#include <atcoder/all>
using namespace std;
using ll = long long;
using mint = atcoder::modint998244353;

int main(){
    int n, k;
    cin >> n >> k;
    vector<ll> a(k);
    vector<mint> fact(n + 1);
    for(auto &&v:a)cin >> v;
    fact[0] = 1;
    for(int i = 1; i <= n; i++)fact[i] = i * fact[i - 1];
    a.push_back(0);
    a.push_back((1ll << n) - 1);
    sort(a.begin(), a.end());
    a.erase(unique(a.begin(), a.end()), a.end());
    mint ans = 1;
    for(int i = 0; i + 1 < a.size(); i++){
        if((a[i] & a[i + 1]) != a[i]){
            cout << 0 << endl;
            return 0;
        }
        ans *= fact[__builtin_popcountll(a[i] ^ a[i + 1])];
    }
    cout << ans.val() << endl;
}