#include <algorithm>
#include <cassert>
#include <iostream>
#include <vector>
using namespace std;

const int MOD = 1e9 + 7;

struct mod_int {
    int val;

    mod_int(long long v = 0) {
        if (v < 0) v = v % MOD + MOD;
        if (v >= MOD) v %= MOD;
        val = v;
    }

    static int mod_inv(int a, int m = MOD) {
        // https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm#Example
        int g = m, r = a, x = 0, y = 1;

        while (r != 0) {
            int q = g / r;
            g %= r; swap(g, r);
            x -= q * y; swap(x, y);
        }

        return x < 0 ? x + m : x;
    }

    explicit operator int() const {
        return val;
    }

    mod_int& operator+=(const mod_int &other) {
        val += other.val;
        if (val >= MOD) val -= MOD;
        return *this;
    }

    mod_int& operator-=(const mod_int &other) {
        val -= other.val;
        if (val < 0) val += MOD;
        return *this;
    }

    static unsigned fast_mod(uint64_t x, unsigned m = MOD) {
#if !defined(_WIN32) || defined(_WIN64)
        return x % m;
#endif
        // Optimized mod for Codeforces 32-bit machines.
        // x must be less than 2^32 * m for this to work, so that x / m fits in a 32-bit integer.
        unsigned x_high = x >> 32, x_low = (unsigned) x;
        unsigned quot, rem;
        asm("divl %4\n"
            : "=a" (quot), "=d" (rem)
            : "d" (x_high), "a" (x_low), "r" (m));
        return rem;
    }

    mod_int& operator*=(const mod_int &other) {
        val = fast_mod((uint64_t) val * other.val);
        return *this;
    }

    mod_int& operator/=(const mod_int &other) {
        return *this *= other.inv();
    }

    friend mod_int operator+(const mod_int &a, const mod_int &b) { return mod_int(a) += b; }
    friend mod_int operator-(const mod_int &a, const mod_int &b) { return mod_int(a) -= b; }
    friend mod_int operator*(const mod_int &a, const mod_int &b) { return mod_int(a) *= b; }
    friend mod_int operator/(const mod_int &a, const mod_int &b) { return mod_int(a) /= b; }

    mod_int& operator++() {
        val = val == MOD - 1 ? 0 : val + 1;
        return *this;
    }

    mod_int& operator--() {
        val = val == 0 ? MOD - 1 : val - 1;
        return *this;
    }

    mod_int operator++(int) { mod_int before = *this; ++*this; return before; }
    mod_int operator--(int) { mod_int before = *this; --*this; return before; }

    mod_int operator-() const {
        return val == 0 ? 0 : MOD - val;
    }

    bool operator==(const mod_int &other) const { return val == other.val; }
    bool operator!=(const mod_int &other) const { return val != other.val; }

    mod_int inv() const {
        return mod_inv(val);
    }

    mod_int pow(long long p) const {
        assert(p >= 0);
        mod_int a = *this, result = 1;

        while (p > 0) {
            if (p & 1)
                result *= a;

            a *= a;
            p >>= 1;
        }

        return result;
    }

    friend ostream& operator<<(ostream &stream, const mod_int &m) {
        return stream << m.val;
    }
};

vector<mod_int> inv = {0, 1}, factorial = {1, 1}, inv_factorial = {1, 1};

void prepare_factorials(int maximum) {
    // Make sure MOD is prime, which is necessary for the inverse algorithm below.
    for (int p = 2; p * p <= MOD; p++)
        assert(MOD % p != 0);

    maximum = max(maximum, 1);
    inv.resize(maximum + 1);
    factorial.resize(maximum + 1);
    inv_factorial.resize(maximum + 1);

    for (int i = 2; i <= maximum; i++) {
        inv[i] = inv[MOD % i] * (MOD - MOD / i);
        factorial[i] = i * factorial[i - 1];
        inv_factorial[i] = inv[i] * inv_factorial[i - 1];
    }
}

mod_int choose(long long n, long long r) {
    if (r < 0 || r > n) return 0;
    return factorial[n] * inv_factorial[r] * inv_factorial[n - r];
}

mod_int inv_choose(long long n, long long r) {
    assert(0 <= r && r <= n);
    return inv_factorial[n] * factorial[r] * factorial[n - r];
}

mod_int permute(long long n, long long k) {
    if (k < 0 || k > n) return 0;
    return factorial[n] * inv_factorial[n - k];
}

mod_int inv_permute(long long n, long long k) {
    assert(0 <= k && k <= n);
    return inv_factorial[n] * factorial[n - k];
}


const int N_MAX = 16, M_MAX = 16, P_MAX = 1 << N_MAX;

int N, M;
vector<int> A;
mod_int dp[M_MAX + 1][P_MAX];

int main() {
    cin >> N >> M;
    prepare_factorials(1 << N);
    A.resize(M);

    for (int &a : A)
        cin >> a;

    sort(A.rbegin(), A.rend());
    dp[0][0] = 1;

    for (int m = 0; m < M; m++)
        for (int mask = 0; mask < 1 << N; mask++) {
            dp[m + 1][mask] += dp[m][mask];

            for (int which = 0; which < N; which++)
                if ((mask >> which & 1) == 0) {
                    int how_many = 1 << which;
                    int remaining = (1 << N) - A[m] - mask;

                    if (remaining >= 0)
                        dp[m + 1][mask | 1 << which] += dp[m][mask] * choose(remaining, how_many - 1) * factorial[how_many];
                }
        }

    mod_int total = 0;

    for (int mask = 0; mask < 1 << N; mask++) {
        mod_int multiplier = __builtin_popcount(mask) % 2 == 0 ? +1 : -1;
        int missing = (1 << N) - 1 - mask;
        mod_int ways = dp[M][mask] * factorial[missing];
        total += multiplier * ways;
    }

    total *= 1 << N;
    cout << total << '\n';
}


Measured memory_bytes: 5376