#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define rep(i, n) for(ll i = 0, i##_len = (n); i < i##_len; i++)
#define reps(i, s, n) for(ll i = (s), i##_len = (n); i < i##_len; i++)
#define rrep(i, n) for(ll i = (n) - 1; i >= 0; i--)
#define rreps(i, e, n) for(ll i = (n) - 1; i >= (e); i--)
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define sz(x) ((ll)(x).size())
#define len(x) ((ll)(x).length())
#define endl "\n"

struct BinomialCoefficient {
    BinomialCoefficient() {}
    BinomialCoefficient(int n) : fac(n + 2), finv(n + 2), inv(n + 2) {
        fac[0] = fac[1] = 1;
        finv[0] = finv[1] = 1;
        inv[1] = 1;
        for (int i = 2; i <= n; i++) {
            fac[i] = fac[i - 1] * i % mod;
            inv[i] = mod - inv[mod % i] * (mod / i) % mod;
            finv[i] = finv[i - 1] * inv[i] % mod;
        }
    }
    
    long long factorial(int n) {
        return fac[n];
    }
    
    long long combination(int n, int r) {
        if ((n < r) || (n < 0) || (r < 0)) return 0;
        return fac[n] * (finv[r] * finv[n - r] % mod) % mod;
    }
    
    long long permutation(int n, int r) {
        if ((n < r) || (n < 0) || (r < 0)) return 0;
        return fac[n] * finv[n - r] % mod;
    }
    
private:
    int mod = 1000000007;
    vector<long long> fac, finv, inv;
};

struct mint {
    constexpr static int mod = 1000000007;
    long long x;
    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 { return mint(*this) += a; }
    mint operator-(const mint a) const { return mint(*this) -= a; }
    mint operator*(const mint a) const { return mint(*this) *= a; }
    mint pow(long long t) const {
        if (!t) return 1;
        mint a = pow(t >> 1);
        a *= a;
        if (t & 1) a *= *this;
        return a;
    }
    mint inv() const { return pow(mod - 2); }
    mint& operator/=(const mint a) { return *this *= a.inv(); }
    mint operator/(const mint a) const { return mint(*this) /= a; }
};

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    // ifstream in("input.txt");
    // cin.rdbuf(in.rdbuf());
    ll n, k;
    cin >> n >> k;
    vector<ll> a(k + 1);
    rep(i, k) cin >> a[i];
    sort(all(a));
    a[k] = (1LL << n) - 1;
    BinomialCoefficient bc(n);
    ll bv = 0;
    mint ans = 1;
    rep(i, k + 1) {
        rep(j, n) {
            bool bf = (bv & (1LL << j)) != 0;
            bool cf = (a[i] & (1LL << j)) != 0;
            if (bf && !cf) {
                cout << 0 << endl;
                return 0;
            }
        }
        ll cnt = __builtin_popcountll(a[i]) - __builtin_popcountll(bv);
        ans *= bc.factorial(cnt);
        bv = a[i];
    }
    cout << ans.x << endl;
    return 0;
}