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()))
sx = sum(x)
dp=[[0]*(N+1) for i in range(sx+1)]
dp[0][0]=1
for i in range(N):
  dp_sub=[[0]*(N+1) for j in range(sx+1)]#k枚のカードでsxを表す場合が何通りあるかを記録しておく
  for j in range(sx+1):
    for k in range(N+1):
      if dp[j][k]!=0:
        dp_sub[j+x[i]][k+1]=dp[j][k]
  for j in range(sx+1):
    for k in range(N+1):
      dp[j][k]+=dp_sub[j][k]#dp_subの結果をdpに反映

cnt=0

for i in range(min(sx//A,N)):
  cnt+=dp[A*(i+1)][i+1]
print(cnt)