mod = 998244353 n = 300000 inv = [1 for j in range(n + 1)] for a in range(2,n + 1): # ax + py = 1 <=> rx + p(-x-qy) = -q => x = -(inv[r]) * (p//a) (r = p % a) res = (mod - inv[mod % a]) * (mod // a) inv[a] = res % mod fact = [1 for i in range(n + 1)] for i in range(1,n + 1): fact[i] = fact[i - 1] * i % mod fact_inv = [1 for i in range(n + 1)] fact_inv[-1] = pow(fact[-1],mod - 2,mod) for i in range(n,0,-1): fact_inv[i - 1] = fact_inv[i] * i % mod def binom(n,r): if n < r or n < 0 or r < 0: return 0 res = fact_inv[n - r] * fact_inv[r] % mod res *= fact[n] res %= mod return res NTT_friend = [120586241,167772161,469762049,754974721,880803841,924844033,943718401,998244353,1045430273,1051721729,1053818881] NTT_dict = {} for i in range(len(NTT_friend)): NTT_dict[NTT_friend[i]] = i NTT_info = [[20,74066978],[25,17],[26,30],[24,362],[23,211],[21,44009197],[22,663003469],[23,31],[20,363],[20,330],[20,2789]] def popcount(n): c = (n&0x5555555555555555) + ((n>>1)&0x5555555555555555) c = (c&0x3333333333333333) + ((c>>2)&0x3333333333333333) c = (c&0x0f0f0f0f0f0f0f0f) + ((c>>4)&0x0f0f0f0f0f0f0f0f) c = (c&0x00ff00ff00ff00ff) + ((c>>8)&0x00ff00ff00ff00ff) c = (c&0x0000ffff0000ffff) + ((c>>16)&0x0000ffff0000ffff) c = (c&0x00000000ffffffff) + ((c>>32)&0x00000000ffffffff) return c def topbit(n): h = n.bit_length() h -= 1 return h def prepared_fft(mod = 998244353): rank2 = NTT_info[NTT_dict[mod]][0] root,iroot = [0] * 30,[0] * 30 rate2,irate2= [0] * 30,[0] * 30 rate3,irate3= [0] * 30,[0] * 30 root[rank2] = NTT_info[NTT_dict[mod]][1] iroot[rank2] = pow(root[rank2],mod - 2,mod) for i in range(rank2 - 1,-1,-1): root[i] = root[i + 1] * root[i + 1] % mod iroot[i] = iroot[i + 1] * iroot[i + 1] % mod prod,iprod = 1,1 for i in range(rank2-1): rate2[i] = root[i + 2] * prod % mod irate2[i] = iroot[i + 2] * iprod % mod prod = prod * iroot[i + 2] % mod iprod = iprod * root[i + 2] % mod prod,iprod = 1,1 for i in range(rank2-2): rate3[i] = root[i + 3] * prod % mod irate3[i] = iroot[i + 3] * iprod % mod prod = prod * iroot[i + 3] % mod iprod = iprod * root[i + 3] % mod return root,iroot,rate2,irate2,rate3,irate3 root,iroot,rate2,irate2,rate3,irate3 = prepared_fft() def ntt(a): n = len(a) h = topbit(n) assert (n == 1 << h) le = 0 while le < h: if h - le == 1: p = 1 << (h - le - 1) rot = 1 for s in range(1 << le): offset = s << (h - le) for i in range(p): l = a[i + offset] r = a[i + offset + p] * rot % mod a[i + offset] = (l + r) % mod a[i + offset + p] = (l - r) % mod rot = rot * rate2[topbit(~s & -~s)] % mod le += 1 else: p = 1 << (h - le - 2) rot,imag = 1,root[2] for s in range(1 << le): rot2 = rot * rot % mod rot3 = rot2 * rot % mod offset = s << (h - le) 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) % mod * imag a[i + offset] = (a0 + a2 + a1 + a3) % mod a[i + offset + p] = (a0 + a2 - a1 - a3) % mod a[i + offset + p * 2] = (a0 - a2 + a1na3imag) % mod a[i + offset + p * 3] = (a0 - a2 - a1na3imag) % mod rot = rot * rate3[topbit(~s & -~s)] % mod le += 2 def intt(a): n = len(a) h = topbit(n) assert (n == 1 << h) coef = pow(n,mod - 2,mod) for i in range(n): a[i] = a[i] * coef % mod le = h while le: if le == 1: p = 1 << (h - le) irot = 1 for s in range(1 << (le - 1)): offset = s << (h - le + 1) for i in range(p): l = a[i + offset] r = a[i + offset + p] a[i + offset] = (l + r) % mod a[i + offset + p] = (l - r) * irot % mod irot = irot * irate2[topbit(~s & -~s)] % mod le -= 1 else: p = 1 << (h - le) irot,iimag = 1,iroot[2] for s in range(1 << (le - 2)): irot2 = irot * irot % mod irot3 = irot2 * irot % mod offset = s << (h - le + 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 % mod a[i + offset] = (a0 + a1 + a2 + a3) % mod a[i + offset + p] = (a0 - a1 + a2na3iimag) * irot % mod a[i + offset + p * 2] = (a0 + a1 - a2 - a3) * irot2 % mod a[i + offset + p * 3] = (a0 - a1 - a2na3iimag) * irot3 % mod irot *= irate3[topbit(~s & -~s)] irot %= mod le -= 2 def convolute_naive(a,b): res = [0] * (len(a) + len(b) - 1) for i in range(len(a)): for j in range(len(b)): res[i + j] = (res[i + j] + a[i] * b[j] % mod) % mod return res def convolute(a,b): s = a[:] t = b[:] n = len(s) m = len(t) if min(n,m) <= 60: return convolute_naive(s,t) le = 1 while le < n + m - 1: le *= 2 s += [0] * (le - n) t += [0] * (le - m) ntt(s) ntt(t) for i in range(le): s[i] = s[i] * t[i] % mod intt(s) s = s[:n + m - 1] return s N,K = map(int,input().split()) A = list(map(int,input().split())) f = [0 for i in range(N)] f[0] = 1 for i in range(2,N,2): j = i // 2 f[i] = binom(j + K // 2 - 1,j) f = convolute(f,A)[:N] if K % 2: for i in range(N): if i % 2: f[i] = mod - f[i] for i in range(N - 1): f[i + 1] += f[i] f[i + 1] %= mod print(*f)