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()))

MAXSUM = sum(X)+5
dp = [[[0 for _ in range(MAXSUM)] for _ in range(N+5)] for _ in range(N+5)]
for i in range(N):
  dp[i+1][1][X[i]] += 1
  for k in range(N):
    for j in range(MAXSUM):
      dp[i+1][k][j] += dp[i][k][j]
      if X[i]+j < MAXSUM:
        dp[i+1][k+1][X[i]+j] += dp[i][k][j]
#print(dp)
ans = 0
for i in range(N):
  if A*(i+1) < MAXSUM:
    ans += dp[N][i+1][A*(i+1)]
print(ans)