# https://judge.yosupo.jp/submission/222202 mod = 998244353 imag = 911660635 iimag = 86583718 rate2 = (0, 911660635, 509520358, 369330050, 332049552, 983190778, 123842337, 238493703, 975955924, 603855026, 856644456, 131300601, 842657263, 730768835, 942482514, 806263778, 151565301, 510815449, 503497456, 743006876, 741047443, 56250497, 867605899, 0) irate2 = (0, 86583718, 372528824, 373294451, 645684063, 112220581, 692852209, 155456985, 797128860, 90816748, 860285882, 927414960, 354738543, 109331171, 293255632, 535113200, 308540755, 121186627, 608385704, 438932459, 359477183, 824071951, 103369235, 0) rate3 = (0, 372528824, 337190230, 454590761, 816400692, 578227951, 180142363, 83780245, 6597683, 70046822, 623238099, 183021267, 402682409, 631680428, 344509872, 689220186, 365017329, 774342554, 729444058, 102986190, 128751033, 395565204, 0) irate3 = (0, 509520358, 929031873, 170256584, 839780419, 282974284, 395914482, 444904435, 72135471, 638914820, 66769500, 771127074, 985925487, 262319669, 262341272, 625870173, 768022760, 859816005, 914661783, 430819711, 272774365, 530924681, 0) def fft(a): n = len(a) h = (n - 1).bit_length() le = 0 while le < h: if h == le + 1: p = 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 a[i + offset] = (l + r) % mod a[i + offset + p] = (l - r) % mod rot *= rate2[(~s & -~s).bit_length()] rot %= mod le += 1 else: p = 1 << (h - le - 2) rot = 1 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 *= rate3[(~s & -~s).bit_length()] rot %= mod le += 2 def fft_inv(a): n = len(a) h = (n - 1).bit_length() 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 *= irate2[(~s & -~s).bit_length()] irot %= mod le -= 1 else: p = 1 << (h - le) irot = 1 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[(~s & -~s).bit_length()] irot %= mod le -= 2 def ntt(a): if len(a) <= 1: return fft(a) def ntt_inv(a): if len(a) <= 1: return fft_inv(a) iv = pow(len(a),mod-2,mod) for i in range(len(a)): a[i] = a[i] * iv % mod def convolute(a,b): aa = a[:] bb = b[:] n = len(aa) m = len(bb) if min(n,m) <= 60: return convolute_naive(a,b) z = 1 << (n + m - 2).bit_length() aa += [0] * (z - n) bb += [0] * (z - m) fft(aa) fft(bb) for i in range(z): aa[i] = aa[i] * bb[i] % mod fft_inv(aa) aa = aa[:n + m - 1] iz = pow(z, mod - 2, mod) for i in range(n+m-1): aa[i] = (aa[i] * iz) % mod return aa 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_slice(a : list[int], b : list[int], l : int, r : int) -> list[int]: if r < 30: res = [0] * (r - l) for i in range(len(a)): for j in range(max(0, l - i), min(len(b), r - i)): res[i + j - l] = (res[i + j - l] + a[i] * b[j] % mod) % mod return res else: n = len(a) + len(b) - 2 m = max(len(a), len(b)) sz = 1 while sz < m or r > sz or n >= l + sz: sz *= 2 na = a[:] nb = b[:] na += [0] * (sz - len(na)) nb += [0] * (sz - len(nb)) fft(na) fft(nb) iz = pow(sz, mod - 2, mod) for i in range(sz): na[i] = na[i] * nb[i] % mod na[i] = na[i] * iz % mod fft_inv(na) return na[l : r] N, K = map(int, input().split()) L = N fact = [1] * (L + 1) inv_fact = [1] * (L + 1) for i in range(L): fact[i + 1] = fact[i] * (i + 1) % mod inv_fact[L] = pow(fact[L], mod - 2, mod) for i in range(L, 1, -1): inv_fact[i - 1] = inv_fact[i] * i % mod g = [1] * N for i in range(N): g[i] = pow(N - i - 1, K, mod) def f(l : int, r : int, v : list[int], ans : list[int]) -> tuple[list[int], list[int]]: if l + 1 == r: ans[l] = v[-1] return [l + 1], [l + 1, 2] m = (l + r) // 2 nv = [0] * (m - l) for i in range(m - l): nv[i] = v[i + r - m] LA, LB = f(l, m, nv, ans) nv = [0] * (r - m) nv1 = convolute_slice(v, LB, m - l, r - l) ng = [0] * (r - l) for i in range(r - l): ng[i] = g[i + N - r + l] nv2 = convolute_slice(ng, LA, m - l, r - l) for i in range(r - m): nv[i] = (nv1[i] + nv2[i] * fact[l]) % mod RA, RB = f(m, r, nv, ans) if r == N: return [], [] nA = convolute(LA, RB) tmp = fact[m] * inv_fact[l] % mod for i, a in enumerate(RA): nA[i] = (nA[i] + a * tmp) % mod return nA, convolute(LB, RB) ans = [0] * N f(0, N, g, ans) res = [0] * N for i in range(1, N): res[i] = (ans[i] - ans[i - 1] * i) % mod res[i] = res[i] * fact[N - 1] % mod res[i] = res[i] * inv_fact[i] % mod # print(sum(res)) for i in range(N): print(res[i] * inv_fact[2] % mod)