#include namespace { #pragma GCC diagnostic ignored "-Wunused-function" #include #pragma GCC diagnostic warning "-Wunused-function" using namespace std; using namespace atcoder; #define rep(i,n) for(int i = 0; i < (int)(n); i++) #define rrep(i,n) for(int i = (int)(n) - 1; i >= 0; i--) #define all(x) begin(x), end(x) #define rall(x) rbegin(x), rend(x) template bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; } else return false; } template bool chmin(T& a, const T& b) { if (b < a) { a = b; return true; } else return false; } using ll = long long; using P = pair; using VI = vector; using VVI = vector; using VL = vector; using VVL = vector; using mint = modint998244353; constexpr int FACT_SIZE = 1000000; mint Fact[FACT_SIZE + 1]; mint iFact[FACT_SIZE + 1]; const auto fact_init = [] { Fact[0] = mint::raw(1); for(int i = 1; i <= FACT_SIZE; ++i) { Fact[i] = Fact[i-1] * i; } iFact[FACT_SIZE] = Fact[FACT_SIZE].inv(); for(int i = FACT_SIZE; i; --i) { iFact[i-1] = iFact[i] * i; } return false; }(); mint comb(int n, int k) { if (k == 0) return mint::raw(1); assert(n >= 0 && k >= 0); if (k > n) return mint::raw(0); return Fact[n] * iFact[n - k] * iFact[k]; } mint icomb(int n, int k) { return iFact[n] * Fact[n - k] * Fact[k]; } mint fact(int n) {return Fact[n];} mint perm(int n, int k) { assert(0 <= n); return Fact[n] * iFact[n - k]; } vector fps_inv(vector f, int precision=-1) { if (precision == -1) precision = f.size(); assert(precision >= 1 && f.size() >= 1 && f[0] != 0); auto f0 = f[0]; if (f0 != 1) { f0 = f0.inv(); for (auto& x : f) x *= f0; } int sz_tgt = bit_ceil(0U + precision); vector g(sz_tgt), g_ftt, fg; g_ftt.reserve(sz_tgt), fg.reserve(sz_tgt); g[0] = 1; static_assert(mint::mod() > 1 && (mint::mod() - 1) % 4 == 0); const mint i4 = mint::raw(mint::mod() - (mint::mod() - 1) / 4); mint iz = -1; for (int n = 1; n < sz_tgt; n *= 2) { fg.assign(f.begin(), f.begin() + min(2 * n, f.size())), fg.resize(2 * n); g_ftt.assign(g.begin(), g.begin() + 2 * n); internal::butterfly(fg), internal::butterfly(g_ftt); for (int i = 0; i < 2 * n; i++) fg[i] *= g_ftt[i]; internal::butterfly_inv(fg); for (int i = 0; i < n; i++) fg[i] = 0; internal::butterfly(fg); for (int i = 0; i < 2 * n; i++) fg[i] *= g_ftt[i]; internal::butterfly_inv(fg); iz *= i4; for (int i = n; i < 2 * n; i++) g[i] = fg[i] * iz; } g.resize(precision); if (f0 != 1) for (auto& x : g) x *= f0; return g; } vector fps_log(vector f, int precision=-1) { if (precision == -1) precision = f.size(); assert(precision >= 1 && f.size() >= 1 && f[0] == 1); auto f_inv = fps_inv(f, precision); for (int i = 0; i < ssize(f); i++) f[i] *= mint::raw(i); auto g = convolution(f, f_inv); g.resize(precision); for (int i = 1; i < precision; i++) g[i] *= iFact[i] * Fact[i-1]; return g; } } int main() { ios::sync_with_stdio(false); cin.tie(0); int n, m; cin >> n >> m; vector a(n); rep(_, m) { int x; cin >> x; a[x-1] = true; } vector f(n); rep(i, n) f[i] = Fact[i+1]; auto g = fps_log(f); rep(i, n) g[i] *= i; g[0] = 2; g.insert(g.begin(), 1, 0); vector dp[2]; rep(i, 2) dp[i].resize(n); dp[0][0] = 1; auto dfs = [&](auto&& self, int l, int r) -> void { if (r - l == 1) { if (a[l]) swap(dp[0][l], dp[1][l]); return; } int c = (l + r) / 2; self(self, l, c); static vector ff, gg; gg.assign(g.begin(), g.begin() + r - l); rep(p, 2) { ff.assign(dp[p].begin() + l, dp[p].begin() + c); auto t = convolution(ff, gg); for (int i = c; i < r; i++) dp[p][i] += t[i - l]; } self(self, c, r); }; dfs(dfs, 0, n); cout << dp[0][n-1].val() << '\n'; }