// need #include #include // data structure #include //#include #include #include #include #include #include #include #include //#include //#include #include #include //#include //#include // stream //#include //#include //#include // etc #include #include #include //#include #include #include #include #define INIT std::ios::sync_with_stdio(false);std::cin.tie(0); #define VAR(type, ...)type __VA_ARGS__;MACRO_VAR_Scan(__VA_ARGS__); template void MACRO_VAR_Scan(T& t) { std::cin >> t; } templatevoid MACRO_VAR_Scan(First& first, Rest&...rest) { std::cin >> first; MACRO_VAR_Scan(rest...); } #define VEC_ROW(type, n, ...)std::vector __VA_ARGS__;MACRO_VEC_ROW_Init(n, __VA_ARGS__); for(int i=0; i void MACRO_VEC_ROW_Init(int n, T& t) { t.resize(n); } templatevoid MACRO_VEC_ROW_Init(int n, First& first, Rest&...rest) { first.resize(n); MACRO_VEC_ROW_Init(n, rest...); } template void MACRO_VEC_ROW_Scan(int p, T& t) { std::cin >> t[p]; } templatevoid MACRO_VEC_ROW_Scan(int p, First& first, Rest&...rest) { std::cin >> first[p]; MACRO_VEC_ROW_Scan(p, rest...); } #define OUT(d) std::cout< c(n);for(auto& i:c)std::cin>>i; #define MAT(type, c, m, n) std::vector> c(m, std::vector(n));for(auto& r:c)for(auto& i:r)std::cin>>i; #define ALL(a) (a).begin(),(a).end() #define FOR(i, a, b) for(int i=(a);i<(b);++i) #define RFOR(i, a, b) for(int i=(b)-1;i>=(a);--i) #define REP(i, n) for(int i=0;i=0;--i) #define FORLL(i, a, b) for(ll i=ll(a);i=ll(a);--i) #define REPLL(i, n) for(ll i=0;i=0;--i) #define PAIR std::pair #define PAIRLL std::pair #define IN(a, x, b) (a<=x && x tmp(a);std::cerr << #a << "\t:";for(int i=0; i(a.size()); ++i){std::cerr << tmp.front() << "\n";tmp.pop();}std::cerr << "\n";} template inline T CHMAX(T& a, const T b) { return a = (a < b) ? b : a; } template inline T CHMIN(T& a, const T b) { return a = (a > b) ? b : a; } #define EXCEPTION(msg) throw std::string("Exception : " msg " [ in ") + __func__ + " : " + std::to_string(__LINE__) + " lines ]" #define TRY(cond, msg) try {if (cond) EXCEPTION(msg);}catch (std::string s) {std::cerr << s << std::endl;} void CHECKTIME(std::function f) { auto start = std::chrono::system_clock::now(); f(); auto end = std::chrono::system_clock::now(); auto res = std::chrono::duration_cast((end - start)).count(); std::cerr << "[Time:" << res << "ns (" << res / (1.0e9) << "s)]\n"; } #define int ll using ll = long long; using ull = unsigned long long; constexpr int INFINT = 1 << 30; // 1.07x10^ 9 constexpr int INFINT_LIM = (1LL << 31) - 1; // 2.15x10^ 9 constexpr ll INFLL = 1LL << 60; // 1.15x10^18 constexpr ll INFLL_LIM = (1LL << 62) - 1 + (1LL << 62); // 9.22x10^19 constexpr double EPS = 1e-7; constexpr int MOD = 1000000007; constexpr double PI = 3.141592653589793238462643383279; //組み合わせ(コンビネーション) const int FACT_MAX_N = 1000000; int fact[FACT_MAX_N]; void FactrialInitialize(ll n, ll mod) { fact[0] = 1; FORLL(i, 1, n) { fact[i] = i * fact[i - 1] % mod; } } ll Factrial(ll n, ll mod) { if (fact[0] == 0) FactrialInitialize(FACT_MAX_N, mod); if (fact[n] != 0) return fact[n]; if (n == 0) return fact[n] = 1; return fact[n] = Factrial(n - 1, mod) * n % mod; } ll powMod(ll n, ll p, ll mod) { if (n == 0) return 0; if (p <= 0 || n == 1) return 1; if (p % 2 == 0) { ll t = powMod(n, p / 2, mod); return t*t % mod; } return n*powMod(n, p - 1, mod) % mod; } ll Permutation(ll n, ll r, ll mod) { if (n < r) return 0; if (n == r) return Factrial(n, mod); ll ans = 1; ans *= Factrial(n, mod); ans %= mod; ans *= powMod(Factrial(n - r, mod), mod - 2, mod); ans %= mod; return ans; } /*fact準備O(n), クエリO(log(mod))*/ ll Combination(ll n, ll r, ll mod) { if (r == 0) return 1; if (n < r) return 0; ll ans = 1; ans *= Factrial(n, mod); ans %= mod; ans *= powMod(Factrial(n - r, mod), mod - 2, mod); ans %= mod; ans *= powMod(Factrial(r, mod), mod - 2, mod); ans %= mod; return ans; } /*n<=10^9, r<=10^5のときなど, O(r)*/ /*ll Combination(ll n, ll r, ll mod) { if (n < r) return 0; ll ans = 1; if (n < 2 * r) r = n - r; for (int i = 1; i <= r; ++i) { ans *= n - i + 1; ans %= mod; ans *= powMod(Factrial(i, mod), mod - 2, mod); ans %= mod; } return ans; }*/ ll CombinationWithRepetition(ll n, ll r, ll mod) { return Combination(n + r - 1, r, mod); } int popcount(ll n) { int cnt = 0; while (n) { if (n & 1) ++cnt; n /= 2; } return cnt; } signed main() { INIT; VAR(int, n, k); VEC(int, a, k); if (k == 0) { OUT(Factrial(n, MOD))BR; return 0; } std::sort(ALL(a)); if (*a.rbegin() != (1LL << n) - 1) { a.emplace_back((1LL << n) - 1); } int p = 0; int ans = 1; REP(i, a.size()) { if ((p | a[i]) != a[i]) { OUT(0)BR; return 0; } int s = popcount(a[i]); int t = popcount(p); if (s - t > 1) { ans *= Factrial(s - t, MOD); ans %= MOD; } p = a[i]; } OUT(ans)BR; return 0; }