program main
  implicit none
  integer*8::N,k,total,i,j
  integer*8,allocatable::a(:),b(:)
  integer*8,parameter::modular=1000000007
  integer*8::perm(0:60)
  data perm/ 1,     1,        2,        6,       24,      120,&
                  720,     5040,    40320,   362880,  3628800,&
             39916800,479001600,227020758,178290591,674358851,&
            789741546,425606191,660911389,557316307,146326063,&
             72847302,602640637,860734560,657629300,440732388,&
            459042011,394134213, 35757887, 36978716,109361473,&
            390205642,486580460, 57155068,943272305, 14530444,&
            523095984,354551275,472948359,444985875,799434881,&
            776829897,626855450,954784168, 10503098,472639410,&
            741412713,846397273,627068824,726372166,318608048,&
            249010336,948537388,272481214,713985458,269199917,&
             75195247,286129051,595484846,133605669, 16340084 /
  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
     if(IAND(b(i),b(i+1)).ne.b(i)) then
        print '(i0)',0
        return
     end if
  end do

  total = 1
  do i=0, k
     total = MOD(total * perm(POPCNT(b(i+1))-POPCNT(b(i))), 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