#include <iostream>
#include <string>
#include <queue>
#include <stack>
#include <algorithm>
#include <list>
#include <vector>
#include <complex>
#include <utility>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <climits>
#include <bitset>
#include <ctime>
#include <map>
#include <unordered_map>
#include <set>
#include <unordered_set>
#include <cassert>
#include <cstddef>
#include <iomanip>
#include <numeric>
#include <tuple>
#include <sstream>
#include <fstream>

using namespace std;
#define REP(i, n) for (int (i) = 0; (i) < (n); (i)++)
#define FOR(i, a, b) for (int (i) = (a); (i) < (b); (i)++)
#define RREP(i, a) for(int (i) = (a) - 1; (i) >= 0; (i)--)
#define FORR(i, a, b) for(int (i) = (a) - 1; (i) >= (b); (i)--)
#define DEBUG(C) cerr << #C << " = " << C << endl;
using LL = long long;
using VI = vector<int>;
using VVI = vector<VI>;
using VL = vector<LL>;
using VVL = vector<VL>;
using VD = vector<double>;
using VVD = vector<VD>;
using PII = pair<int, int>;
using PDD = pair<double, double>;
using PLL = pair<LL, LL>;
using VPII = vector<PII>;
template<typename T> using VT = vector<T>;
#define ALL(a) begin((a)), end((a))
#define RALL(a) rbegin((a)), rend((a))
#define SORT(a) sort(ALL((a)))
#define RSORT(a) sort(RALL((a)))
#define REVERSE(a) reverse(ALL((a)))
#define MP make_pair
#define FORE(a, b) for (auto &&a : (b))
#define FIND(s, e) ((s).find(e) != (s).end())
#define EB emplace_back

const int INF = 1e9;
const int MOD = INF + 7;
const LL LLINF = 1e18;

LL N, K;
VL a;

void outbin(int n, int size) {
	string res = "";
	while (n) res += n % 2 + '0', n /= 2;
	while (res.length() != size) res += '0';
	REVERSE(res);
	cout << res << endl;
}

#if 1
int main(void) {
	cin >> N >> K;
	a.resize(K);
	REP(i, K) cin >> a[i];
	SORT(a);
	LL ans = 1;
	if (K == 0) {
		REP(i, N) (ans *= (i + 1)) %= MOD;
		cout << ans <<endl;
		return 0;
	}
	REP(i, K - 1) {
		if ((a[i] | a[i + 1]) != a[i + 1]) {
			DEBUG((a[i] | a[i + 1]))
			DEBUG(a[i + 1])
			cout << 0 << endl;
			return 0;
		}
		LL buf = __builtin_popcount(a[i + 1]) - __builtin_popcount(a[i]);
		REP(i, buf) (ans *= (i + 1)) %= MOD;
	}
	LL ma = (1 << N) - 1;
	ma = __builtin_popcount(ma) - __builtin_popcount(a.back());
	REP(i, ma) (ans *= (i + 1)) %= MOD;
	cout << ans << endl;
}
#else
int main(void) {
	VI v1{0,2,3,11,15}, v2{0,1,3,12,15};
	FORE(e, v1) outbin(e, 4);puts("");
	FORE(e, v2) outbin(e, 4);puts("");
}
#endif