#include using namespace std; #define rep(i, n) for (int i = 0; i < n; i++) #define rep2(i, x, n) for (int i = x; i <= n; i++) #define rep3(i, x, n) for (int i = x; i >= n; i--) #define each(e, v) for (auto &e : v) #define pb push_back #define eb emplace_back #define all(x) x.begin(), x.end() #define rall(x) x.rbegin(), x.rend() #define sz(x) (int)x.size() using ll = long long; using pii = pair; using pil = pair; using pli = pair; using pll = pair; template bool chmax(T &x, const T &y) { return (x < y) ? (x = y, true) : false; } template bool chmin(T &x, const T &y) { return (x > y) ? (x = y, true) : false; } template int flg(T x, int i) { return (x >> i) & 1; } template void print(const vector &v, T x = 0) { int n = v.size(); for (int i = 0; i < n; i++) cout << v[i] + x << (i == n - 1 ? '\n' : ' '); if (v.empty()) cout << '\n'; } template void printn(const vector &v, T x = 0) { int n = v.size(); for (int i = 0; i < n; i++) cout << v[i] + x << '\n'; } template int lb(const vector &v, T x) { return lower_bound(begin(v), end(v), x) - begin(v); } template int ub(const vector &v, T x) { return upper_bound(begin(v), end(v), x) - begin(v); } template void rearrange(vector &v) { sort(begin(v), end(v)); v.erase(unique(begin(v), end(v)), end(v)); } template vector id_sort(const vector &v, bool greater = false) { int n = v.size(); vector ret(n); iota(begin(ret), end(ret), 0); sort(begin(ret), end(ret), [&](int i, int j) { return greater ? v[i] > v[j] : v[i] < v[j]; }); return ret; } template pair operator+(const pair &p, const pair &q) { return make_pair(p.first + q.first, p.second + q.second); } template pair operator-(const pair &p, const pair &q) { return make_pair(p.first - q.first, p.second - q.second); } template istream &operator>>(istream &is, pair &p) { S a; T b; is >> a >> b; p = make_pair(a, b); return is; } template ostream &operator<<(ostream &os, const pair &p) { return os << p.first << ' ' << p.second; } struct io_setup { io_setup() { ios_base::sync_with_stdio(false); cin.tie(NULL); cout << fixed << setprecision(15); } } io_setup; const int inf = (1 << 30) - 1; const ll INF = (1LL << 60) - 1; // const int MOD = 1000000007; const int MOD = 998244353; template struct Mod_Int { int x; Mod_Int() : x(0) {} Mod_Int(long long y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {} static int get_mod() { return mod; } Mod_Int &operator+=(const Mod_Int &p) { if ((x += p.x) >= mod) x -= mod; return *this; } Mod_Int &operator-=(const Mod_Int &p) { if ((x += mod - p.x) >= mod) x -= mod; return *this; } Mod_Int &operator*=(const Mod_Int &p) { x = (int)(1LL * x * p.x % mod); return *this; } Mod_Int &operator/=(const Mod_Int &p) { *this *= p.inverse(); return *this; } Mod_Int &operator++() { return *this += Mod_Int(1); } Mod_Int operator++(int) { Mod_Int tmp = *this; ++*this; return tmp; } Mod_Int &operator--() { return *this -= Mod_Int(1); } Mod_Int operator--(int) { Mod_Int tmp = *this; --*this; return tmp; } Mod_Int operator-() const { return Mod_Int(-x); } Mod_Int operator+(const Mod_Int &p) const { return Mod_Int(*this) += p; } Mod_Int operator-(const Mod_Int &p) const { return Mod_Int(*this) -= p; } Mod_Int operator*(const Mod_Int &p) const { return Mod_Int(*this) *= p; } Mod_Int operator/(const Mod_Int &p) const { return Mod_Int(*this) /= p; } bool operator==(const Mod_Int &p) const { return x == p.x; } bool operator!=(const Mod_Int &p) const { return x != p.x; } Mod_Int inverse() const { assert(*this != Mod_Int(0)); return pow(mod - 2); } Mod_Int pow(long long k) const { Mod_Int now = *this, ret = 1; for (; k > 0; k >>= 1, now *= now) { if (k & 1) ret *= now; } return ret; } friend ostream &operator<<(ostream &os, const Mod_Int &p) { return os << p.x; } friend istream &operator>>(istream &is, Mod_Int &p) { long long a; is >> a; p = Mod_Int(a); return is; } }; using mint = Mod_Int; template struct Combination { static vector _fac, _ifac; Combination() {} static void init(int n) { _fac.resize(n + 1), _ifac.resize(n + 1); _fac[0] = 1; for (int i = 1; i <= n; i++) _fac[i] = _fac[i - 1] * i; _ifac[n] = _fac[n].inverse(); for (int i = n; i >= 1; i--) _ifac[i - 1] = _ifac[i] * i; } static T fac(int k) { return _fac[k]; } static T ifac(int k) { return _ifac[k]; } static T inv(int k) { return fac(k - 1) * ifac(k); } static T P(int n, int k) { if (k < 0 || n < k) return 0; return fac(n) * ifac(n - k); } static T C(int n, int k) { if (k < 0 || n < k) return 0; return fac(n) * ifac(n - k) * ifac(k); } static T H(int n, int k) { // k 個の区別できない玉を n 個の区別できる箱に入れる場合の数 if (n < 0 || k < 0) return 0; return k == 0 ? 1 : C(n + k - 1, k); } static T second_stirling_number(int n, int k) { // n 個の区別できる玉を、k 個の区別しない箱に、各箱に 1 個以上玉が入るように入れる場合の数 T ret = 0; for (int i = 0; i <= k; i++) { T tmp = C(k, i) * T(i).pow(n); ret += ((k - i) & 1) ? -tmp : tmp; } return ret * ifac(k); } static T bell_number(int n, int k) { // n 個の区別できる玉を、k 個の区別しない箱に入れる場合の数 if (n == 0) return 1; k = min(k, n); vector pref(k + 1); pref[0] = 1; for (int i = 1; i <= k; i++) { if (i & 1) { pref[i] = pref[i - 1] - ifac(i); } else { pref[i] = pref[i - 1] + ifac(i); } } T ret = 0; for (int i = 1; i <= k; i++) ret += T(i).pow(n) * ifac(i) * pref[k - i]; return ret; } }; template vector Combination::_fac = vector(); template vector Combination::_ifac = vector(); using comb = Combination; template struct Number_Theoretic_Transform { static int max_base; static T root; static vector r, ir; Number_Theoretic_Transform() {} static void init() { if (!r.empty()) return; int mod = T::get_mod(); int tmp = mod - 1; root = 2; while (root.pow(tmp >> 1) == 1) root++; max_base = 0; while (tmp % 2 == 0) tmp >>= 1, max_base++; r.resize(max_base), ir.resize(max_base); for (int i = 0; i < max_base; i++) { r[i] = -root.pow((mod - 1) >> (i + 2)); // r[i] := 1 の 2^(i+2) 乗根 ir[i] = r[i].inverse(); // ir[i] := 1/r[i] } } static void ntt(vector &a) { init(); int n = a.size(); assert((n & (n - 1)) == 0); assert(n <= (1 << max_base)); for (int k = n; k >>= 1;) { T w = 1; for (int s = 0, t = 0; s < n; s += 2 * k) { for (int i = s, j = s + k; i < s + k; i++, j++) { T x = a[i], y = w * a[j]; a[i] = x + y, a[j] = x - y; } w *= r[__builtin_ctz(++t)]; } } } static void intt(vector &a) { init(); int n = a.size(); assert((n & (n - 1)) == 0); assert(n <= (1 << max_base)); for (int k = 1; k < n; k <<= 1) { T w = 1; for (int s = 0, t = 0; s < n; s += 2 * k) { for (int i = s, j = s + k; i < s + k; i++, j++) { T x = a[i], y = a[j]; a[i] = x + y, a[j] = w * (x - y); } w *= ir[__builtin_ctz(++t)]; } } T inv = T(n).inverse(); for (auto &e : a) e *= inv; } static vector convolve(vector a, vector b) { int k = (int)a.size() + (int)b.size() - 1, n = 1; while (n < k) n <<= 1; a.resize(n), b.resize(n); ntt(a), ntt(b); for (int i = 0; i < n; i++) a[i] *= b[i]; intt(a), a.resize(k); return a; } }; template int Number_Theoretic_Transform::max_base = 0; template T Number_Theoretic_Transform::root = T(); template vector Number_Theoretic_Transform::r = vector(); template vector Number_Theoretic_Transform::ir = vector(); using NTT = Number_Theoretic_Transform; vector> f; vector rec(int l, int r) { int m = (l + r) / 2; if (r - l == 1) return f[l]; return NTT::convolve(rec(l, m), rec(m, r)); } int main() { int N; mint S; cin >> N >> S; S = S.inverse(); comb::init(N); f.resize(N); rep(i, N) { mint x; cin >> x; f[i] = {1, x * S}; } auto g = rec(0, N); // print(g); mint ans = 0; rep(i, N + 1) ans += g[i] * comb::fac(i); cout << ans << '\n'; }