#define DEB
#include<bits/stdc++.h>
#define REP(i,m) for(int i=0;i<(m);++i)
#define REPN(i,m,in) for(int i=(in);i<(m);++i)
#define ALL(t) (t).begin(),(t).end()
#define CLR(a) memset((a),0,sizeof(a))
#define pb push_back
#define mp make_pair
#define fr first
#define sc second

using namespace std;


#ifdef DEB
#define dump(x)  cerr << #x << " = " << (x) << endl
#define prl cerr<<"called:"<< __LINE__<<endl
#define dumpR(x) cerr<<"\x1b[31m"<<#x<<" = " <<(x)<<"\x1b[39m"<<endl
#define dumpY(x) cerr<<"\x1b[33m"<<#x<<" = " <<(x)<<"\x1b[39m"<<endl
#define dumpG(x) cerr<<"\x1b[32m"<<#x<<" = " <<(x)<<"\x1b[39m"<<endl
template<class T> void debug(T a,T b){ for(;a!=b;++a) cerr<<*a<<' ';cerr<<endl;}
#else
#define dump(x) ;
#define dumpR(x) ;
#define dumpY(x) ;
#define dumpG(x) ;
#define prl ;
template<class T> void debug(T a,T b){ ;}
#endif

template<class T> bool chmin(T& a,const T& b) {
  if(a>b) {
    a=b;
    return true;
  }
  return false;
}
template<class T> bool chmax(T& a,const T& b) {
  if(a<b){
    a=b;
    return true;
  }
  return false;
}

typedef long long int lint;
typedef pair<int,int> pi;

namespace std{
  template<class S,class T>
  ostream &operator <<(ostream& out,const pair<S,T>& a){
    out<<'('<<a.fr<<','<<a.sc<<')';
    return out;
  }
}

//const int INF=5e8;
template<lint mod>
struct Int_{
  unsigned x;
  static unsigned mpow(Int_ a,unsigned k){
    Int_ res=1;
    while(k){
      if(k&1) res=res*a;
      a=a*a;
      k>>=1;
    }
    return res.x;
  }
  static unsigned inverse(Int_ a){
    return mpow(a,mod-2);
  }
  Int_(): x(0) { }
  Int_(long long sig) {
    int sigt=sig%mod;
    if(sigt<0) sigt+=mod;
    x=sigt;
  }
  unsigned get() const { return (unsigned)x; }
  
  Int_ &operator+=(Int_ that) { if((x += that.x) >= mod) x -= mod; return *this; }
  Int_ &operator-=(Int_ that) { if((x += mod - that.x) >= mod) x -= mod; return *this; }
  Int_ &operator*=(Int_ that) { x = (unsigned long long)x * that.x % mod; return *this; }
  Int_ &operator=(Int_ that) { x=that.x; return *this;}
  Int_ &operator/=(Int_ that) { x=(unsigned long long) x * inverse(that.x)%mod; return *this;}
  bool operator==(Int_ that) const { return x==that.x; }
  bool operator!=(Int_ that) const { return x!=that.x; }

  Int_ operator-() const { return Int_(0)-Int_(*this);}
  Int_ operator+(Int_ that) const { return Int_(*this) += that; }
  Int_ operator-(Int_ that) const { return Int_(*this) -= that; }
  Int_ operator*(Int_ that) const { return Int_(*this) *= that; }
  Int_ operator/(Int_ that) const { return Int_(*this) /= that; }
  Int_ inv(){
    return Int_(mpow(x,mod-2));
  }
};

namespace std{
  template<lint mod>
  ostream &operator <<(ostream& out,const Int_<mod>& a){
    out<<a.get();
    return out;
  }
  template<lint mod>
  istream &operator >>(istream& in,Int_<mod>& a){
    in>>a.x;
    return in;
  }
};

typedef Int_<1000000007> Int;

const int M=(1<<16)+10;
Int fact[M+2],invf[M+2];
void prep(){
  fact[0]=invf[0]=1;
  REP(i,M){
    fact[i+1]=fact[i]*(i+1);
  }
  invf[M]=fact[M].inv();
  for(int i=M-1;i>=0;--i) invf[i]=invf[i+1]*(i+1);
}
Int C(int a,int b){
  if(a<0 || b<0 || a<b) return 0;
  return fact[a]*invf[a-b]*invf[b];
}

int n,m;
int ar[20];

Int dp[20][1<<16];
int main(){
  prep();
  cin>>n>>m;
  REP(i,m) cin>>ar[i],--ar[i];
  int n2=(1<<n);

  dp[m][0]=1;
  for(int i=m-1;i>=0;--i){
    REP(j,n2) if(dp[i+1][j].x){
      REP(k,n) if(!(j>>k&1)){
        int rest=n2-ar[i]-j;
        int size=(1<<k);
        if(rest>=size){
          dp[i][j+size]+=dp[i+1][j]*C(rest-1,size-1);
        }
      }
      dp[i][j]+=dp[i+1][j];
    }
  }

  Int res=0;
  REP(i,n2){
    Int tmp=dp[0][i];
    int rest=n2-1-i;
    REP(j,n) if(!(i>>j&1)) tmp*=C(rest,(1<<j)), rest-=(1<<j);
    assert(rest==0);
    int cnt=__builtin_popcount(i);
    if(cnt%2==0) res+=tmp;
    else res-=tmp;
  }
  dump(res);
  Int ans=res*n2;
  REP(i,n) ans*=fact[(1<<i)];
  cout<<ans<<endl;
  return 0;
}





Measured memory_bytes: 5888