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()))
cnt=x.count(A)
B=[]
for i in x:
  if i != A:
    B.append(i-A)
#print(cnt,B)

plus=[0]*2501
minus=[0]*2501

for i in B:
  if i>0:
    for j in range(2500,0,-1):
      if plus[j]>0 and j+i<=2500:
        plus[j+i]+=plus[j]
    plus[i]+=1
  if i<0:
    i=-i
    for j in range(2500,0,-1):
      if minus[j]>0 and j+i<=2500:
        minus[j+i]+=minus[j]
    minus[i]+=1

#print(plus[:100])
#print(minus[:100])
    
ans=0
for i in range(2501):
  ans+=plus[i]*minus[i] if plus[i]>0 and minus[i]>0 else 0
#print(ans)
ans*=2**cnt
ans+=2**cnt-1

print(ans)