/** author: shobonvip created: 2026.08.10 21:34:23 **/ #include using namespace std; //* ATCODER #include using namespace atcoder; typedef modint998244353 mint; //*/ /* BOOST MULTIPRECISION #include using namespace boost::multiprecision; //*/ typedef long long ll; #define rep(i, s, n) for (int i = (int)(s); i < (int)(n); i++) #define rrep(i, s, n) for (int i = (int)(n)-1; i >= (int)(s); i--) #define all(v) v.begin(), v.end() template bool chmin(T &a, const T &b) { if (a <= b) return false; a = b; return true; } template bool chmax(T &a, const T &b) { if (a >= b) return false; a = b; return true; } template T max(vector &a){ assert(!a.empty()); T ret = a[0]; for (int i=0; i<(int)a.size(); i++) chmax(ret, a[i]); return ret; } template T min(vector &a){ assert(!a.empty()); T ret = a[0]; for (int i=0; i<(int)a.size(); i++) chmin(ret, a[i]); return ret; } template T sum(vector &a){ T ret = 0; for (int i=0; i<(int)a.size(); i++) ret += a[i]; return ret; } // https://noshi91.hatenablog.com/entry/2024/03/16/224034 // https://atcoder.jp/contests/abc345/submissions/51359643 // https://qoj.ac/submission/356957 // hos_lyricさんの提出を改変 /* q: rev([0, m]) * [0, n], [t^0] q(t, x) = 1 omitted ret: [0, m-1] * [0, n] */ vector comRec(int m, int n, const vector &as, const vector &qss) { if (!n) { auto ret = as; ret.resize(m, 0); return ret; } // reuse DFT(q(t, -x)); (2n+2) instead of (2n+1) int len; for (len = 2; len < (2*m) * (2*n+2); len <<= 1) {} vector qs(len, 0); for (int i = 0; i < m; ++i) for (int j = 0; j <= n; ++j) qs[i * (2*n+2) + j] = qss[i * (n+1) + j]; internal::butterfly(qs); vector work(len >> 1, 0); for (int k = 0; k < len >> 1; ++k) { work[k] = qs[k << 1] * qs[k << 1 | 1]; swap(qs[k << 1], qs[k << 1 | 1]); } internal::butterfly_inv(work); { mint tmp = mint((int)work.size()).inv(); for (int k = 0; k < len >> 1; ++k) work[k] *= tmp; } vector qqss((2*m) * (n/2+1), 0); for (int i = 0; i < 2*m-1; ++i) for (int j = 0; j <= n/2; ++j) qqss[i * (n/2+1) + j] = work[i * (n+1) + j]; for (int i = 0; i < m; ++i) for (int j = 0; j <= n/2; ++j) qqss[(m+i) * (n/2+1) + j] += qss[i * (n+1) + 2*j] + qss[i * (n+1) + 2*j]; const auto res = comRec(2*m, n/2, as, qqss); vector ps(len, 0); for (int i = 0; i < 2*m; ++i) for (int j = 0; j <= n/2; ++j) ps[i * (2*n+2) + (2*n+1) - (2*j+(n&1))] = res[i * (n/2+1) + j]; internal::butterfly(ps); for (int k = 0; k < len; ++k) ps[k] *= qs[k]; internal::butterfly_inv(ps); { mint tmp = mint((int)ps.size()).inv(); for (int k = 0; k < len; ++k) ps[k] *= tmp; } vector ret(m * (n+1)); for (int i = 0; i < m; ++i) for (int j = 0; j <= n; ++j) ret[i * (n+1) + j] = ps[(m+i) * (2*n+2) + (2*n+1) - j]; for (int i = 0; i < m; ++i) for (int j = 0; j <= n/2; ++j) ret[i * (n+1) + (2*j+(n&1))] += res[i * (n/2+1) + j]; return ret; } /* a(b(x)) transpose and rev: p(x) -> [x^(N-1)] p(x) b(x)^i for each i [x^(N-1)] p(x) / (1 - t b(x)) */ vector com(int n, const vector &as, const vector &bs) { assert((int)as.size() <= n); assert((int)bs.size() <= n); vector qss(n, 0); for (int j = 0; j < (int)bs.size(); ++j) qss[j] = -bs[j]; auto cs = comRec(1, n - 1, as, qss); reverse(cs.begin(), cs.end()); return cs; } // ここまで hos_lyricさんの提出を一部改変 int main(){ ios_base::sync_with_stdio(false); cin.tie(NULL); int n,m; cin >> n >> m; vector a(n), b(n), c(n); rep(i,0,n) {int x; cin >> x; a[i] = x;} rep(i,0,n) {int x; cin >> x; b[i] = x;} rep(i,0,n) {int x; cin >> x; c[i] = x;} mint v = a[1].pow(m); vector f = b; for (auto &x: f) x *= v; f = com(n, c, f); for (auto &x: f) cout << x.val() << ' '; cout << '\n'; }