program main
  implicit none
  integer*8::N,k,tmp,total,i,j
  integer*8,allocatable::a(:),b(:)
  integer*8,parameter::modular=1000000007
  read *,N,k
  allocate(a(0:k+1))
  allocate(b(0:k+1))

  a(0)   = 0
  a(k+1) = 2**N-1
  if(k.ne.0) then
     read *, a(1:k)
  end if
  b = qsort(a)

  do i=1, k-1
     tmp = IAND(b(i),b(i+1))
     if(tmp.ne.b(i)) then
        print '(i0)',0
        return
     end if
  end do

  total = 1
  do i=0, k
     tmp = 1
     do j=2,POPCNT(b(i+1))-POPCNT(b(i))
        tmp = MOD(tmp * j, modular)
     end do
     total = MOD(total * tmp, modular)
  end do
  print '(i0)', total
contains
  recursive function qsort(x) result(y)
    integer*8,intent(in) ::x(:)
    integer*8,allocatable::y(:)
    integer*8::pivot,total
    total = size(x)
    if (total <=1) then
       y = x
    else
       pivot = x(total/2)
       y = [qsort(pack(x, x .lt. pivot)), &
            pack(x, x .eq. pivot),        &
            qsort(pack(x, x .gt. pivot))]
    endif
  end function qsort
end program main