#include <bits/stdc++.h>

using namespace std;

typedef long long ll;
typedef pair<ll, ll> P;

#define each(i,a) for (auto&& i : a)
#define FOR(i,a,b) for (ll i=(a),__last_##i=(b);i<__last_##i;i++)
#define RFOR(i,a,b) for (ll i=(b)-1,__last_##i=(a);i>=__last_##i;i--)
#define REP(i,n) FOR(i,0,n)
#define RREP(i,n) RFOR(i,0,n)
#define __GET_MACRO3(_1, _2, _3, NAME, ...) NAME
#define rep(...) __GET_MACRO3(__VA_ARGS__, FOR, REP)(__VA_ARGS__)
#define rrep(...) __GET_MACRO3(__VA_ARGS__, RFOR, RREP)(__VA_ARGS__)
#define pb push_back
#define all(a) (a).begin(),(a).end()
#define chmin(x,v) x = min(x, v)
#define chmax(x,v) x = max(x, v)

const ll linf = 1e18;
const double eps = 1e-12;
const double pi = acos(-1);

template<typename T>
istream& operator>>(istream& is, vector<T>& vec) {
    each(x,vec) is >> x;
    return is;
}
template<typename T>
ostream& operator<<(ostream& os, const vector<T>& vec) {
    rep(i,vec.size()) {
        if (i) os << " ";
        os << vec[i];
    }
    return os;
}
template<typename T>
ostream& operator<<(ostream& os, const vector< vector<T> >& vec) {
    rep(i,vec.size()) {
        if (i) os << endl;
        os << vec[i];
    }
    return os;
}
const ll mod = 1e9+7;
ll mul(ll a, ll b) {
    return a * b % mod;
}
ll mul(initializer_list<ll> t) {
    ll res = 1;
    each(v, t) res = mul(res, v);
    return res;
}
ll add(ll a, ll b) {
    return (a + b) % mod;
}
ll add(initializer_list<ll> t) {
    ll res = 0;
    each(v, t) res = add(res, v);
    return res;
}
ll sub(ll a, ll b) {
    return (a - b + mod) % mod;
}
ll sub(initializer_list<ll> t) {
    auto it = t.begin();
    ll res = *(it++);
    while (it != t.end()) {
        res = sub(res, *(it++));
    }
    return res;
}
ll power(ll x, ll n) {
    ll res = 1;
    for (ll i = 1; i <= n; i <<= 1) {
        if (i & n) res = mul(res, x);
        x = mul(x, x);
    }
    return res;
}
ll inv(ll n) {
    return power(n, mod-2);
}
ll divi(ll a, ll b) {
    return mul(a, inv(b));
}
ll divi(initializer_list<ll> t) {
    auto it = t.begin();
    ll res = *(it++);
    while (it != t.end()) {
        res = divi(res, *(it++));
    }
    return res;
}
vector<ll> fact;
void init_fact(ll n) {
    fact.assign(n+1, 1);
    FOR(i, 1, fact.size()) {
        fact[i] = mul(fact[i-1], i);
    }
}

ll comb(ll n, ll r) {
    if (r < 0) return 0;
    if (r > n) return 0;
    return divi(fact[n], mul(fact[r], fact[n-r]));
}

using Row = vector<ll>;
using Matrix = vector<Row>;
Matrix E(ll n) {
    Matrix res(n, Row(n, 0));
    rep(i, n) res[i][i] = 1;
    return res;
}
Matrix mul(const Matrix& A, const Matrix& B) {
    const ll n = A.size(), m = A[0].size(), l = B[0].size();
    assert(m == B.size());
    Matrix res(n, Row(l, 0));
    rep(i, n) rep(j, m) rep(k, l) {
        res[i][k] = add(res[i][k], mul(A[i][j], B[j][k]));
    }
    return res;
}
Matrix power(Matrix A, ll n) {
    assert(A.size() == A[0].size());
    Matrix res = E(A.size());
    for (ll i = 1; i <= n; i <<= 1) {
        if (i & n) res = mul(res, A);
        A = mul(A, A);
    }
    return res;
}
void gen_fact_result(ll d, ll num) {
    ll x = 1;
    cout << "#define FACT";
    cout << "vector<P> facts = {";
    rep(i, d*(num-1)+1) {
        if (i % d == 0) {
            cout << "{" << i << "," << x << "},";
        }
        x = mul(x, i+1);
    }
    cout << "};";
}
#define FACT
vector<P> facts = {{0,1},{10000000,682498929},{20000000,491101308},{30000000,76479948},{40000000,723816384},{50000000,67347853},{60000000,27368307},{70000000,625544428},{80000000,199888908},{90000000,888050723},{100000000,927880474},{110000000,281863274},{120000000,661224977},{130000000,623534362},{140000000,970055531},{150000000,261384175},{160000000,195888993},{170000000,66404266},{180000000,547665832},{190000000,109838563},{200000000,933245637},{210000000,724691727},{220000000,368925948},{230000000,268838846},{240000000,136026497},{250000000,112390913},{260000000,135498044},{270000000,217544623},{280000000,419363534},{290000000,500780548},{300000000,668123525},{310000000,128487469},{320000000,30977140},{330000000,522049725},{340000000,309058615},{350000000,386027524},{360000000,189239124},{370000000,148528617},{380000000,940567523},{390000000,917084264},{400000000,429277690},{410000000,996164327},{420000000,358655417},{430000000,568392357},{440000000,780072518},{450000000,462639908},{460000000,275105629},{470000000,909210595},{480000000,99199382},{490000000,703397904},{500000000,733333339},{510000000,97830135},{520000000,608823837},{530000000,256141983},{540000000,141827977},{550000000,696628828},{560000000,637939935},{570000000,811575797},{580000000,848924691},{590000000,131772368},{600000000,724464507},{610000000,272814771},{620000000,326159309},{630000000,456152084},{640000000,903466878},{650000000,92255682},{660000000,769795511},{670000000,373745190},{680000000,606241871},{690000000,825871994},{700000000,957939114},{710000000,435887178},{720000000,852304035},{730000000,663307737},{740000000,375297772},{750000000,217598709},{760000000,624148346},{770000000,671734977},{780000000,624500515},{790000000,748510389},{800000000,203191898},{810000000,423951674},{820000000,629786193},{830000000,672850561},{840000000,814362881},{850000000,823845496},{860000000,116667533},{870000000,256473217},{880000000,627655552},{890000000,245795606},{900000000,586445753},{910000000,172114298},{920000000,193781724},{930000000,778983779},{940000000,83868974},{950000000,315103615},{960000000,965785236},{970000000,492741665},{980000000,377329025},{990000000,847549272},};
#ifdef FACT
ll bigfact(ll n) {
    if (n >= mod) return 0;
    auto it = upper_bound(all(facts), P(n, linf));
    assert(it != facts.begin());
    --it;
    ll s = it->first;
    ll res = it->second;
    rep(i, s+1, n+1) {
        res = mul(res, i);
    }
    return res;
}
#endif

int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    init_fact(ll(1e6));
    ll n, m; cin >> n >> m;
    vector<ll> a(m); cin >> a;
    sort(all(a), greater<ll>());
    // vector<ll> num((1LL<<n)+1, 1);
    // rep(i, m) num[a[i]] = 0;
    // rrep(i, 1, num.size()) num[i-1] += num[i];
    vector<ll> block_size(1LL<<n, 0);
    rep(i, 1LL<<n) rep(j, n) {
        if (i>>j & 1) block_size[i] += 1LL<<j;
    }
    vector<vector<ll>> dp(m+1, vector<ll>(1LL<<n, 0));
    dp[0][0] = 1;
    rep(i, m) rep(j, 1LL<<n) {
        rep(k, n) {
            if (j>>k & 1) continue;
            // a[i]をサイズ2^kのところに使う
            ll nj = j|(1LL<<k);
            dp[i+1][nj] = add(dp[i+1][nj], mul(dp[i][j], mul(fact[1LL<<k], comb((1LL<<n)-a[i]-block_size[j], (1LL<<k)-1))));
        }
        // 使わない
        dp[i+1][j] = add(dp[i+1][j], dp[i][j]);
    }
    // rep(i, 1LL<<n) {
    //     cout << i << " " << dp[m][i] << endl;
    // }
    // cout << endl;
    ll ans = 0;
    rep(i, 1LL<<n) {
        ll val = mul(dp[m][i], fact[block_size[(1LL<<n) - i - 1]]);
        // cout << i << " " << val << endl;
        if (__builtin_popcountll(i) % 2 == 0) {
            ans = add(ans, val);
        }
        else {
            ans = sub(ans, val);
        }
    }
    ans = mul(ans, 1LL<<n);
    cout << ans << endl;
    // ll ans = sub(fact[1LL<<n], mul(sum, 1LL<<n));
    // cout << ans << endl;
}


Measured memory_bytes: 17920