#comb(a, b)の前計算 mod = 998244353 N = 10 ** 6 + 2 F = [1] * N E = [1] * N for i in range(2, N): F[i] = F[i-1]*i%mod E[-1] = pow(F[-1], -1, mod) for i in range(N-1, 0, -1): E[i-1] = E[i]*i%mod def comb(a, b): if b < 0: return 0 if a < b: return 0 return F[a] * E[b] * E[a-b] % mod _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 for le in range(0, h - 1, 2): 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 = rot * _rate3[(~s & -~s).bit_length()] % mod if h - le & 1: rot = 1 for s in range(1 << (h - 1)): offset = s << 1 l = a[offset] r = a[offset + 1] * rot a[offset] = (l + r) % mod a[offset + 1] = (l - r) % mod rot = rot * _rate2[(~s & -~s).bit_length()] % mod def _ifft(a): n = len(a) h = (n - 1).bit_length() le = h for le in range(h, 1, -2): 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 = irot * _irate3[(~s & -~s).bit_length()] % mod if le & 1: p = 1 << (h - 1) for i in range(p): l = a[i] r = a[i + p] a[i] = l + r if l + r < mod else l + r - mod a[i + p] = l - r if l - r >= 0 else l - r + mod def ntt(a) -> None: if len(a) <= 1: return _fft(a) def intt(a) -> None: if len(a) <= 1: return _ifft(a) iv = pow(len(a), mod - 2, mod) for i, x in enumerate(a): a[i] = x * iv % mod def multiply(s: list, t: list) -> list: n, m = len(s), len(t) l = n + m - 1 if min(n, m) <= 60: a = [0] * l for i, x in enumerate(s): for j, y in enumerate(t): a[i + j] += x * y return [x % mod for x in a] z = 1 << (l - 1).bit_length() a = s + [0] * (z - n) b = t + [0] * (z - m) _fft(a) _fft(b) for i, x in enumerate(b): a[i] = a[i] * x % mod _ifft(a) a[l:] = [] iz = pow(z, mod - 2, mod) return [x * iz % mod for x in a] # 入力 n, edge_s, edge_t = map(int, input().split()) edge_s -= 1 edge_t -= 1 # Edge_cnt[i]: 頂点iの次数 # Node[i]: 頂点iと隣接してる頂点リスト # Dist[i]: 頂点iにおける、始点の候補からの距離 Edge_cnt = [0] * N Node = [[] for _ in range(n)] Dist = [-1] * n for i in range(n-1): u, v = [int(x)-1 for x in input().split()] if i == edge_s: Points_s = [u, v] #始点の候補 elif i == edge_t: Points_t = [u, v] #終点の候補 Node[u].append(v) Node[v].append(u) Edge_cnt[u] += 1 Edge_cnt[v] += 1 # Stuckを用いたBFSで、終点を見つける Stuck = [] for u in Points_s: Dist[u] = 0 Stuck.append(u) while Stuck: now = Stuck.pop() if now in Points_t: point_t = now else: for nxt in Node[now]: if Dist[nxt] == -1: Dist[nxt] = Dist[now] + 1 Stuck.append(nxt) # 終点から始点までのパスにおける、各頂点の次数をメモる now = point_t Used_edges = [] while Dist[now] > 0: Used_edges.append(Edge_cnt[now]-2) for nxt in Node[now]: if Dist[nxt] < Dist[now]: now = nxt break Used_edges.append(Edge_cnt[now]-2) # F[i]: iの階上 def merge(l, r): if l+1 == r: cnt = Used_edges[l] return [(comb(cnt, i) * F[i]) % mod for i in range(cnt+1)] mid = l + r >> 1 return multiply(merge(l, mid), merge(mid, r)) Ans = [0] * len(Used_edges) + merge(0, len(Used_edges)) Ans = Ans + [0] * (n - len(Ans)) print(*Ans)