mod = 998244353 sum_e = (911660635, 509520358, 369330050, 332049552, 983190778, 123842337, 238493703, 975955924, 603855026, 856644456, 131300601, 842657263, 730768835, 942482514, 806263778, 151565301, 510815449, 503497456, 743006876, 741047443, 56250497) sum_ie = (86583718, 372528824, 373294451, 645684063, 112220581, 692852209, 155456985, 797128860, 90816748, 860285882, 927414960, 354738543, 109331171, 293255632, 535113200, 308540755, 121186627, 608385704, 438932459, 359477183, 824071951) import random def cipolla(a, p): a %= p if p == 2: return a if a == 0: return 0 k = (p - 1) // 2 if pow(a, k, p) != 1: return -1 while True: c = random.randint(2, p - 1) theta = (c * c - a) % p if theta == 0: return c if pow(theta, k, p) == p - 1: break k += 1 f0, f1 = c, 1 g0, g1 = 1, 0 while k: if k & 1: g0, g1 = f0 * g0 + theta * f1 * g1, f1 * g0 + f0 * g1 f0, f1 = f0 * f0 + theta * f1 * f1, 2 * f0 * f1 f0 %= p f1 %= p g0 %= p g1 %= p k >>= 1 return g0 def inv_gcd(a, b): a %= b if a == 0: return b, 0 s, t = b, a m0, m1 = 0, 1 while t: u = s // t s -= t * u m0 -= m1 * u s, t = t, s m0, m1 = m1, m0 if m0 < 0: m0 += b // s return s, m0 def inv_mod(x): return inv_gcd(x, mod)[1] class Binomial: def __init__(self): self.fac_ = [1, 1] self.finv_ = [1, 1] self.inv_ = [1, 1] def extend(self): n = len(self.fac_) a = self.fac_[-1] * n % mod b = (-self.inv_[mod % n]) * (mod // n) % mod c = self.finv_[-1] * b % mod self.fac_.append(a) self.inv_.append(b) self.finv_.append(c) def fac(self, i): while i >= len(self.fac_): self.extend() return self.fac_[i] def finv(self, i): while i >= len(self.finv_): self.extend() return self.finv_[i] def inv(self, i): while i >= len(self.inv_): self.extend() return self.inv_[i] def comb(self, n, k): if n < k or k < 0: return 0 return self.fac(n) * self.finv(n - r) * self.finv(r) % mod def perm(self, n, k): if n < k or r < 0: return 0 return self.fac(n) * self.finv(n - k) % mod bi = Binomial() def butterfly(A): n = len(A) h = (n - 1).bit_length() for ph in range(1, h + 1): w = 1 << (ph - 1) p = 1 << (h - ph) now = 1 for s in range(w): offset = s << (h - ph + 1) for i in range(p): l = A[i + offset] r = A[i + offset + p] * now A[i + offset] = (l + r) % mod A[i + offset + p] = (l - r) % mod now *= sum_e[(~s & -~s).bit_length() - 1] now %= mod def butterfly_inv(A): n = len(A) h = (n - 1).bit_length() for ph in range(h, 0, -1): w = 1 << (ph - 1) p = 1 << (h - ph) inow = 1 for s in range(w): offset = s << (h - ph + 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] = (mod + l - r) * inow % mod inow *= sum_ie[(~s & -~s).bit_length() - 1] inow %= mod def convolution(_A, _B): A = _A.copy() B = _B.copy() n = len(A) m = len(B) if not n or not m: return [] if min(n, m) <= 60: if n < m: n, m = m, n A, B = B, A res = [0] * (n + m - 1) for i in range(n): for j in range(m): res[i + j] += A[i] * B[j] res[i + j] %= mod return res z = 1 << (n + m - 2).bit_length() A += [0] * (z - n) B += [0] * (z - m) butterfly(A) butterfly(B) for i in range(z): A[i] *= B[i] A[i] %= mod butterfly_inv(A) A = A[:n + m - 1] iz = inv_mod(z) for i in range(n + m - 1): A[i] *= iz A[i] %= mod return A def autocorrelation(_A): A = _A.copy() n = len(A) if not n: return [] if n <= 60: res = [0] * (n + n - 1) for i in range(n): for j in range(n): res[i + j] += A[i] * A[j] res[i + j] %= mod return res z = 1 << (n + n - 2).bit_length() A += [0] * (z - n) butterfly(A) for i in range(z): A[i] *= A[i] A[i] %= mod butterfly_inv(A) A = A[:n + n - 1] iz = inv_mod(z) for i in range(n + n - 1): A[i] *= iz A[i] %= mod return A class formal_power_series: def __init__(self, poly=[]): self.poly = [p % mod for p in poly] def __getitem__(self, key): if isinstance(key, slice): res = self.poly[key] return formal_power_series(res) else: if key < 0: raise IndexError("list index out of range") if key >= len(self.poly): return 0 else: return self.poly[key] def __setitem__(self, key, value): if key < 0: raise IndexError("list index out of range") if key >= len(self.poly): self.poly += [0] * (key - len(self.poly) + 1) self.poly[key] = value % mod def __len__(self): return len(self.poly) def times(self, n): n %= mod res = [p * n for p in self.poly] return formal_power_series(res) def __pos__(self): return self def __neg__(self): return self.times(-1) def __add__(self, other): if other.__class__ == formal_power_series: s = len(self) t = len(other) n = min(s, t) res = [self.poly[i] + other.poly[i] for i in range(n)] if s >= t: res += self.poly[t:] else: res += other.poly[s:] return formal_power_series(res) else: self.poly[0] += other self.poly[0] %= mod return self def __radd__(self, other): return self + other def __sub__(self, other): return self + (-other) def __rsub__(self, other): return (-self) + other def __mul__(self, other): if other.__class__ == formal_power_series: res = convolution(self.poly, other.poly) return formal_power_series(res) else: return self.times(other) def __rmul__(self, other): return self.times(other) def __lshift__(self, other): return formal_power_series(([0] * other) + self.poly) def __rshift__(self, other): return self[other:] def square(self): res = autocorrelation(self.poly) return formal_power_series(res) def inv(self, deg=-1): assert self.poly[0] if deg == -1: deg = len(self) - 1 r = inv_mod(self.poly[0]) m = 1 T = [0] * (deg + 1) T[0] = r res = formal_power_series(T) t = 748683265 iz = 1 while m <= deg: F = [0] * (2 * m) G = [0] * (2 * m) for j in range(min(len(self), 2 * m)): F[j] = self.poly[j] for j in range(m): G[j] = res[j] butterfly(F) butterfly(G) for j in range(2 * m): F[j] *= G[j] F[j] %= mod butterfly_inv(F) for j in range(m): F[j] = 0 butterfly(F) for j in range(2 * m): F[j] *= G[j] F[j] %= mod butterfly_inv(F) iz *= t iz %= mod for j in range(m, min(2 * m, deg + 1)): res[j] = -F[j]*iz m <<= 1 return res #P/Q def __truediv__(self, other): if other.__class__ == formal_power_series: return (self * other.inv()) else: return self * inv_mod(other) def __rtruediv__(self, other): return other * self.inv() #P,Qを多項式として見たときのPをQで割った商を求める def __floordiv__(self, other): if other.__class__ == formal_power_series: if len(self) < len(other): return formal_power_series() else: m = len(self) - len(other) + 1 res = (self[-1:-m-1:-1] * other[::-1].inv(m))[m-1::-1] return res else: return self * inv_mod(other) def __rfloordiv__(self, other): return other * self.inv() def __mod__(self, other): if len(self) < len(other): return self[:] else: res = self[:len(other) - 1] - ((self // other) * other)[:len(other) - 1] return res def differentiate(self): res = [k * p for k, p in enumerate(self.poly[1:], 1)] return formal_power_series(res) def integrate(self): res = [0] + [bi.inv(k) * p for k, p in enumerate(self.poly, 1)] return formal_power_series(res) def log(self, deg=-1): if deg == -1: deg = len(self) - 1 return (self.differentiate() * self.inv(deg))[:deg].integrate() def exp(self, deg=-1): if deg == -1: deg = len(self) - 1 res = formal_power_series([1]) G = formal_power_series([1]) df = self.differentiate() m = 1 while m <= deg: G = G * 2 - (res * G.square())[:m] m <<= 1 dft = df[:m] W = dft + (G * (res.differentiate() - (res * dft)[:m]))[:m] res += (res * (self[:m] - W.integrate()[:m]))[:m] return res[:deg + 1] def __pow__(self, n, deg=-1): if deg == -1: deg = len(self) - 1 m = abs(n) for d, p in enumerate(self.poly): if p: break else: return formal_power_series() if d * m >= len(self): return formal_power_series() G = self[d:] G = ((G * inv_mod(p)).log() * m).exp() * pow(p, m, mod) res = formal_power_series([0] * (d * m) + G.poly) if n >= 0: return res[:deg + 1] else: return res.inv()[:deg + 1] def sqrt(self, deg=-1): if deg == -1: deg = len(self) - 1 if len(self) == 0: return formal_power_series() if self.poly[0] == 0: for d in range(1, len(self)): if self.poly[d]: if d & 1: return -1 if deg < d // 2: break res = self[d:].sqrt(deg - d // 2) if res == -1: return -1 res = res << (d // 2) return res return formal_power_series() sqr = cipolla(self.poly[0], mod) if sqr == -1: return -1 T = [0] * (deg + 1) T[0] = sqr res = formal_power_series(T) two_inv = (mod + 1) // 2 m = 1 while m <= deg: m <<= 1 k = min(m, deg + 1) res = res + (self[:k] * res.inv(k -1))[:k] res = res * two_inv return res #各p_i(0<=i> 1] % G[i] res = [G[i][0] for i in range(size, size + m)] return res def taylor_shift(self, a): n = len(self) res = self[:] for i in range(n): res[i] *= bi.fac(i) res = res[::-1] G = formal_power_series([0] * n) G[0] = 1 for i in range(1, n): G[i] = G[i - 1] * a * bi.inv(i) res = (res * G)[:n] res = res[::-1] for i in range(n): res[i] *= bi.finv(i) return res #[x^n]P/Qを求める def poly_coef(Q, P, n): while n: R = [0] * len(Q.poly) for i, q in enumerate(Q.poly): if i & 1: R[i] = -q else: R[i] = q R = formal_power_series(R) P = P * R Q = Q * R if n & 1: P = P[1::2] else: P = P[::2] Q = Q[::2] n >>= 1 return P[0] def subset_sum(A, limit): C = [0] * (limit + 1) for a in A: C[a] += 1 res = formal_power_series([0] * (limit + 1)) for i in range(1, limit + 1): for k in range(1, limit // i + 1): j = i * k res[j] += ((k & 1) * 2 - 1) * C[i] * bi.inv(k) return res.exp(limit).poly def partition_function(n): res = formal_power_series([0] * (n + 1)) res[0] = 1 for k in range(1, n+1): k1 = k * (3 * k + 1 )// 2 k2 = k * (3 * k - 1) // 2 if k2 > n: break if k1 <= n: res[k1] += 1 - (k & 1) * 2 if k2 <= n: res[k2] += 1 - (k & 1) * 2 return res.inv().poly def bernoulli_number(n): n += 1 Q = formal_power_series([bi.finv(i + 1) for i in range(n)]).inv(n - 1) res = [v * bi.fac(i) % mod for i, v in enumerate(Q.poly)] return res def stirling_first(n): if n <= 0: return formal_power_series([1]) lg = (n - 1).bit_length() res = formal_power_series([0, 1]) for i in range(lg - 1, -1, -1): k = n >> i F *= F.taylor_shift(k >> 1) def stirling_second(n): F = formal_power_series([0] * (n + 1)) G = formal_power_series([0] * (n + 1)) for i in range(n + 1): F[i] = pow(i, n, mod) * bi.finv(i) G[i] = (1 - (i & 1) * 2) * bi.finv(i) return (F * G)[:n + 1].poly import sys input = sys.stdin.readline n, m = map(int, input().split()) A = tuple(map(int, input().split())) F = formal_power_series([0]*(m+1)) for a in A: T = formal_power_series([1, -a]).log(m) F += T L = [] for k in range(1, m+1): L.append(-F[k] * k % mod) print(*L)