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()))

p=[];z=0;n=[]
for xi in x:
    if xi>A:
        p.append(xi-A)
    elif xi==A:
        z+=1
    elif xi<A:
        n.append(A-xi)

K=min(sum(p),sum(n))

Pa=[0 for j in range(K+1)];Pa[0]=1
Na=[0 for j in range(K+1)];Na[0]=1

for pi in p:
    for j in range(K,pi-1,-1):
        Pa[j]+=Pa[j-pi]
for ni in n:
    for j in range(K,ni-1,-1):
        Na[j]+=Na[j-ni]

ans=2**z-1 # zのみ
for j in range(1,K+1):
    ans+=2**z*Pa[j]*Na[j]

print(ans)