#include <bits/stdc++.h>
#define rep(i, a, n) for(int i = a; i < n; i++)
#define repb(i, a, b) for(int i = a; i >= b; i--)
#define all(a) a.begin(), a.end()
#define o(a) cout << a << endl
#define int long long
using namespace std;
typedef pair<int, int> P;

const int mod = 1e9 + 7;
int n, k;

long long mod_pow(long long x,long long n){
    if(n == 0) return 1;
    long long res = mod_pow(x*x % mod, n / 2);
    if(n & 1) res = res*x % mod;
    return res;
}

signed main(){
    cin >> n >> k;
    vector<int> d;
    vector<bool> f(n);
    rep(i, 0, k){
        int a;
        cin >> a;
        if(a != 0) d. push_back(a);
    }
    int MAX = mod_pow(2, n) - 1;
    if(k == 0 || d[k] != MAX) d.push_back(MAX);
    int ans = 1;
    bool g = true;
    int now = 0;
    rep(i, 0, d.size()){
        // cout << -1 << endl;
        int tmp = d[i] - now;
        now = d[i];
        int cnt = 0;
        if(tmp < 0){
            g = false;
            break;
        }
        rep(j, 0, n){
            if(tmp & (1 << j)){
                if(!f[j]){
                    cnt++;
                    f[j] = true;
                }else{
                    g = false;
                    break;
                }
            }
        }
        rep(j, 0, cnt){
            ans = (ans * (j + 1)) % mod;
        }
        // cout << cnt << endl;
    }
    if(!g) ans = 0;
    cout << ans << endl;
}