#include <bits/stdc++.h>
using namespace std;

typedef long long ll;
typedef vector< int > vi;
typedef vector< vi > vvi;
typedef vector< ll > vl;
typedef vector< vl > vvl;
typedef pair< int, int > pii;
typedef vector< pii > vp;
typedef vector< double > vd;
typedef vector< vd > vvd;
typedef vector< string > vs;

template< class T1, class T2 >
int upmin( T1 &x, T2 v ){
  if( x > v ){
    x = v;
    return 1;
  }
  return 0;
}

template< class T1, class T2 >
int upmax( T1 &x, T2 v ){
  if( x < v ){
    x = v;
    return 1;
  }
  return 0;
}

const int INF = 0x3f3f3f3f;

const int MOD7 = ( int ) 1e9 + 7;

int N;
ll K;
vl A;

void init(){
  cin >> N >> K;
  A = vl( K );
  for( int i = 0; i < K; ++i ){
    cin >> A[ i ];
  }
}

int fact( int x ){
  int res = 1;
  for( int i = 2; i <= x; ++i ){
    res = 1LL * res * i % MOD7;
  }
  return res;
}

void preprocess(){

}

void solve(){
  int ans = 1;
  A.emplace_back( 0 );
  A.emplace_back( ( 1LL << N ) - 1 );
  sort( A.begin(), A.end() );
  A.erase( unique( A.begin(), A.end() ), A.end() );
  for( int i = 1; i < A.size(); ++i ){
    if( ~A[ i ] & A[ i - 1 ] ){
      cout << 0 << endl;
      exit( 0 );
    }
    int diff = __builtin_popcountll( A[ i ] ) - __builtin_popcountll( A[ i - 1 ] );
    ans = 1LL * ans * fact( diff ) % MOD7;
  }
  cout << ans << endl;
}

signed main(){
  ios::sync_with_stdio( 0 );
  init();
  preprocess();
  solve();
  return 0;
}