#include #include using namespace std; using namespace atcoder; // using mint = modint1000000007; // const int mod = 1000000007; using mint = modint998244353; const int mod = 998244353; // const int INF = 1e9; // const long long LINF = 1e18; #define rep(i, n) for (int i = 0; i < (n); ++i) #define rep2(i, l, r) for (int i = (l); i < (r); ++i) #define rrep(i, n) for (int i = (n)-1; i >= 0; --i) #define rrep2(i, l, r) for (int i = (r)-1; i >= (l); --i) #define all(x) (x).begin(), (x).end() #define allR(x) (x).rbegin(), (x).rend() #define P pair template inline bool chmax(A &a, const B &b) { if (a < b) { a = b; return true; } return false; } template inline bool chmin(A &a, const B &b) { if (a > b) { a = b; return true; } return false; } // combination mod prime // https://www.youtube.com/watch?v=8uowVvQ_-Mo&feature=youtu.be&t=1619 struct combination { std::vector fact, ifact; combination(int n) :fact(n + 1), ifact(n + 1) { assert(n < mod); fact[0] = 1; for (int i = 1; i <= n; ++i) fact[i] = fact[i - 1] * i; ifact[n] = fact[n].inv(); for (int i = n; i >= 1; --i) ifact[i - 1] = ifact[i] * i; } mint operator()(int n, int k) { return com(n, k); } mint com(int n, int k) { //負の二項係数を考慮する場合にコメントアウトを外す //if (n < 0) return com(-n, k) * (k % 2 ? -1 : 1); if (k < 0 || k > n) return 0; return fact[n] * ifact[k] * ifact[n - k]; } mint comsub(long long n, long long k) { if (n - k < k) k = n - k; assert(k < (int)fact.size()); mint val = ifact[k]; for (int i = 0; i < k; ++i) val *= n - i; return val; } template ...>, std::nullptr_t> = nullptr> mint polynom(const int n, const Ms & ...ms) { mint res = fact[n]; int sum = 0; for (int m : { ms... }) { if (m < 0 or m > n) return 0; res *= ifact[m]; sum += m; } if (sum > n)return 0; res *= ifact[n - sum]; return res; } mint div(int x) { if (x >= (int)fact.size())return mint(x).inv(); return fact[x - 1] * ifact[x]; } mint inv(int n, int k) { //if (n < 0) return inv(-n, k) * (k % 2 ? -1 : 1); if (k < 0 || k > n) return 0; return ifact[n] * fact[k] * fact[n - k]; } mint p(int n, int k) { return fact[n] * ifact[n - k]; } }c(2000006); int main() { std::ios::sync_with_stdio(false); std::cin.tie(nullptr); int n, m; cin >> n >> m; vectora(m), p(n); rep(i, m)cin >> a[i]; rep(i, m)p[a[i] - 1] = 1; vectordp(n); mint ans = 0; auto f = [&](auto && self, int l, int r)->void { if (l + 1 == r) { if (p[l])dp[l] += c.fact[l + 1] * -2; else dp[l] = 0; ans += dp[l] * c.fact[n - l]; return; } int m = (l + r) / 2; self(self, l, m); vector s(m - l); rep(i, m - l) s[i] = dp[i + l]; vector t(r - l); rep(i, r - l)t[i] = c.fact[i + 1]; auto u = convolution(s, t); rep2(i, m, r)dp[i] += u[i - l] * -2; self(self, m, r); }; f(f, 0, n); ans /= 2; ans += c.fact[n]; cout << ans.val() << endl; return 0; }