class NTT998: # fmt: off 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) # fmt: on def butterfly(A): n = len(A) h = (n - 1).bit_length() 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 A[i + offset] = (l + r) % 998244353 A[i + offset + p] = (l - r) % 998244353 rot *= NTT998.rate2[(~s & -~s).bit_length()] rot %= 998244353 le += 1 else: p = 1 << (h - le - 2) rot = 1 for s in range(1 << le): rot2 = rot * rot % 998244353 rot3 = rot2 * rot % 998244353 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) % 998244353 * 911660635 A[i + offset] = (a0 + a2 + a1 + a3) % 998244353 A[i + offset + p] = (a0 + a2 - a1 - a3) % 998244353 A[i + offset + p * 2] = (a0 - a2 + a1na3imag) % 998244353 A[i + offset + p * 3] = (a0 - a2 - a1na3imag) % 998244353 rot *= NTT998.rate3[(~s & -~s).bit_length()] rot %= 998244353 le += 2 def butterfly_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) % 998244353 A[i + offset + p] = (l - r) * irot % 998244353 irot *= NTT998.irate2[(~s & -~s).bit_length()] irot %= 998244353 le -= 1 else: p = 1 << (h - le) irot = 1 for s in range(1 << (le - 2)): irot2 = irot * irot % 998244353 irot3 = irot2 * irot % 998244353 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) * 86583718 % 998244353 A[i + offset] = (a0 + a1 + a2 + a3) % 998244353 A[i + offset + p] = (a0 - a1 + a2na3iimag) * irot % 998244353 A[i + offset + p * 2] = (a0 + a1 - a2 - a3) * irot2 % 998244353 A[i + offset + p * 3] = ( (a0 - a1 - a2na3iimag) * irot3 % 998244353 ) irot *= NTT998.irate3[(~s & -~s).bit_length()] irot %= 998244353 le -= 2 def multiply(A, B): n = len(A) m = len(B) if min(n, m) <= 60: C = [0] * (n + m - 1) for i in range(n): if i % 8 == 0: for j in range(m): C[i + j] += A[i] * B[j] C[i + j] %= 998244353 else: for j in range(m): C[i + j] += A[i] * B[j] return [c % 998244353 for c in C] A = A[:] B = B[:] z = 1 << (n + m - 2).bit_length() A += [0] * (z - n) B += [0] * (z - m) NTT998.butterfly(A) NTT998.butterfly(B) for i in range(z): A[i] *= B[i] A[i] %= 998244353 NTT998.butterfly_inv(A) A = A[: n + m - 1] iz = pow(z, 998244353 - 2, 998244353) return [a * iz % 998244353 for a in A] def modinv(a, MOD): b = MOD u = 1 v = 0 while b > 0: t = a // b a -= t * b u -= t * v a, b = b, a u, v = v, u if a != 1: return -1 if u != 0: u += MOD return u class Combination: def __init__(self, n, MOD=998244353): self.fact = [1] * (n + 1) self.invfact = [1] * (n + 1) self.MOD = MOD for i in range(1, n + 1): self.fact[i] = self.fact[i - 1] * i % MOD self.invfact[n] = pow(self.fact[n], MOD - 2, MOD) for i in range(n - 1, -1, -1): self.invfact[i] = self.invfact[i + 1] * (i + 1) % MOD def extend(self, n): le = len(self.fact) if n < le: return self.fact.extend([1] * (n - le + 1)) self.invfact.extend([1] * (n - le + 1)) for i in range(le, n + 1): self.fact[i] = self.fact[i - 1] * i % self.MOD self.invfact[n] = pow(self.fact[n], self.MOD - 2, self.MOD) for i in range(n - 1, le - 1, -1): self.invfact[i] = self.invfact[i + 1] * (i + 1) % self.MOD def nPk(self, n, k): if k < 0 or n < k: return 0 if n >= len(self.fact): self.extend(n) return self.fact[n] * self.invfact[n - k] % self.MOD def nCk(self, n, k): if k < 0 or n < k: return 0 if n >= len(self.fact): self.extend(n) return ( (self.fact[n] * self.invfact[n - k] % self.MOD) * self.invfact[k] % self.MOD ) def nHk(self, n, k): if n == 0 and k == 0: return 1 return self.nCk(n + k - 1, k) def Catalan(self, n): return (self.nCk(2 * n, n) - self.nCk(2 * n, n - 1)) % self.MOD def cipolla(x, MOD): if MOD == 2: return x elif x == 0: return 0 elif pow(x, (MOD - 1) // 2, MOD) != 1: return -1 y = 1 while pow((y * y - x) % MOD, (MOD - 1) // 2, MOD) == 1: y += 1 base = (y * y - x) % MOD def multi(a0, b0, a1, b1): return (a0 * a1 + base * (b0 * b1 % MOD)) % MOD, (a0 * b1 + a1 * b0) % MOD def pow_(a, b, n): if n == 0: return 1, 0 tmp = multi(a, b, a, b) ret = pow_(tmp[0], tmp[1], n >> 1) if n & 1: ret = multi(ret[0], ret[1], a, b) return ret return pow_(y, 1, (MOD + 1) // 2)[0] class FormalPowerSeries998(list): Comb = Combination(200000) def __init__(self, n): if isinstance(n, int): super().__init__([0] * n) else: super().__init__(n) def __getitem__(self, i): if isinstance(i, slice): return FormalPowerSeries998(super().__getitem__(i)) return super().__getitem__(i) def resize(self, n): if n > len(self): self.extend([0] * (n - len(self))) else: del self[n:] def __add__(self, other): if len(self) > len(other): res = self[:] for i, x in enumerate(other): res[i] += x if res[i] >= 998244353: res[i] -= 998244353 else: res = other[:] for i, x in enumerate(self): res[i] += x if res[i] >= 998244353: res[i] -= 998244353 return res def __iadd__(self, other): if len(self) < len(other): super().__iadd__([0] * (len(other) - len(self))) for i, x in enumerate(other): self[i] += x if self[i] >= 998244353: self[i] -= 998244353 return self def __sub__(self, other): res = self[:] if len(res) < len(other): super(FormalPowerSeries998, res).__iadd__([0] * (len(other) - len(res))) for i, x in enumerate(other): res[i] -= x if res[i] < 0: res[i] += 998244353 return FormalPowerSeries998(res) def __isub__(self, other): if len(self) < len(other): super().__iadd__([0] * (len(other) - len(self))) for i, x in enumerate(other): self[i] -= x if self[i] < 0: self[i] += 998244353 return self def __mul__(self, other): if isinstance(other, int): return FormalPowerSeries998([x * other % 998244353 for x in self]) return FormalPowerSeries998(NTT998.multiply(list(self), list(other))) def __imul__(self, other): return self.__mul__(other) def inv(self, deg=None): if deg is None: deg = len(self) if deg == 0: return FormalPowerSeries998([]) g = FormalPowerSeries998([modinv(self[0], 998244353)]) l = 1 while l < deg: l *= 2 g = g * 2 - (g * g * self[:l]) del g[l:] return g[:deg] def __floordiv__(self, other): return self * other.inv(len(self)) def differential(self): return FormalPowerSeries998( [i * x % 998244353 for i, x in enumerate(self[1:], 1)] ) def integral(self): FormalPowerSeries998.Comb.extend(len(self) + 1) return FormalPowerSeries998( [0] + [ ( FormalPowerSeries998.Comb.fact[i] * FormalPowerSeries998.Comb.invfact[i + 1] % 998244353 ) * x % 998244353 for i, x in enumerate(self) ] ) def log(self, deg=None): if deg is None: deg = len(self) return (self.differential() * self.inv(deg))[:deg].integral()[:deg] def exp(self, deg=None): if deg is None: deg = len(self) g = FormalPowerSeries998([1]) l = 1 while l < deg: l *= 2 g *= (FormalPowerSeries998([1]) - g.log(deg=l) + self[:l])[:l] del g[l:] return g[:deg] def pow(self, k, deg=None): if deg is None: deg = len(self) if k == 0: res = FormalPowerSeries998(deg) res[0] = 1 return res p = -1 for i in range(deg): if self[i] != 0: p = i break if p == -1 or p > deg // k: return FormalPowerSeries998(deg) inv = modinv(self[p], 998244353) A = self[p:] * inv A = A.log(deg) A *= k % 998244353 A = A.exp(deg) B = FormalPowerSeries998(p * k) super(FormalPowerSeries998, B).__iadd__(A[: deg - p * k]) times = 1 pp = self[p] while k > 0: if k & 1: times = times * pp % 998244353 pp = pp * pp % 998244353 k >>= 1 B *= times return B def __pow__(self, k): return self.pow(k) def __ipow__(self, k): return self.pow(k) def sqrt(self, deg=None): if deg is None: deg = len(self) if len(self) == 0: return FormalPowerSeries998(deg) if self[0] == 0: for i in range(1, deg): if self[i] != 0: if i % 2 == 1: return FormalPowerSeries998([]) if deg <= i // 2: break ret = self[i:].sqrt(deg - i // 2) if len(ret) == 0: return FormalPowerSeries998([]) ret = FormalPowerSeries998([0] * (i // 2) + list(ret)) if len(ret) < deg: ret.resize(deg) return ret else: return FormalPowerSeries998(deg) sq = cipolla(self[0], 998244353) if sq == -1: return FormalPowerSeries998([]) inv2 = 499122177 g = FormalPowerSeries998([sq]) l = 1 while l < deg: l *= 2 g = (g + self[:l] * g.inv(l)) * inv2 del g[l:] return g[:deg] class Combination: def __init__(self, n, MOD=998244353): self.fact = [1] * (n + 1) self.invfact = [1] * (n + 1) self.MOD = MOD for i in range(1, n + 1): self.fact[i] = self.fact[i - 1] * i % MOD self.invfact[n] = pow(self.fact[n], MOD - 2, MOD) for i in range(n - 1, -1, -1): self.invfact[i] = self.invfact[i + 1] * (i + 1) % MOD def extend(self, n): le = len(self.fact) if n < le: return self.fact.extend([1] * (n - le + 1)) self.invfact.extend([1] * (n - le + 1)) for i in range(le, n + 1): self.fact[i] = self.fact[i - 1] * i % self.MOD self.invfact[n] = pow(self.fact[n], self.MOD - 2, self.MOD) for i in range(n - 1, le - 1, -1): self.invfact[i] = self.invfact[i + 1] * (i + 1) % self.MOD def nPk(self, n, k): if k < 0 or n < k: return 0 if n >= len(self.fact): self.extend(n) return self.fact[n] * self.invfact[n - k] % self.MOD def nCk(self, n, k): if k < 0 or n < k: return 0 if n >= len(self.fact): self.extend(n) return ( (self.fact[n] * self.invfact[n - k] % self.MOD) * self.invfact[k] % self.MOD ) def nHk(self, n, k): if n == 0 and k == 0: return 1 return self.nCk(n + k - 1, k) def Catalan(self, n): return (self.nCk(2 * n, n) - self.nCk(2 * n, n - 1)) % self.MOD MOD = 998244353 FPS = FormalPowerSeries998 h, w = map(int, input().split()) A = FPS(h + 1) B = FPS(w + 1) Comb = Combination(h + w + 10, MOD) for i in range(1, h + 1): A[i] = Comb.nCk(i, h - i) * Comb.invfact[i] % MOD for i in range(1, w + 1): B[i] = Comb.nCk(i, w - i) * Comb.invfact[i] % MOD C = A * B ans = 0 for i, c in enumerate(C): ans += c * Comb.fact[i] % MOD print(ans % MOD)