class INPUT:
  def __init__(self):
    from sys import argv
    if argv[-1] in ["./Main.py","prog.py","Main.py"]:#Atcoder:./Main.py,Wandbox:prog.py,yukicoder:Main.py
      self.l=open(0).read().split()[::-1]
    else:
      self.l=open("_input.txt",mode="r").read().split()[::-1]
    self.length=len(self.l)
    return

  def stream(self,k=1,f=int,f2=False):
    assert(-1<k)
    m=self.length
    if m==0 or m<k:
      raise Exception("There is no input!")
    elif f!=str:
      if k==0:
        self.length=0
        return list(map(f,self.l[::-1]))
      if k==1 and not f2:
        self.length-=1
        return f(self.l.pop())
      if k==1 and f2:
        self.length-=1
        return [f(self.l.pop())]
      ret=[]
      for _ in [0]*k:
        ret.append(f(self.l.pop()))
      self.length-=k
      return ret
    else:
      if k==0:
        self.length=0
        return self.l[::-1]
      if k==1 and not f2:
        self.length-=1
        return self.l.pop()
      if k==1 and f2:
        self.length-=1
        return [self.l.pop()]
      ret=[]
      for _ in [0]*k:
        ret.append(self.l.pop())
      self.length-=k
      return ret
pin=INPUT().stream

"""
pin(number[default:1],f[default:int],f2[default:False])
if number==0 -> return left all
eclipse 等では_input.txtを使うこと。
listを変数で受け取るとき、必ずlistをTrueにすること。
"""
from collections import Counter
from sys import setrecursionlimit
setrecursionlimit(10000000)

N,W=pin(2)
A=pin(0)
if W==0 and A==[0]*N:
  exit(print(pow(2,N)-1))
n=pow(2,N)
b=[[Counter()for __ in [0]*n]for _ in [0]*N]
cnt=[[Counter()for __ in [0]*n]for _ in [0]*N]
f=[pow(2,i)for i in range(N)]
def rec(m,w,d):
  if m==0:
    if w==0:
      #print(d)
      return set([d])
    else:
      return set([0])
#   if b[m-1][0][w-A[m-1]]==0:
#     r1=set()
#     #if w-A[m-1]>=0:
#     r1=rec(m-1,w-A[m-1],d+pow(2,m-1))
#     #print(type(r1))
#     cnt[m-1][0][w-A[m-1]]=r1
#     b[m-1][0][w-A[m-1]]=1
#
#   if b[m-1][1][w-A[m-1]//2]==0:
#     r2=set()
#     #if w-A[m-1]//2>=0:
#     r2=rec(m-1,w-A[m-1]//2,d+pow(2,m-1))
#     #print(type(r2))
#     cnt[m-1][1][w-A[m-1]//2]=r2
#     b[m-1][1][w-A[m-1]//2]=1
#   if b[m-1][2][w]==0:
#     r3=rec(m-1,w,d)
#     #print(type(r3))
#     cnt[m-1][2][w]=r3
#     b[m-1][2][w]=1
#   if 0 in [cnt[m-1][0][w-A[m-1]],cnt[m-1][1][w-A[m-1]//2],cnt[m-1][2][w]]:
#     print(cnt[m-1][0][w-A[m-1]],cnt[m-1][1][w-A[m-1]//2],cnt[m-1][2][w])
#     print(b[m-1][0][w-A[m-1]],b[m-1][1][w-A[m-1]//2],b[m-1][2][w])
#     print(m,w,d)
#     raise Exception
  #print(cnt[m-1][w-A[m-1]],cnt[m-1][w-A[m-1]//2],cnt[m-1][w])
  #print(type(cnt[m-1][w-A[m-1]]),type(cnt[m-1][w-A[m-1]//2]),type(cnt[m-1][w]))
  #return cnt[m-1][0][w-A[m-1]]|cnt[m-1][1][w-A[m-1]//2]|cnt[m-1][2][w]
  if b[m-1][d+f[m-1]][w-A[m-1]]==0:
    b[m-1][d+f[m-1]][w-A[m-1]]=1
    cnt[m-1][d+f[m-1]][w-A[m-1]]=rec(m-1,w-A[m-1],d+f[m-1])
  if b[m-1][d+f[m-1]][w-A[m-1]//2]==0:
    b[m-1][d+f[m-1]][w-A[m-1]//2]=1
    cnt[m-1][d+f[m-1]][w-A[m-1]//2]=rec(m-1,w-A[m-1]//2,d+f[m-1])
  if b[m-1][d][w]==0:
    b[m-1][d][w]=1
    cnt[m-1][d][w]=rec(m-1,w,d)
  return cnt[m-1][d+f[m-1]][w-A[m-1]]|cnt[m-1][d+f[m-1]][w-A[m-1]//2]|cnt[m-1][d][w]
 # return rec(m-1,w-A[m-1],d+f[m-1])|rec(m-1,w-A[m-1]//2,d+f[m-1])|rec(m-1,w,d)
ans=rec(N,W,0)
#print(ans)
print(len(ans)-1)
# for i in cnt:
#   print(i)