#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; //#define int long long typedef long long ll; typedef unsigned long long ul; typedef unsigned int ui; constexpr ll mod = 998244353; const ll INF = mod * mod; typedef pairP; #define stop char nyaa;cin>>nyaa; #define rep(i,n) for(int i=0;i=0;i--) #define Rep(i,sta,n) for(int i=sta;i=1;i--) #define Rep1(i,sta,n) for(int i=sta;i<=n;i++) #define all(v) (v).begin(),(v).end() typedef pair LP; typedef long double ld; typedef pair LDP; const ld eps = 1e-12; const ld pi = acosl(-1.0); ll mod_pow(ll x, ll n, ll m=mod) { ll res = 1; while (n) { if (n & 1)res = res * x % m; x = x * x % m; n >>= 1; } return res; } struct modint { ll n; modint() :n(0) { ; } modint(ll m) :n(m) { if (n >= mod)n %= mod; else if (n < 0)n = (n % mod + mod) % mod; } operator int() { return n; } }; bool operator==(modint a, modint b) { return a.n == b.n; } modint operator+=(modint& a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= mod; return a; } modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += mod; return a; } modint operator*=(modint& a, modint b) { a.n = ((ll)a.n * b.n) % mod; return a; } modint operator+(modint a, modint b) { return a += b; } modint operator-(modint a, modint b) { return a -= b; } modint operator*(modint a, modint b) { return a *= b; } modint operator^(modint a, ll n) { if (n == 0)return modint(1); modint res = (a * a) ^ (n / 2); if (n % 2)res = res * a; return res; } ll inv(ll a, ll p) { return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p); } modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); } const int max_n = 1 << 1; modint fact[max_n], factinv[max_n]; void init_f() { fact[0] = modint(1); for (int i = 0; i < max_n - 1; i++) { fact[i + 1] = fact[i] * modint(i + 1); } factinv[max_n - 1] = modint(1) / fact[max_n - 1]; for (int i = max_n - 2; i >= 0; i--) { factinv[i] = factinv[i + 1] * modint(i + 1); } } modint comb(int a, int b) { if (a < 0 || b < 0 || a < b)return 0; return fact[a] * factinv[b] * factinv[a - b]; } modint mod_inverse(modint a) { return mod_pow(a, mod - 2); } modint root[24], invroot[24]; void init() { rep(i, 24) { int n = (1 << i); root[i] = mod_pow(3, (mod - 1) / n); invroot[i] = mod_inverse(root[i]); } } typedef vector poly; poly dft(poly f, bool inverse = false) { int n = f.size(); int i, j, k; //bit左右反転 for (i = 0, j = 1; j < n - 1; j++) { for (k = n >> 1; k > (i ^= k); k >>= 1); if (i > j)swap(f[i], f[j]); } for (int j = 1; (1 << j) <= n; j++) { int m = 1 << j; modint zeta = root[j]; if (inverse)zeta = invroot[j]; for (i = 0; i < n; i += m) { modint powzeta = 1; for (k = i; k < i + m / 2; k++) { ll t1 = f[k], t2 = powzeta * f[k + m / 2]; f[k] = t1 + t2; f[k + m / 2] = t1 - t2; (powzeta *= zeta); } } } if (inverse) { modint rv = mod_inverse(n); for (i = 0; i < n; i++) { (f[i] *= rv); } } return f; } poly multiply(poly g, poly h) { int n = 1; int pi = 0, qi = 0; rep(i, g.size())if (g[i])pi = i; rep(i, h.size())if (h[i])qi = i; int sz = pi + qi + 2; while (n < sz)n *= 2; g.resize(n); h.resize(n); /*while (g.size() < n) { g.push_back(0); } while (h.size() < n) { h.push_back(0); }*/ poly gg = dft(g); poly hh = dft(h); poly ff; ff.resize(n); rep(i, n) { ff[i] = gg[i] * hh[i]; } return dft(ff, true); } struct FormalPowerSeries :vector { using vector::vector; using fps = FormalPowerSeries; void shrink() { while (this->size() && this->back() == (modint)0)this->pop_back(); } fps operator+(const fps& r)const { return fps(*this) += r; } fps operator+(const modint& v)const { return fps(*this) += v; } fps operator-(const fps& r)const { return fps(*this) -= r; } fps operator-(const modint& v)const { return fps(*this) -= v; } fps operator*(const fps& r)const { return fps(*this) *= r; } fps operator*(const modint& v)const { return fps(*this) *= v; } fps& operator+=(const fps& r) { if (r.size() > this->size())this->resize(r.size()); rep(i, r.size())(*this)[i] += r[i]; shrink(); return *this; } fps& operator+=(const modint& v) { if (this->empty())this->resize(1); (*this)[0] += v; shrink(); return *this; } fps& operator-=(const fps& r) { if (r.size() > this->size())this->resize(r.size()); rep(i, r.size())(*this)[i] -= r[i]; shrink(); return *this; } fps& operator-=(const modint& v) { if (this->empty())this->resize(1); (*this)[0] -= v; shrink(); return *this; } fps& operator*=(const fps& r) { if (this->empty() || r.empty())this->clear(); else { poly ret = multiply(*this, r); *this = fps(all(ret)); } return *this; } fps& operator*=(const modint& v) { for (auto& x : (*this))x *= v; shrink(); return *this; } fps operator-()const { fps ret = *this; for (auto& v : ret)v = -v; return ret; } fps pre(int sz)const { fps ret(this->begin(), this->begin() + min((int)this->size(), sz)); ret.shrink(); return ret; } fps inv(int deg) { const int n = this->size(); if (deg == -1)deg = n; fps ret({ (modint)1 / (*this)[0] }); for (int i = 1; i < deg; i <<= 1) { ret = (ret + ret - ret * ret * pre(i<<1)).pre(i << 1); } ret = ret.pre(deg); ret.shrink(); return ret; } }; using fps = FormalPowerSeries; struct pfps { fps a,b; }; pfps operator+(const pfps& a, const pfps& b) { return { a.a * b.b + a.b * b.a,a.b * b.b }; } void solve() { int n; cin >> n; int m; cin >> m; vector v(n); rep(i, n) { int a; cin >> a; v[i] = { {1},{1,-a} }; } while (v.size() > 1) { vector nex; int len = v.size(); rep(j, len / 2) { pfps to = v[2 * j] + v[2 * j + 1]; if (to.a.size() > m + 1)to.a.resize(m + 1); if (to.b.size() > m + 1)to.b.resize(m + 1); nex.push_back(to); } if (len % 2)nex.push_back(v.back()); swap(nex, v); } fps ans = v[0].a * (v[0].b).inv(m + 1); rep1(i, m) { if (i>1)cout << " "; cout << ans[i]; } cout << "\n"; } signed main() { ios::sync_with_stdio(false); cin.tie(0); //cout << fixed << setprecision(15); //init_f(); init(); //expr(); //int t; cin >> t; rep(i, t) solve(); return 0; }