#pragma GCC target("avx2") #pragma GCC optimize("Ofast") #pragma GCC optimize("unroll-loops") #include using namespace std; const long long MOD = 998244353; unordered_map mp; long long modpow(long long a, long long b){ if (mp.count(b)){ return mp[b]; } else { long long ans = 1; while (b > 0){ if (b % 2 == 1){ ans *= a; ans %= MOD; } a *= a; a %= MOD; b /= 2; } mp[b] = ans; return mp[b]; } } unordered_map mp2; long long modinv(long long a){ if (mp2.count(a)){ return mp2[a]; } else { mp2[a] = modpow(a, MOD - 2); return mp2[a]; } } vector ntt(vector A, bool inv){ int N = A.size(); int M = 0; for (int i = 1; i < N; i *= 2){ M++; } for (int i = 0; i < N; i++){ int j = 0; for (int k = 0; k < M; k++){ if ((i >> k) & 1){ j |= 1 << (M - 1 - k); } } if (i < j){ swap(A[i], A[j]); } } for (int i = 1; i < N; i *= 2){ long long z = modpow(3, (MOD - 1) / (i * 2)); if (inv){ z = modinv(z); } long long z2 = 1; for (int j = 0; j < i; j++){ for (int k = 0; k < N; k += i * 2){ long long s = A[j + k]; long long t = A[j + k + i] * z2 % MOD; A[j + k] = (s + t) % MOD; A[j + k + i] = (s - t + MOD) % MOD;; } z2 = z2 * z % MOD; } } if (inv){ int Ninv = modinv(N); for (int i = 0; i < N; i++){ A[i] = A[i] * Ninv % MOD; } } return A; } vector convolution(vector &A, vector &B, int d = 0){ int deg = A.size() + B.size() - 1; if (d == 0){ d = deg; } if (d < 100){ vector ans(d, 0); int N = A.size(); int M = B.size(); for (int i = 0; i < N; i++){ for (int j = 0; j < M; j++){ if (i + j < d){ ans[i + j] += A[i] * B[j] % MOD; } else { break; } } } for (int i = 0; i < d; i++){ ans[i] %= MOD; } return ans; } int N = 1; while (N < deg){ N *= 2; } while (A.size() < N){ A.push_back(0); } while (B.size() < N){ B.push_back(0); } vector a = ntt(A, false); vector b = ntt(B, false); vector c(N); for (int i = 0; i < N; i++){ c[i] = a[i] * b[i] % MOD; } c = ntt(c, true); c.resize(d); return c; } vector add(vector A, vector B){ int N = max(A.size(), B.size()); while (A.size() < N){ A.push_back(0); } while (B.size() < N){ B.push_back(0); } vector ans(N, 0); for (int i = 0; i < N; i++){ ans[i] = A[i] + B[i]; if (ans[i] > MOD){ ans[i] -= MOD; } } return ans; } vector inverse(vector &P){ int N = P.size(); vector ans(1); ans[0] = modinv(P[0]); for (int i = 1; i < N; i *= 2){ vector ans2 = ans; ans2.resize(i * 4); vector f(min(N, i * 2)); for (int j = 0; j < min(N, i * 2); j++){ f[j] = P[j]; } f.resize(i * 4); ans2 = convolution(ans2, ans2); ans2 = convolution(ans2, f); ans2.resize(i * 2); for (int j = 0; j < i; j++){ ans2[j] = MOD - ans2[j] + ans[j] * 2; ans2[j] %= MOD; } swap(ans, ans2); } ans.resize(N); return ans; } int main(){ int N, M; cin >> N >> M; vector A(N); for (int i = 0; i < N; i++){ cin >> A[i]; } int N2 = 1; while (N2 < N){ N2 *= 2; } while (A.size() < N2){ A.push_back(0); } N = N2; vector, int>> ST1(N2 * 2 - 1); for (int i = 0; i < N; i++){ vector f = {1, MOD - A[i]}; ST1[N2 - 1 + i] = make_pair(f, 1); } for (int i = N2 - 2; i >= 0; i--){ int deg = min(M + 1, ST1[i * 2 + 1].second + ST1[i * 2 + 2].second + 1); ST1[i] = make_pair(convolution(ST1[i * 2 + 1].first, ST1[i * 2 + 2].first, deg), deg); } while (ST1[0].first.size() <= M * 2){ ST1[0].first.push_back(0); } /* for (int i = 0; i <= M; i++){ cout << ST1[0].first[i] << ' '; } cout << endl; */ vector, int>> ST2(N2 * 2 - 1); for (int i = 0; i < N; i++){ vector f = {1}; ST2[N2 - 1 + i] = make_pair(f, 1); } for (int i = N2 - 2; i >= 0; i--){ if (ST2[i * 2 + 2].second == 0){ ST2[i] = ST2[i * 2 + 1]; } else { int deg = min(M + 1, ST2[i * 2 + 1].second + ST2[i * 2 + 2].second); ST2[i] = make_pair(add(convolution(ST2[i * 2 + 1].first, ST1[i * 2 + 2].first, deg), convolution(ST1[i * 2 + 1].first, ST2[i * 2 + 2].first, deg)), deg); } } while (ST2[0].first.size() <= M * 2){ ST2[0].first.push_back(0); } /* for (int i = 0; i <= M; i++){ cout << ST2[0].first[i] << ' '; } cout << endl; */ vector g = ST1[0].first; vector f = ST2[0].first; //f/g vector g_inv = inverse(g); /* vector h = convolution(g, g_inv); for (int i = 0; i <= M; i++){ cout << h[i] << ' '; } cout << endl; */ vector ans = convolution(f, g_inv); for (int i = 1; i <= M; i++){ cout << ans[i]; if (i < M){ cout << ' '; } } cout << endl; }