local bls, brs = bit.lshift, bit.rshift
local bxor = bit.bxor

local function grayCode(x)
  return bxor(x, brs(x, 1))
end

-- add_func(idx), rm_func(idx), work_func()
local function grayWalk(size, add_func, rm_func, work_func)
  local prv = 0
  local total = bls(1, size) - 1
  local bpos = {}
  for i = 1, size do
    bpos[bls(1, i - 1)] = i
  end
  work_func()
  for i = 1, total do
    local v = grayCode(i)
    if prv < v then
      prv, v = v, v - prv
      add_func(bpos[v])
    else
      prv, v = v, prv - v
      rm_func(bpos[v])
    end
    work_func()
  end
end


local n, w = io.read("*n", "*n")
local a = {}
for i = 1, n do
  a[i] = io.read("*n")
end

local ret = 0
local box = {}
local subbox = {}
local subcnt = 0
local subv = 0
local f = false
local function subadd(idx)
  subv = subv - brs(a[subbox[idx]], 1)
end
local function subrm(idx)
  subv = subv + brs(a[subbox[idx]], 1)
end
local function subwork()
  if w == subv then
    f = true
  end
end

for i = 1, n do box[i] = false end
local function add_func(idx)
  box[idx] = true
end
local function rm_func(idx)
  box[idx] = false
end
local function work_func()
  subcnt = 0
  subv = 0
  f = false
  for i = 1, n do
    if box[i] then
      subcnt = subcnt + 1
      subbox[subcnt] = i
      subv = subv + a[i]
    end
  end
  grayWalk(subcnt, subadd, subrm, subwork)
  if f then ret = ret + 1 end
end
grayWalk(n, add_func, rm_func, work_func)
if w == 0 then ret = ret - 1 end
print(ret)