package contest191122; import java.io.ByteArrayInputStream; import java.io.IOException; import java.io.InputStream; import java.io.PrintWriter; import java.util.Arrays; import java.util.InputMismatchException; public class F { InputStream is; PrintWriter out; String INPUT = ""; void solve() { int n = ni(); int[] a = na(n-1); int[] b = na(n-1); int[] vals = new int[n-1]; if(n == 2) { out.println((long)a[0]*b[0]%998244353); return; } for(int i = 2;i < n;i++) { int p = 0; for(long j = i;j != 1;) { vals[p++] = (int)j; j = j * i % n; } vals[p++] = 1; if(p == n-1)break; } long[] ua = new long[n-1]; for(int i = 0;i < n-1;i++) { ua[(i+1)%(n-1)] = a[vals[i]-1]; } long[] ub = new long[n-1]; for(int i = 0;i < n-1;i++) { ub[(i+1)%(n-1)] = b[vals[i]-1]; } long[] uc = convoluteSimply(ua, ub, 998244353, 3); int[] c = new int[n-1]; for(int i = 0;i < n-1;i++) { c[vals[i]-1] = (int)((uc[(i+1)%(n-1)] + uc[(i+1)%(n-1)+n-1]) % 998244353); } for(int i = 0;i < n-1;i++) { out.print(c[i] + " "); } } public static long[] convoluteSimply(long[] a, long[] b, int P, int g) { int m = Math.max(2, Integer.highestOneBit(Math.max(a.length, b.length)-1)<<2); long[] fa = nttmb(a, m, false, P, g); long[] fb = a == b ? fa : nttmb(b, m, false, P, g); for(int i = 0;i < m;i++){ fa[i] = fa[i]*fb[i]%P; } return nttmb(fa, m, true, P, g); } // static int[] wws = new int[270000]; // outer faster // Modifed Montgomery + Barrett private static long[] nttmb(long[] src, int n, boolean inverse, int P, int g) { long[] dst = Arrays.copyOf(src, n); int h = Integer.numberOfTrailingZeros(n); long K = Integer.highestOneBit(P)<<1; int H = Long.numberOfTrailingZeros(K)*2; long M = K*K/P; int[] wws = new int[1<= 2*P)dst[s] -= 2*P; // long Q = (u&(1L<<32)-1)*J&(1L<<32)-1; long Q = (u<<32)*J>>>32; dst[t] = (u>>>32)-(Q*P>>>32)+P; } } if(i < h-1){ for(int k = 0;k < 1<= P)dst[i] -= P; } for(int i = 0;i < n;i++){ int rev = Integer.reverse(i)>>>-h; if(i < rev){ long d = dst[i]; dst[i] = dst[rev]; dst[rev] = d; } } if(inverse){ long in = invl(n, P); for(int i = 0;i < n;i++)dst[i] = modh(dst[i]*in, M, H, P); } return dst; } // Modified Shoup + Barrett private static long[] nttsb(long[] src, int n, boolean inverse, int P, int g) { long[] dst = Arrays.copyOf(src, n); int h = Integer.numberOfTrailingZeros(n); long K = Integer.highestOneBit(P)<<1; int H = Long.numberOfTrailingZeros(K)*2; long M = K*K/P; long dw = inverse ? pow(g, P-1-(P-1)/n, P) : pow(g, (P-1)/n, P); long[] wws = new long[1<= 2*P)ndsts -= 2*P; long T = dst[s] - dst[t] + 2*P; long Q = wws[k]*T>>>32; dst[s] = ndsts; dst[t] = ws[k]*T-Q*P&(1L<<32)-1; } } // dw = dw * dw % P; if(i < h-1){ for(int k = 0;k < 1<= P)dst[i] -= P; } for(int i = 0;i < n;i++){ int rev = Integer.reverse(i)>>>-h; if(i < rev){ long d = dst[i]; dst[i] = dst[rev]; dst[rev] = d; } } if(inverse){ long in = invl(n, P); for(int i = 0;i < n;i++){ dst[i] = modh(dst[i] * in, M, H, P); } } return dst; } static final long mask = (1L<<31)-1; public static long modh(long a, long M, int h, int mod) { long r = a-((M*(a&mask)>>>31)+M*(a>>>31)>>>h-31)*mod; return r < mod ? r : r-mod; } private static long[] garnerPrepare(int[] m) { int n = m.length; assert n == m.length; if(n == 0)return new long[0]; long[] gamma = new long[n]; for(int k = 1;k < n;k++){ long prod = 1; for(int i = 0;i < k;i++){ prod = prod * m[i] % m[k]; } gamma[k] = invl(prod, m[k]); } return gamma; } private static long[] garnerBatch(int[] u, int[] m, long[] gamma) { int n = u.length; assert n == m.length; long[] v = new long[n]; v[0] = u[0]; for(int k = 1;k < n;k++){ long temp = v[k-1]; for(int j = k-2;j >= 0;j--){ temp = (temp * m[j] + v[j]) % m[k]; } v[k] = (u[k] - temp) * gamma[k] % m[k]; if(v[k] < 0)v[k] += m[k]; } return v; } private static long pow(long a, long n, long mod) { // a %= mod; long ret = 1; int x = 63 - Long.numberOfLeadingZeros(n); for (; x >= 0; x--) { ret = ret * ret % mod; if (n << 63 - x < 0) ret = ret * a % mod; } return ret; } private static long invl(long a, long mod) { long b = mod; long p = 1, q = 0; while (b > 0) { long c = a / b; long d; d = a; a = b; b = d % b; d = p; p = q; q = d - c * q; } return p < 0 ? p + mod : p; } void run() throws Exception { is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes()); out = new PrintWriter(System.out); long s = System.currentTimeMillis(); solve(); out.flush(); if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms"); // Thread t = new Thread(null, null, "~", Runtime.getRuntime().maxMemory()){ // @Override // public void run() { // long s = System.currentTimeMillis(); // solve(); // out.flush(); // if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms"); // } // }; // t.start(); // t.join(); } public static void main(String[] args) throws Exception { new F().run(); } private byte[] inbuf = new byte[1024]; public int lenbuf = 0, ptrbuf = 0; private int readByte() { if(lenbuf == -1)throw new InputMismatchException(); if(ptrbuf >= lenbuf){ ptrbuf = 0; try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); } if(lenbuf <= 0)return -1; } return inbuf[ptrbuf++]; } private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); } private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; } private double nd() { return Double.parseDouble(ns()); } private char nc() { return (char)skip(); } private String ns() { int b = skip(); StringBuilder sb = new StringBuilder(); while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ') sb.appendCodePoint(b); b = readByte(); } return sb.toString(); } private char[] ns(int n) { char[] buf = new char[n]; int b = skip(), p = 0; while(p < n && !(isSpaceChar(b))){ buf[p++] = (char)b; b = readByte(); } return n == p ? buf : Arrays.copyOf(buf, p); } private int[] na(int n) { int[] a = new int[n]; for(int i = 0;i < n;i++)a[i] = ni(); return a; } private long[] nal(int n) { long[] a = new long[n]; for(int i = 0;i < n;i++)a[i] = nl(); return a; } private char[][] nm(int n, int m) { char[][] map = new char[n][]; for(int i = 0;i < n;i++)map[i] = ns(m); return map; } private int[][] nmi(int n, int m) { int[][] map = new int[n][]; for(int i = 0;i < n;i++)map[i] = na(m); return map; } private int ni() { return (int)nl(); } private long nl() { long num = 0; int b; boolean minus = false; while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')); if(b == '-'){ minus = true; b = readByte(); } while(true){ if(b >= '0' && b <= '9'){ num = num * 10 + (b - '0'); }else{ return minus ? -num : num; } b = readByte(); } } private static void tr(Object... o) { System.out.println(Arrays.deepToString(o)); } }