#include <bits/stdc++.h>
#define FOR(i, begin, end) for(int i=(begin);i<(end);i++)
#define REP(i, n) FOR(i,0,n)
#define IFOR(i, begin, end) for(int i=(end)-1;i>=(begin);i--)
#define IREP(i, n) IFOR(i,0,n)
#define Sort(a) sort(a.begin(), a.end())
#define Reverse(a) reverse(a.begin(), a.end())
#define Lower_bound(v, x) distance(v.begin(), lower_bound(v.begin(), v.end(), x))
#define Upper_bound(v, x) distance(v.begin(), upper_bound(v.begin(), v.end(), x))
#define Max(a, b) a = max(a, b)
#define Min(a, b) a = min(a, b)
#define Ans(f, y, n) if(f) cout << y << endl; else cout << n << endl;
#define int long long
#define INF 1000000000000000000
using namespace std;

using vec = vector<int>;
using mat = vector<vec>;
using Pii = pair<int, int>;
using PiP = pair<int, Pii>;
using PPi = pair<Pii, int>;
using bools = vector<bool>;

template<typename T>
void readv(vector<T> &a){ REP(i, a.size()) cin >> a[i]; }
void readi(vector<int> &a){ REP(i, a.size()){cin >> a[i]; a[i]--;} }
template<typename T>
void debug(vector<vector<T>> m){ REP(i, m.size()){ REP(j, m[i].size()){ cout << m[i][j] << ","; } cout << endl;} }

int modpow(int x, int n, int m){
    int a = 1;
    IREP(i, 64){
        a = (a * a) % m;
        if(((n >> i) & 1) == 1) a = (a * x) % m;
    }
    return a;
}

class Combination
{
public:

    vec fact, invfact;
    int MAX_N, mod;

    Combination(int MAX_N, int mod): MAX_N(MAX_N), mod(mod) {
        initialize();
    }

    void initialize(){
        fact = vec(MAX_N + 1);
        invfact = vec(MAX_N + 1);
        fact[0] = 1;
        FOR(i, 1, MAX_N + 1){
            fact[i] = (fact[i - 1] * i) % mod;
        }
        invfact[MAX_N] = modpow(fact[MAX_N], mod - 2, mod);
        IREP(i, MAX_N){
            invfact[i] = (invfact[i + 1] * (i + 1)) % mod;
        }
    }

    int nCr(int n, int r){
        if(r > n || r < 0 || n < 0) return 0;
        if(n > MAX_N){
            MAX_N = n;
            initialize();
        }
        int a = fact[n];
        a = (a * invfact[r]) % mod;
        a = (a * invfact[n - r]) % mod;
        return a;
    }

    int nPr(int n, int r){
        if(r > n || r < 0 || n < 0) return 0;
        if(n > MAX_N){
            MAX_N = n;
            initialize();
        }
        int a = fact[n];
        a = (a * invfact[n - r]) % mod;
        return a;
    }
};

signed main(){

    int N, M; cin >> N >> M;
    vec A(M); readv(A);
    Reverse(A);
    int n = 1 << N;
    REP(i, M) A[i] = n - A[i] + 1;

    int mod = 1000000007;
    Combination comb(n, mod);

    mat dp(M + 1, vec(n, 0));
    dp[0][0] = 1;

    REP(i, M){
        REP(j, A[i] + 1){
            dp[i + 1][j] += dp[i][j];
            dp[i + 1][j] %= mod;
            REP(k, N) if(j & (1 << k)){
                int c = (comb.nPr(A[i] - 1 - (j ^ (1 << k)), (1 << k) - 1) * (1 << k)) % mod;
                dp[i + 1][j] += dp[i][j ^ (1 << k)] * c;
                dp[i + 1][j] %= mod;
            }
        }
    }
    //debug(dp);
    int ans = 0;
    REP(i, n){
        int p;
        if(__builtin_popcountll(i) % 2 == 0) p = 1;
        else p = -1;
        ans += p * dp[M][i] * comb.fact[n - 1 - i];
        ans = (ans % mod + mod) % mod;
    }
    ans = (ans * n) % mod; 

    cout << ans << endl;
    
    return 0;
}

Measured memory_bytes: 10496