//#pragma GCC optimize("Ofast") //#pragma GCC optimize("unroll-loops") #include <bits/stdc++.h> using namespace std; using ll = int64_t; using ull = uint64_t; using pii = pair<int, int>; template <class T> using V = vector<T>; template <class T> using VV = V<V<T>>; #define pb push_back #define eb emplace_back #define mp make_pair #define fi first #define se second #define rep(i, n) rep2(i, 0, n) #define rep2(i, m, n) for (int i = m; i < (n); i++) #define per(i, b) per2(i, 0, b) #define per2(i, a, b) for (int i = int(b) - 1; i >= int(a); i--) #define ALL(c) (c).begin(), (c).end() #define SZ(x) ((int)(x).size()) constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n - 1); } template <class T, class U> void chmin(T& t, const U& u) { if (t > u) t = u; } template <class T, class U> void chmax(T& t, const U& u) { if (t < u) t = u; } template <class T, class U> ostream& operator<<(ostream& os, const pair<T, U>& p) { os << "(" << p.first << "," << p.second << ")"; return os; } template <class T> ostream& operator<<(ostream& os, const vector<T>& v) { os << "{"; rep(i, v.size()) { if (i) os << ","; os << v[i]; } os << "}"; return os; } #ifdef LOCAL void debug_out() { cerr << endl; } template <typename Head, typename... Tail> void debug_out(Head H, Tail... T) { cerr << " " << H; debug_out(T...); } #define debug(...) \ cerr << __LINE__ << " [" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__) #define dump(x) cerr << __LINE__ << " " << #x << " = " << (x) << endl #else #define debug(...) (void(0)) #define dump(x) (void(0)) #endif template <unsigned int MOD> struct ModInt { using uint = unsigned int; using ull = unsigned long long; using M = ModInt; uint v; ModInt(ll _v = 0) { set_norm(_v % MOD + MOD); } M& set_norm(uint _v) { //[0, MOD * 2)->[0, MOD) v = (_v < MOD) ? _v : _v - MOD; return *this; } explicit operator bool() const { return v != 0; } explicit operator int() const { return v; } M operator+(const M& a) const { return M().set_norm(v + a.v); } M operator-(const M& a) const { return M().set_norm(v + MOD - a.v); } M operator*(const M& a) const { return M().set_norm(ull(v) * a.v % MOD); } M operator/(const M& a) const { return *this * a.inv(); } M& operator+=(const M& a) { return *this = *this + a; } M& operator-=(const M& a) { return *this = *this - a; } M& operator*=(const M& a) { return *this = *this * a; } M& operator/=(const M& a) { return *this = *this / a; } M operator-() const { return M() - *this; } M& operator++(int) { return *this = *this + 1; } M& operator--(int) { return *this = *this - 1; } M pow(ll n) const { if (n < 0) return inv().pow(-n); M x = *this, res = 1; while (n) { if (n & 1) res *= x; x *= x; n >>= 1; } return res; } M inv() const { ll a = v, b = MOD, p = 1, q = 0, t; while (b != 0) { t = a / b; swap(a -= t * b, b); swap(p -= t * q, q); } return M(p); } friend ostream& operator<<(ostream& os, const M& a) { return os << a.v; } friend istream& operator>>(istream& in, M& x) { ll v_; in >> v_; x = M(v_); return in; } bool operator<(const M& r) const { return v < r.v; } bool operator>(const M& r) const { return v < *this; } bool operator<=(const M& r) const { return !(r < *this); } bool operator>=(const M& r) const { return !(*this < r); } bool operator==(const M& a) const { return v == a.v; } bool operator!=(const M& a) const { return v != a.v; } static uint get_mod() { return MOD; } }; // using Mint = ModInt<1000000007>; using Mint = ModInt<998244353>; /** * @docs docs/ntt.md */ template <class D> struct NumberTheoreticTransform { D root; V<D> roots = {0, 1}; V<int> rev = {0, 1}; int base = 1, max_base = -1; void init() { int mod = D::get_mod(); int tmp = mod - 1; max_base = 0; while (tmp % 2 == 0) { tmp /= 2; max_base++; } root = 2; while (true) { if (root.pow(1 << max_base).v == 1) { if (root.pow(1 << (max_base - 1)).v != 1) { break; } } root++; } } void ensure_base(int nbase) { if (max_base == -1) init(); if (nbase <= base) return; assert(nbase <= max_base); rev.resize(1 << nbase); for (int i = 0; i < (1 << nbase); ++i) { rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1)); } roots.resize(1 << nbase); while (base < nbase) { D z = root.pow(1 << (max_base - 1 - base)); for (int i = 1 << (base - 1); i < (1 << base); ++i) { roots[i << 1] = roots[i]; roots[(i << 1) + 1] = roots[i] * z; } ++base; } } void ntt(V<D>& a, bool inv = false) { int n = a.size(); // assert((n & (n - 1)) == 0); int zeros = __builtin_ctz(n); ensure_base(zeros); int shift = base - zeros; for (int i = 0; i < n; i++) { if (i < (rev[i] >> shift)) { swap(a[i], a[rev[i] >> shift]); } } for (int k = 1; k < n; k <<= 1) { for (int i = 0; i < n; i += 2 * k) { for (int j = 0; j < k; j++) { D x = a[i + j]; D y = a[i + j + k] * roots[j + k]; a[i + j] = x + y; a[i + j + k] = x - y; } } } int v = D(n).inv().v; if (inv) { reverse(a.begin() + 1, a.end()); for (int i = 0; i < n; i++) { a[i] *= v; } } } V<D> mul(V<D> a, V<D> b) { if (a.size() == 0 && b.size() == 0) return {}; int s = a.size() + b.size() - 1; int nbase = 1; while ((1 << nbase) < s) nbase++; int sz = 1 << nbase; a.resize(sz); b.resize(sz); ntt(a); ntt(b); for (int i = 0; i < sz; i++) { a[i] *= b[i]; } ntt(a, true); a.resize(s); return a; } }; // T : modint template <class T> void ntt_2d(VV<T>& a, bool rev) { if (a.size() == 0 || a[0].size() == 0) return; int h = a.size(), w = a[0].size(); NumberTheoreticTransform<T> fft; fft.init(); for (auto& v : a) { fft.ntt(v, rev); } rep(j, w) { V<T> vh(h); rep(i, h) { vh[i] = a[i][j]; } fft.ntt(vh, rev); rep(i, h) { a[i][j] = vh[i]; } } } // depends on FFT libs // basically use with ModInt NumberTheoreticTransform<Mint> ntt; template <class D> struct Poly : public V<D> { template <class... Args> Poly(Args... args) : V<D>(args...) {} Poly(initializer_list<D> init) : V<D>(init.begin(), init.end()) {} int size() const { return V<D>::size(); } D at(int p) const { return (p < this->size() ? (*this)[p] : D(0)); } // first len terms Poly pref(int len) const { return Poly(this->begin(), this->begin() + min(this->size(), len)); } // for polynomial division Poly rev() const { Poly res = *this; reverse(res.begin(), res.end()); return res; } Poly shiftr(int d) const { int n = max(size() + d, 0); Poly res(n); for (int i = 0; i < size(); ++i) { if (i + d >= 0) { res[i + d] = at(i); } } return res; } Poly operator+(const Poly& r) const { auto n = max(size(), r.size()); V<D> tmp(n); for (int i = 0; i < n; ++i) { tmp[i] = at(i) + r.at(i); } return tmp; } Poly operator-(const Poly& r) const { auto n = max(size(), r.size()); V<D> tmp(n); for (int i = 0; i < n; ++i) { tmp[i] = at(i) - r.at(i); } return tmp; } // scalar Poly operator*(const D& k) const { int n = size(); V<D> tmp(n); for (int i = 0; i < n; ++i) { tmp[i] = at(i) * k; } return tmp; } Poly operator*(const Poly& r) const { Poly a = *this; Poly b = r; auto v = ntt.mul(a, b); return v; } // scalar Poly operator/(const D& k) const { return *this * k.inv(); } Poly operator/(const Poly& r) const { if (size() < r.size()) { return {{}}; } int d = size() - r.size() + 1; return (rev().pref(d) * r.rev().inv(d)).pref(d).rev(); } Poly operator%(const Poly& r) const { auto res = *this - *this / r * r; while (res.size() && !res.back()) { res.pop_back(); } return res; } Poly diff() const { V<D> res(max(0, size() - 1)); for (int i = 1; i < size(); ++i) { res[i - 1] = at(i) * i; } return res; } Poly inte() const { V<D> res(size() + 1); for (int i = 0; i < size(); ++i) { res[i + 1] = at(i) / (D)(i + 1); } return res; } // f * f.inv(m) === 1 mod (x^m) // f_0 ^ -1 must exist Poly inv(int m) const { Poly res = Poly({D(1) / at(0)}); for (int i = 1; i < m; i *= 2) { res = (res * D(2) - res * res * pref(i * 2)).pref(i * 2); } return res.pref(m); } // f_0 = 1 must hold Poly log(int n) const { auto f = pref(n); return (f.diff() * f.inv(n - 1)).pref(n - 1).inte(); } // f_0 = 0 must hold Poly exp(int n) const { auto h = diff(); Poly f({1}), g({1}); for (int m = 1; m < n; m *= 2) { g = (g * D(2) - f * g * g).pref(m); auto q = h.pref(m - 1); auto w = (q + g * (f.diff() - f * q)).pref(m * 2 - 1); f = (f + f * (*this - w.inte()).pref(m * 2)).pref(m * 2); } return f.pref(n); } // be careful when k = 0 Poly pow(int n, ll k) const { return (log(n) * (D)k).exp(n); } // f_0 = 1 must hold (use it with modular sqrt) // CF250E Poly sqrt(int n) const { Poly f = pref(n); Poly g({1}); for (int i = 1; i < n; i *= 2) { g = (g + f.pref(i * 2) * g.inv(i * 2)) * D(2).inv(); } return g.pref(n); } D eval(D x) const { D res = 0, c = 1; for (auto a : *this) { res += a * c; c *= x; } return res; } Poly powmod(ll k, const Poly& md) { auto v = *this % md; Poly res{1}; while (k) { if (k & 1) { res = res * v % md; } v = v * v % md; k /= 2; } return res; } Poly& operator+=(const Poly& r) { return *this = *this + r; } Poly& operator-=(const Poly& r) { return *this = *this - r; } Poly& operator*=(const D& r) { return *this = *this * r; } Poly& operator*=(const Poly& r) { return *this = *this * r; } Poly& operator/=(const Poly& r) { return *this = *this / r; } Poly& operator/=(const D& r) { return *this = *this / r; } Poly& operator%=(const Poly& r) { return *this = *this % r; } friend ostream& operator<<(ostream& os, const Poly& pl) { if (pl.size() == 0) return os << "0"; for (int i = 0; i < pl.size(); ++i) { if (pl[i]) { os << pl[i] << "x^" << i; if (i + 1 != pl.size()) os << ","; } } return os; } explicit operator bool() const { bool f = false; for (int i = 0; i < size(); ++i) { if (at(i)) { f = true; } } return f; } }; // calculate characteristic polynomial // c_0 * s_i + c_1 * s_{i+1} + ... + c_k * s_{i+k} = 0 // c_k = -1 template <class T> Poly<T> berlekamp_massey(const V<T>& s) { int n = int(s.size()); V<T> b = {T(-1)}, c = {T(-1)}; T y = Mint(1); for (int ed = 1; ed <= n; ed++) { int l = int(c.size()), m = int(b.size()); T x = 0; for (int i = 0; i < l; i++) { x += c[i] * s[ed - l + i]; } b.push_back(0); m++; if (!x) { continue; } T freq = x / y; if (l < m) { auto tmp = c; c.insert(begin(c), m - l, Mint(0)); for (int i = 0; i < m; i++) { c[m - 1 - i] -= freq * b[m - 1 - i]; } b = tmp; y = x; } else { for (int i = 0; i < m; i++) { c[l - 1 - i] -= freq * b[m - 1 - i]; } } } return c; } // HUPC 2020 day3 K // calculate vec[0] * vec[1] * ... // deg(result) must be bounded template <class T> Poly<T> prod(const V<Poly<T>>& vec) { auto comp = [](const auto& a, const auto& b) -> bool { return a.size() > b.size(); }; priority_queue<Poly<T>, V<Poly<T>>, decltype(comp)> que(comp); que.push(Poly<T>{1}); for (auto& pl : vec) que.push(pl); while (que.size() > 1) { auto va = que.top(); que.pop(); auto vb = que.top(); que.pop(); que.push(va * vb); } return que.top(); } int main() { cin.tie(nullptr); ios::sync_with_stdio(false); ntt.init(); int N, M; cin >> N >> M; V<Mint> A(N); rep(i, N) cin >> A[i]; using P = Poly<Mint>; V<P> vec; rep(i, N) vec.eb(P{1, -A[i]}); auto v = prod(vec); v = v.log(M + 1); for (int i = 1; i <= M; ++i) { cout << -v[i] * i << (i == M ? '\n' : ' '); } return 0; }