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()))
X = list(map(lambda x: x - A, X))
maxx = max(max(X), -min(X))
#前から(i + 1)個見て、和が(j - N * maxx)のもの
dp = [[0] * (2 * N * maxx + 1) for _ in range(N + 1)]
dp[0][N * maxx] = 1
for i in range(N):
  for j in range(2 * N * maxx + 1):
    if 0 <= j + X[i] <= 2 * N * maxx:
      dp[i + 1][j + X[i]] = dp[i][j] + dp[i][j + X[i]]
    else:
      dp[i + 1][j] = dp[i][j]
print(dp[N][N * maxx] - 1)
#print(dp)
#print(X)