import sys # sys.setrecursionlimit(200005) # sys.set_int_max_str_digits(200005) int1 = lambda x: int(x)-1 pDB = lambda *x: print(*x, end="\n", file=sys.stderr) p2D = lambda x: print(*x, sep="\n", end="\n\n", file=sys.stderr) def II(): return int(sys.stdin.readline()) def LI(): return list(map(int, sys.stdin.readline().split())) def LLI(rows_number): return [LI() for _ in range(rows_number)] def LI1(): return list(map(int1, sys.stdin.readline().split())) def LLI1(rows_number): return [LI1() for _ in range(rows_number)] def SI(): return sys.stdin.readline().rstrip() dij = [(0, 1), (-1, 0), (0, -1), (1, 0)] # dij = [(0, 1), (-1, 0), (0, -1), (1, 0), (1, 1), (1, -1), (-1, 1), (-1, -1)] # inf = -1-(-1 << 31) inf = -1-(-1 << 63) # md = 10**9+7 # md = 998244353 md = 998244353 imag = 911660635 iimag = 86583718 rate2 = ( 911660635, 509520358, 369330050, 332049552, 983190778, 123842337, 238493703, 975955924, 603855026, 856644456, 131300601, 842657263, 730768835, 942482514, 806263778, 151565301, 510815449, 503497456, 743006876, 741047443, 56250497, 867605899) irate2 = ( 86583718, 372528824, 373294451, 645684063, 112220581, 692852209, 155456985, 797128860, 90816748, 860285882, 927414960, 354738543, 109331171, 293255632, 535113200, 308540755, 121186627, 608385704, 438932459, 359477183, 824071951, 103369235) rate3 = ( 372528824, 337190230, 454590761, 816400692, 578227951, 180142363, 83780245, 6597683, 70046822, 623238099, 183021267, 402682409, 631680428, 344509872, 689220186, 365017329, 774342554, 729444058, 102986190, 128751033, 395565204) irate3 = ( 509520358, 929031873, 170256584, 839780419, 282974284, 395914482, 444904435, 72135471, 638914820, 66769500, 771127074, 985925487, 262319669, 262341272, 625870173, 768022760, 859816005, 914661783, 430819711, 272774365, 530924681) def Tonelli_Shanks(N, p): if pow(N, p >> 1, p) == p-1: retu = None elif p%4 == 3: retu = pow(N, (p+1)//4, p) else: for nonresidue in range(1, p): if pow(nonresidue, p >> 1, p) == p-1: break pp = p-1 cnt = 0 while pp%2 == 0: pp //= 2 cnt += 1 s = pow(N, pp, p) retu = pow(N, (pp+1)//2, p) for i in range(cnt-2, -1, -1): if pow(s, 1 << i, p) == p-1: s *= pow(nonresidue, p >> 1+i, p) s %= p retu *= pow(nonresidue, p >> 2+i, p) retu %= p return retu def butterfly(a): n = len(a) h = (n-1).bit_length() len_ = 0 while len_ < h: if h-len_ == 1: p = 1 << (h-len_-1) rot = 1 for s in range(1 << len_): offset = s << (h-len_) for i in range(p): l = a[i+offset] r = a[i+offset+p]*rot%md a[i+offset] = (l+r)%md a[i+offset+p] = (l-r)%md if s+1 != 1 << len_: rot *= rate2[(~s & -~s).bit_length()-1] rot %= md len_ += 1 else: p = 1 << (h-len_-2) rot = 1 for s in range(1 << len_): rot2 = rot*rot%md rot3 = rot2*rot%md offset = s << (h-len_) for i in range(p): a0 = a[i+offset] a1 = a[i+offset+p]*rot a2 = a[i+offset+p*2]*rot2 a3 = a[i+offset+p*3]*rot3 a1na3imag = (a1-a3)%md*imag a[i+offset] = (a0+a2+a1+a3)%md a[i+offset+p] = (a0+a2-a1-a3)%md a[i+offset+p*2] = (a0-a2+a1na3imag)%md a[i+offset+p*3] = (a0-a2-a1na3imag)%md if s+1 != 1 << len_: rot *= rate3[(~s & -~s).bit_length()-1] rot %= md len_ += 2 def butterfly_inv(a): n = len(a) h = (n-1).bit_length() len_ = h while len_: if len_ == 1: p = 1 << (h-len_) irot = 1 for s in range(1 << (len_-1)): offset = s << (h-len_+1) for i in range(p): l = a[i+offset] r = a[i+offset+p] a[i+offset] = (l+r)%md a[i+offset+p] = (l-r)*irot%md if s+1 != (1 << (len_-1)): irot *= irate2[(~s & -~s).bit_length()-1] irot %= md len_ -= 1 else: p = 1 << (h-len_) irot = 1 for s in range(1 << (len_-2)): irot2 = irot*irot%md irot3 = irot2*irot%md offset = s << (h-len_+2) for i in range(p): a0 = a[i+offset] a1 = a[i+offset+p] a2 = a[i+offset+p*2] a3 = a[i+offset+p*3] a2na3iimag = (a2-a3)*iimag%md a[i+offset] = (a0+a1+a2+a3)%md a[i+offset+p] = (a0-a1+a2na3iimag)*irot%md a[i+offset+p*2] = (a0+a1-a2-a3)*irot2%md a[i+offset+p*3] = (a0-a1-a2na3iimag)*irot3%md if s+1 != (1 << (len_-2)): irot *= irate3[(~s & -~s).bit_length()-1] irot %= md len_ -= 2 def integrate(a): a = a.copy() n = len(a) assert n > 0 a.pop() a.insert(0, 0) inv = [1, 1] for i in range(2, n): inv.append(-inv[md%i]*(md//i)%md) a[i] = a[i]*inv[i]%md return a def differentiate(a): n = len(a) assert n > 0 for i in range(2, n): a[i] = a[i]*i%md a.pop(0) a.append(0) return a def convolution_naive(a, b): n = len(a) m = len(b) ans = [0]*(n+m-1) if n < m: for j in range(m): for i in range(n): ans[i+j] = (ans[i+j]+a[i]*b[j])%md else: for i in range(n): for j in range(m): ans[i+j] = (ans[i+j]+a[i]*b[j])%md return ans def convolution_ntt(a, b): a = a.copy() b = b.copy() n = len(a) m = len(b) z = 1 << (n+m-2).bit_length() a += [0]*(z-n) butterfly(a) b += [0]*(z-m) butterfly(b) for i in range(z): a[i] = a[i]*b[i]%md butterfly_inv(a) a = a[:n+m-1] iz = pow(z, md-2, md) for i in range(n+m-1): a[i] = a[i]*iz%md return a def convolution_square(a): a = a.copy() n = len(a) z = 1 << (2*n-2).bit_length() a += [0]*(z-n) butterfly(a) for i in range(z): a[i] = a[i]*a[i]%md butterfly_inv(a) a = a[:2*n-1] iz = pow(z, md-2, md) for i in range(2*n-1): a[i] = a[i]*iz%md return a def convolution(a, b): """It calculates (+, x) convolution in md 998244353. Given two arrays a[0], a[1], ..., a[n - 1] and b[0], b[1], ..., b[m - 1], it calculates the array c of length n + m - 1, defined by > c[i] = sum(a[j] * b[i - j] for j in range(i + 1)) % 998244353. It returns an empty list if at least one of a and b are empty. Complexity ---------- > O(n log n), where n = len(a) + len(b). """ n = len(a) m = len(b) if n == 0 or m == 0: return [] if min(n, m) <= 60: return convolution_naive(a, b) if a is b: return convolution_square(a) return convolution_ntt(a, b) def inverse(a): n = len(a) assert n > 0 and a[0] != 0 res = [pow(a[0], md-2, md)] m = 1 while m < n: f = a[:min(n, 2*m)]+[0]*(2*m-min(n, 2*m)) g = res+[0]*m butterfly(f) butterfly(g) for i in range(2*m): f[i] = f[i]*g[i]%md butterfly_inv(f) f = f[m:]+[0]*m butterfly(f) for i in range(2*m): f[i] = f[i]*g[i]%md butterfly_inv(f) iz = pow(2*m, md-2, md) iz = (-iz*iz)%md for i in range(m): f[i] = f[i]*iz%md res += f[:m] m <<= 1 return res[:n] def log(a): a = a.copy() n = len(a) assert n > 0 and a[0] == 1 a_inv = inverse(a) a = differentiate(a) a = convolution(a, a_inv)[:n] a = integrate(a) return a def exp(a): a = a.copy() n = len(a) assert n > 0 and a[0] == 0 g = [1] a[0] = 1 h_drv = a.copy() h_drv = differentiate(h_drv) m = 1 while m < n: f_fft = a[:m]+[0]*m butterfly(f_fft) if m > 1: _f = [f_fft[i]*g_fft[i]%md for i in range(m)] butterfly_inv(_f) _f = _f[m//2:]+[0]*(m//2) butterfly(_f) for i in range(m): _f[i] = _f[i]*g_fft[i]%md butterfly_inv(_f) _f = _f[:m//2] iz = pow(m, md-2, md) iz *= -iz iz %= md for i in range(m//2): _f[i] = _f[i]*iz%md g.extend(_f) t = a[:m] t = differentiate(t) r = h_drv[:m-1] r.append(0) butterfly(r) for i in range(m): r[i] = r[i]*f_fft[i]%md butterfly_inv(r) im = pow(-m, md-2, md) for i in range(m): r[i] = r[i]*im%md for i in range(m): t[i] = (t[i]+r[i])%md t = [t[-1]]+t[:-1] t += [0]*m butterfly(t) g_fft = g+[0]*(2*m-len(g)) butterfly(g_fft) for i in range(2*m): t[i] = t[i]*g_fft[i]%md butterfly_inv(t) t = t[:m] i2m = pow(2*m, md-2, md) for i in range(m): t[i] = t[i]*i2m%md v = a[m:min(n, 2*m)] v += [0]*(m-len(v)) t = [0]*(m-1)+t+[0] t = integrate(t) for i in range(m): v[i] = (v[i]-t[m+i])%md v += [0]*m butterfly(v) for i in range(2*m): v[i] = v[i]*f_fft[i]%md butterfly_inv(v) v = v[:m] i2m = pow(2*m, md-2, md) for i in range(m): v[i] = v[i]*i2m%md for i in range(min(n-m, m)): a[m+i] = v[i] m *= 2 return a def power(a, k): n = len(a) assert n > 0 if k == 0: return [1]+[0]*(n-1) l = 0 while l < len(a) and not a[l]: l += 1 if l*k >= n: return [0]*n ic = pow(a[l], md-2, md) pc = pow(a[l], k, md) a = log([a[i]*ic%md for i in range(l, len(a))]) for i in range(len(a)): a[i] = a[i]*k%md a = exp(a) for i in range(len(a)): a[i] = a[i]*pc%md a = [0]*(l*k)+a[:n-l*k] return a def sqrt(a): if len(a) == 0: return [] if a[0] == 0: for d in range(1, len(a)): if a[d]: if d & 1: return None if len(a)-1 < d//2: break res = sqrt(a[d:]+[0]*(d//2)) if res == None: return None res = [0]*(d//2)+res return res return [0]*len(a) sqr = Tonelli_Shanks(a[0], md) if sqr == None: return None T = [0]*(len(a)) T[0] = sqr res = T.copy() T[0] = pow(sqr, md-2, md) # T:res^{-1} m = 1 two_inv = (md+1)//2 F = [sqr] while m <= len(a)-1: for i in range(m): F[i] *= F[i] F[i] %= md butterfly_inv(F) iz = pow(m, md-2, md) for i in range(m): F[i] = F[i]*iz%md delta = [0]*(2*m) for i in range(m): delta[i+m] = F[i]-a[i]-(a[i+m] if i+m < len(a) else 0) butterfly(delta) G = [0]*(2*m) for i in range(m): G[i] = T[i] butterfly(G) for i in range(2*m): delta[i] *= G[i] delta[i] %= md butterfly_inv(delta) iz = pow(2*m, md-2, md) for i in range(2*m): delta[i] = delta[i]*iz%md for i in range(m, min(2*m, len(a))): res[i] = -delta[i]*two_inv%md res[i] %= md if 2*m > len(a)-1: break F = res[:2*m] butterfly(F) eps = [F[i]*G[i]%md for i in range(2*m)] butterfly_inv(eps) for i in range(m): eps[i] = 0 iz = pow(2*m, md-2, md) for i in range(m, 2*m): eps[i] = eps[i]*iz%md butterfly(eps) for i in range(2*m): eps[i] *= G[i] eps[i] %= md butterfly_inv(eps) for i in range(m, 2*m): T[i] = -eps[i]*iz T[i] %= md iz = iz*iz%md m <<= 1 return res n,q=LI() a=LI() rr=LI() c=[0]*n for i,r in enumerate(rr):c[(n-r)%n]+=1 ans=convolution(a,c) for i in range(n,len(ans)):ans[i-n]+=ans[i] print(*ans[:n])