      dp[j][t] = dp[j-1][t] + dp[j-1][t-y[j-1]]
print(dp[n][m]-1)