/*
ЗАПУСКАЕМ 
░ГУСЯ░▄▀▀▀▄░РАБОТЯГУ░░
▄███▀░◐░░░▌░░░░░░░
░░░░▌░░░░░▐░░░░░░░
░░░░▐░░░░░▐░░░░░░░
░░░░▌░░░░░▐▄▄░░░░░
░░░░▌░░░░▄▀▒▒▀▀▀▀▄
░░░▐░░░░▐▒▒▒▒▒▒▒▒▀▀▄
░░░▐░░░░▐▄▒▒▒▒▒▒▒▒▒▒▀▄
░░░░▀▄░░░░▀▄▒▒▒▒▒▒▒▒▒▒▀▄
░░░░░░▀▄▄▄▄▄█▄▄▄▄▄▄▄▄▄▄▄▀▄
░░░░░░░░░░░▌▌░▌▌░░░░░
░░░░░░░░░░░▌▌░▌▌░░░░░
░░░░░░░░░▄▄▌▌▄▌▌░░░░░ 
 */
// #pragma GCC optimize("O3")
#include <iostream>
#include <complex>
#include <vector>
#include <string>
#include <algorithm>
#include <cstdio>
#include <numeric>
#include <cstring>
#include <ctime>
#include <cstdlib>
#include <set>
#include <map>
#include <unordered_map>
#include <unordered_set>
#include <list>
#include <cmath>
#include <bitset>
#include <cassert>
#include <queue>
#include <stack>
#include <deque>
    
     
using namespace std;
template<typename T1, typename T2>inline void chkmin(T1 &x, T2 y) { if (x > y) x = y; }
template<typename T1, typename T2>inline void chkmax(T1 &x, T2 y) { if (x < y) x = y; } 
template<typename T, typename U> inline ostream &operator<< (ostream &_out, const pair<T, U> &_p) { _out << _p.first << ' ' << _p.second; return _out; }
template<typename T, typename U> inline istream &operator>> (istream &_in, pair<T, U> &_p) { _in >> _p.first >> _p.second; return _in; }
template<typename T> inline ostream &operator<< (ostream &_out, const vector<T> &_v) { if (_v.empty()) { return _out; } _out << _v.front(); for (auto _it = ++_v.begin(); _it != _v.end(); ++_it) { _out << ' ' << *_it; } return _out; }
template<typename T> inline istream &operator>> (istream &_in, vector<T> &_v) { for (auto &_i : _v) { _in >> _i; } return _in; }
template<typename T> inline ostream &operator<< (ostream &_out, const set<T> &_s) { if (_s.empty()) { return _out; } _out << *_s.begin(); for (auto _it = ++_s.begin(); _it != _s.end(); ++_it) { _out << ' ' << *_it; } return _out; }
template<typename T> inline ostream &operator<< (ostream &_out, const multiset<T> &_s) { if (_s.empty()) { return _out; } _out << *_s.begin(); for (auto _it = ++_s.begin(); _it != _s.end(); ++_it) { _out << ' ' << *_it; } return _out; }
template<typename T> inline ostream &operator<< (ostream &_out, const unordered_set<T> &_s) { if (_s.empty()) { return _out; } _out << *_s.begin(); for (auto _it = ++_s.begin(); _it != _s.end(); ++_it) { _out << ' ' << *_it; } return _out; }
template<typename T> inline ostream &operator<< (ostream &_out, const unordered_multiset<T> &_s) { if (_s.empty()) { return _out; } _out << *_s.begin(); for (auto _it = ++_s.begin(); _it != _s.end(); ++_it) { _out << ' ' << *_it; } return _out; }
template<typename T, typename U> inline ostream &operator<< (ostream &_out, const map<T, U> &_m) { if (_m.empty()) { return _out; } _out << '(' << _m.begin()->first << ": " << _m.begin()->second << ')'; for (auto _it = ++_m.begin(); _it != _m.end(); ++_it) { _out << ", (" << _it->first << ": " << _it->second << ')'; } return _out; }
template<typename T, typename U> inline ostream &operator<< (ostream &_out, const unordered_map<T, U> &_m) { if (_m.empty()) { return _out; } _out << '(' << _m.begin()->first << ": " << _m.begin()->second << ')'; for (auto _it = ++_m.begin(); _it != _m.end(); ++_it) { _out << ", (" << _it->first << ": " << _it->second << ')'; } return _out; }
/** Interfacte */
     
inline int readChar();
template <class T = long long> inline T readInt(); 
template <class T> inline void writeInt( T x, char end = 0 );
inline void writeChar( int x ); 
inline void writeWord( const char *s );
     
/** Read */
     
static const int buf_size = 4096;
     
inline int getChar() {
    static char buf[buf_size];
    static int len = 0, pos = 0;
    if (pos == len) {
        pos = 0, len = fread(buf, 1, buf_size, stdin);
    }
    if (pos == len) {
        return -1;
    }
    return buf[pos++];
}
     
inline int readChar() {
    int c = getChar();
    while (c <= 32) {
        c = getChar();
    }
    return c;
}
     
template <class T>
inline T readInt() {
    int s = 1, c = readChar();
    T x = 0;
    if (c == '-')
        s = -1, c = getChar();
    while ('0' <= c && c <= '9')
        x = x * 10 + c - '0', c = getChar();
    return s == 1 ? x : -x;
}
     
/** Write */
     
static int write_pos = 0;
static char write_buf[buf_size];
     
inline void writeChar( int x ) {
    if (write_pos == buf_size)
        fwrite(write_buf, 1, buf_size, stdout), write_pos = 0;
    write_buf[write_pos++] = x;
}
     
template <class T> 
inline void writeInt( T x, char end ) {
    if (x < 0)
        writeChar('-'), x = -x;
     
    char s[24];
    int n = 0;
    while (x || !n)
        s[n++] = '0' + x % 10, x /= 10;
    while (n--)
        writeChar(s[n]);
    if (end)
        writeChar(end);
}
     
inline void writeWord( const char *s ) {     while (*s)
writeChar(*s++); }
     
struct Flusher {
    ~Flusher() {
        if (write_pos)
            fwrite(write_buf, 1, write_pos, stdout), write_pos = 0;
    }
} flusher;   
#define sz(c) (int)(c).size()
#define all(c) (c).begin(), (c).end()
#define rall(c) (c).rbegin(), (c).rend()
#define left left228
#define right right228
#define next next228
#define rank rank228
#define prev prev228
#define y1 y1228                                                         
#define read(FILENAME) freopen((FILENAME + ".in").c_str(), "r", stdin)
#define write(FILENAME) freopen((FILENAME + ".out").c_str(), "w", stdout)
#define files(FILENAME) read(FILENAME), write(FILENAME)
#define pb push_back
const string FILENAME = "input";
//WULD! NAH! KEST!
const int Mod = 1000000007;


int mul(int a, int b) {
	return (1LL * a * b) % Mod;
}


int N,M,A[20],f[20][1 << 16];
long long fact[1 << 17], ifact[1 << 17];


long long inv(int a, int p = Mod){
	return a == 1 ? 1: (1 + p * (a - inv(p % a, a))) / a % p;
}


long long C(int n, int m) {
	return mul(fact[n], mul(ifact[m], ifact[n - m]));
}


int main(){
	cin >> N >> M;
	for (int i = 1; i <= M; i++) {
		cin >> A[i];
	}
	fact[0] = 1;
	for (int i = 1; i <= 1 << N; i++) {
		fact[i] = mul(fact[i - 1], i);
	}
	ifact[1 << N] = inv(fact[1 << N]);
	for (int i = 1 << N; i > 0; i--) {
		ifact[i - 1] = mul(ifact[i], i);
	}
	f[M][0] = 1;
	for (int i = M; i > 0; i--) {
		for (int s = 0; s < 1 << N; s++) {
			if (f[i][s]) {
				int rst = (1 << N) - A[i] - s;
				(f[i - 1][s] += f[i][s]) %= Mod;
				for (int j = N; j--; ) {
					if (!(s >> j & 1) && (1 << j) - 1 <= rst) {
						f[i - 1][s | 1 << j] = (f[i - 1][s | 1 << j] + (Mod - C(rst, (1 << j) - 1)) * f[i][s] % Mod) % Mod;
					}
				}
			} 
		}
	}
	int ans = 0;
	for (int i = 0; i < 1 << N; i++) {
		long long tmp=f[0][i];
		int sz = (1 << N) - 1 - i;
		tmp = mul(tmp, fact[sz]);
		for (int j = 0; j < N; j++) {
			if (!(i >> j & 1)) {
				tmp = mul(tmp, ifact[1 << j]);
			}
		}
		(ans += tmp) %= Mod;
	}
	ans = ans * (1LL << N) % Mod;
	for (int i = 0; i < N; i++) {
		ans = ans * fact[1<<i] % Mod;
	}
	cout << ans << '\n';
	return 0;
}


Measured memory_bytes: 5376