#include "bits/stdc++.h"
using namespace std;
#define FOR(i,j,k) for(int (i)=(j);(i)<(int)(k);++(i))
#define rep(i,j) FOR(i,0,j)
#define each(x,y) for(auto &(x):(y))
#define mp make_pair
#define mt make_tuple
#define all(x) (x).begin(),(x).end()
#define debug(x) cout<<#x<<": "<<(x)<<endl
#define smax(x,y) (x)=max((x),(y))
#define smin(x,y) (x)=min((x),(y))
#define MEM(x,y) memset((x),(y),sizeof (x))
#define sz(x) (int)(x).size()
typedef long long ll;
typedef pair<int, int> pii;
typedef vector<int> vi;
typedef vector<ll> vll;
const int MOD = (int)1e9 + 7;
int add(int a, int b){
    int c = a + b;
    if(c >= MOD)c -= MOD;
    else if(c < 0)c += MOD;
    return c;
}
void sadd(int &a, int b){
    a += b;
    if(a >= MOD)a -= MOD;
    else if(a < 0)a += MOD;
}
int mul(int a, int b){
    return (int)((long long)a*b%MOD);
}

int bitcntll(unsigned long long x) {
    x = (x & 0x5555555555555555) + ((x >> 1) & 0x5555555555555555);
    x = (x & 0x3333333333333333) + ((x >> 2) & 0x3333333333333333);
    x = (x & 0x0f0f0f0f0f0f0f0f) + ((x >> 4) & 0x0f0f0f0f0f0f0f0f);
    x = (x & 0x00ff00ff00ff00ff) + ((x >> 8) & 0x00ff00ff00ff00ff);
    x = (x & 0x0000ffff0000ffff) + ((x >> 16) & 0x0000ffff0000ffff);
    x = (x & 0x00000000ffffffff) + ((x >> 32) & 0x00000000ffffffff);
    return (int)x;
}

int main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    int N, K;
    while(cin >> N >> K) {
        vll A(K);
        int a = 0, b = 0;
        rep(i, K) {
            cin >> A[i];
            if(A[i] == 0)a = 1;
            if(A[i] == (1ll << N) - 1)b = 1;
        }
        if(!a)A.push_back(0);
        if(!b)A.push_back((1ll << N) - 1);
        K = sz(A);
        sort(all(A));

        int ans = 1;
        bool ok = true;
        rep(i, K - 1) {
            if((A[i] & A[i + 1]) != A[i]) {
                ok = false;
                break;
            } else {
                ll x = A[i + 1] - A[i];
                int y = bitcntll(x);
                for(int j = 2; j <= y; ++j) {
                    ans=mul(ans, j);
                }
            }
        }
        if(!ok)ans = 0;
        cout << ans << endl;
    }
}