#include <iostream>
#include <string>
#include <cmath>
#include<algorithm>
#include<stack>
#include<queue>
#include<map>
#include<set>
#include<iomanip>
#define _USE_MATH_DEFINES
#include <math.h>
#include <functional>
#include<complex>
using namespace std;

#define rep(i,x) for(ll i=0;i<x;i++)
#define repn(i,x) for(ll i=1;i<=x;i++)

typedef long long ll;
const ll INF = 1e17;
const ll MOD = 1000000007;
const ll MAX = 4000001;
const long double eps = 1E-14;

ll max(ll a, ll b) {
	if (a > b) { return a; }
	return b;
}

ll min(ll a, ll b) {
	if (a > b) { return b; }
	return a;
}

ll gcd(ll a, ll b) {
	if (b == 0) { return a; }
	if (a < b) { return gcd(b, a); }
	return gcd(b, a % b);
}

ll lcm(ll a, ll b) {
	return a / gcd(a, b) * b;
}

struct edge {
	ll ind;
	ll fr;
	ll to;
	ll d;
};

class mint {
	long long x;
public:
	mint(long long x = 0) : x((x% MOD + MOD) % MOD) {}
	mint operator-() const {
		return mint(-x);
	}
	mint& operator+=(const mint& a) {
		if ((x += a.x) >= MOD) x -= MOD;
		return *this;
	}
	mint& operator-=(const mint& a) {
		if ((x += MOD - a.x) >= MOD) x -= MOD;
		return *this;
	}
	mint& operator*=(const  mint& a) {
		(x *= a.x) %= MOD;
		return *this;
	}
	mint operator+(const mint& a) const {
		mint res(*this);
		return res += a;
	}
	mint operator-(const mint& a) const {
		mint res(*this);
		return res -= a;
	}
	mint operator*(const mint& a) const {
		mint res(*this);
		return res *= a;
	}

	mint pow(ll t) const {
		if (!t) return 1;
		mint a = pow(t >> 1);
		a *= a;
		if (t & 1) a *= *this;
		return a;
	}

	// for prime MOD
	mint inv() const {
		return pow(MOD - 2);
	}
	mint& operator/=(const mint& a) {
		return (*this) *= a.inv();
	}
	mint operator/(const mint& a) const {
		mint res(*this);
		return res /= a;
	}

	friend ostream& operator<<(ostream& os, const mint& m) {
		os << m.x;
		return os;
	}
};

mint pw(mint a, ll b) {
	if (b == 0) { return 1; }
	mint ret = pw(a, b >> 1);
	ret *= ret;
	if (b & 1) { ret *= a; }
	return ret;
}

typedef vector<ll> vll;
typedef vector<vector<ll>> vvll;
typedef vector<vector<vector<ll>>> vvvll;

typedef vector<mint> vmint;
typedef vector<vector<mint>> vvmint;
typedef vector<vector<vector<mint>>> vvvmint;

//////////////////////////////////////
vmint f, finv, inv;

void cominit(ll N) {
	f.assign(N + 1, 1);
	finv.assign(N + 1, 1);
	inv.assign(N + 1, 1);
	inv[1] = 1;

	repn(i, N) {
		f[i] = f[i - 1] * i;
		if (i > 1)inv[i] = -inv[MOD % i] * (MOD / i);
		finv[i] = finv[i - 1] * inv[i];
	}
}

mint per(ll a, ll b) {
	if (a < 0 || b < 0 || a < b) { return 0; }
	return f[a] * finv[a - b];
}

int main() {
	ll N, M;
	cin >> N >> M;

	cominit(1 << (N+1));

	vll A(M + 2, 0);
	A[0] = 1;
	repn(i, M)cin >> A[i];
	A[M + 1] = (1 << N) + 1;

	vvmint dp(M + 2, vmint(1 << N, 0));

	dp[0][0] = 1;

	repn(i, M+1) {

		vmint rdp(1 << N, 0);
		rep(s,1<<N) rdp[s] = dp[i-1][s];

		rep(k,N) rep(s,1<<N) {
			if ((s >> k) & 1) rdp[s] += rdp[s ^ (1 << k)];
		}

		rep(j, 1 << N) {
			rdp[j] *= per(j - (A[i - 1] - 1), A[i] - A[i - 1] - 1);
		}

		rep(s, 1 << N) dp[i][s] = rdp[s];

		rep(k, N) rep(s, 1 << N) {
			if ((s >> k) & 1) dp[i][s] -= dp[i][s ^ (1 << k)];
		}



		if (i <= M) {
			rep(j, 1 << N) {
				dp[i][j] *= (j - (A[i] - 2));
				//cout << i << " " << j << " " << dp[i][j] << endl;
			}
		}
	}

	mint ans = dp[M + 1][(1 << N) - 1];
	ans *= (1 << N);

	cout << ans << endl;
}


Measured memory_bytes: 16124