from collections import deque import math import sys readline=sys.stdin.readline mod = 998244353 class FFT: def __init__(self, mod=998244353): FFT.mod = mod self.make_info(mod) def make_info(self, mod): g = self.primitive_root_constexpr() m = mod - 1 rank2 = (m & -m).bit_length() - 1 root = [0] * (rank2 + 1) iroot = [0] * (rank2 + 1) rate2 = [0] * (rank2 + 1) irate2 = [0] * (rank2 + 1) rate3 = [0] * (rank2) irate3 = [0] * (rank2) root[rank2] = pow(g, (mod - 1) >> rank2, mod) 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 = 1 iprod = 1 for i in range(1, rank2): rate2[i] = root[i + 1] * prod % mod irate2[i] = iroot[i + 1] * iprod % mod prod = prod * iroot[i + 1] % mod iprod = iprod * root[i + 1] % mod prod = 1 iprod = 1 for i in range(1, rank2 - 1): rate3[i] = root[i + 2] * prod % mod irate3[i] = iroot[i + 2] * iprod % mod prod = prod * iroot[i + 2] % mod iprod = iprod * root[i + 2] % mod self.IMAG = rate2[1] self.IIMAG = irate2[1] self.rate2 = rate2 self.irate2 = irate2 self.rate3 = rate3 self.irate3 = irate3 def primitive_root_constexpr(self): if FFT.mod == 998244353: return 3 elif FFT.mod == 200003: return 2 elif FFT.mod == 167772161: return 3 elif FFT.mod == 469762049: return 3 elif FFT.mod == 754974721: return 11 divs = [0] * 20 divs[0] = 2 cnt = 1 x = (FFT.mod - 1) // 2 while x % 2 == 0: x //= 2 i = 3 while i * i <= x: if x % i == 0: divs[cnt] = i cnt += 1 while x % i == 0: x //= i i += 2 if x > 1: divs[cnt] = x cnt += 1 g = 2 while 1: ok = True for i in range(cnt): if pow(g, (FFT.mod - 1) // divs[i], FFT.mod) == 1: ok = False break if ok: return g g += 1 def butterfly(self, 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) % FFT.mod A[i + offset + p] = (l - r) % FFT.mod rot *= self.rate2[(~s & -~s).bit_length()] rot %= FFT.mod le += 1 else: p = 1 << (h - le - 2) rot = 1 for s in range(1 << le): rot2 = rot * rot % FFT.mod rot3 = rot2 * rot % FFT.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) % FFT.mod * self.IMAG A[i + offset] = (a0 + a2 + a1 + a3) % FFT.mod A[i + offset + p] = (a0 + a2 - a1 - a3) % FFT.mod A[i + offset + p * 2] = (a0 - a2 + a1na3imag) % FFT.mod A[i + offset + p * 3] = (a0 - a2 - a1na3imag) % FFT.mod rot *= self.rate3[(~s & -~s).bit_length()] rot %= FFT.mod le += 2 def butterfly_inv(self, 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) % FFT.mod A[i + offset + p] = (l - r) * irot % FFT.mod irot *= self.irate2[(~s & -~s).bit_length()] irot %= FFT.mod le -= 1 else: p = 1 << (h - le) irot = 1 for s in range(1 << (le - 2)): irot2 = irot * irot % FFT.mod irot3 = irot2 * irot % FFT.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) * self.IIMAG % FFT.mod A[i + offset] = (a0 + a1 + a2 + a3) % FFT.mod A[i + offset + p] = (a0 - a1 + a2na3iimag) * irot % FFT.mod A[i + offset + p * 2] = (a0 + a1 - a2 - a3) * irot2 % FFT.mod A[i + offset + p * 3] = (a0 - a1 - a2na3iimag) * irot3 % FFT.mod irot *= self.irate3[(~s & -~s).bit_length()] irot %= FFT.mod le -= 2 def convolve(self, 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] %= FFT.mod else: for j in range(m): C[i + j] += A[i] * B[j] return [c % FFT.mod for c in C] A = A[:] B = B[:] z = 1 << (n + m - 2).bit_length() A += [0] * (z - n) B += [0] * (z - m) self.butterfly(A) self.butterfly(B) for i in range(z): A[i] *= B[i] A[i] %= FFT.mod self.butterfly_inv(A) A = A[:n + m - 1] iz = pow(z, FFT.mod - 2, FFT.mod) return [a * iz % FFT.mod for a in A] class FPS: fact = [1] invfact = [1] mod = None def __init__(self, data, mod=998244353): if FPS.mod is None: FPS.mod = mod FPS.fft = FFT(mod) if type(data) == int: self.f = [data] else: self.f = data[:] def __len__(self): return len(self.f) def __getitem__(self, i): return self.f[i] def __add__(self, other): if len(self) < len(other): other, self = self, other for i in range(len(other)): self.f[i] += other[i] if self.f[i] >= FPS.mod: self.f[i] -= FPS.mod return self def __iadd__(self, other): return self.__add__(other) def __sub__(self, other): self.f += [0] * (len(other) - len(self)) for i in range(len(other)): self.f[i] -= other[i] if self.f[i] < 0: self.f[i] += FPS.mod return self def __isub__(self, other): return self.__sub__(other) def __mul__(self, other): if type(other) == int: f = [other * x % FPS.mod for x in self.f] return FPS(f) f = FPS.fft.convolve(self.f[:], other.f[:]) return FPS(f) def __imul__(self, other): if type(other) == int: self.f = [other * x % FPS.mod for x in self.f] return self self.f = FPS.fft.convolve(self.f, other.f[:]) return self def inv(self, deg=None): if deg is None: deg = len(self) g = FPS(pow(self[0], FPS.mod - 2, FPS.mod)) l = 1 while l < deg: tmp = g * 2 l *= 2 tmp2 = FPS(self.f[:l]) * (g * g) g = tmp - tmp2 del g.f[l:] del g.f[deg:] return g def differential(self): return FPS([x * i % FPS.mod for i, x in enumerate(self.f[1:], 1)]) def extend_fact(self, l): l1 = len(FPS.fact) l += 1 if l1 <= l: FPS.fact += [0] * (l - l1) FPS.invfact += [0] * (l - l1) for i in range(l1, l): FPS.fact[i] = FPS.fact[i - 1] * i % FPS.mod FPS.invfact[l - 1] = pow(FPS.fact[l - 1], FPS.mod - 2, FPS.mod) for i in range(l - 1, l1, -1): FPS.invfact[i - 1] = FPS.invfact[i] * i % FPS.mod def integral(self): self.extend_fact(len(self)) return FPS([0] + [x * (FPS.fact[i] * FPS.invfact[i + 1] % FPS.mod) % FPS.mod for i, x in enumerate(self.f)]) def log(self, deg=None): if deg is None: deg = len(self) tmp = self.differential() * self.inv(deg=deg) del tmp.f[deg:] tmp = tmp.integral() del tmp.f[deg:] return tmp def exp(self, deg=None): if deg is None: deg = len(self) g = FPS(1) l = 1 while l < deg * 2: l *= 2 log = FPS(1) - g.log(deg=l) + FPS(self.f[:l]) del log.f[l:] g *= log del g.f[l:] del g.f[deg:] return g def __pow__(self, k, deg=None): if k == 0: if deg is None: ret = [0] * len(self) else: ret = [0] * deg ret[0] = 1 return FPS(ret) if deg is None: deg = len(self) i = 0 p = None for i in range(deg): if self[i] != 0: a = self[i] p = i break if p is None: if deg is not None: return FPS([0] * deg) else: return FPS(0) elif deg is not None and p * k >= deg: return FPS([0] * deg) inv = pow(a, FPS.mod - 2, FPS.mod) tmp = FPS([x * inv % FPS.mod for x in self.f[p:]]) tmp = tmp.log(deg=deg) if deg is not None: del tmp.f[deg:] tmp *= k tmp = tmp.exp(deg=deg) tmp = [0] * (p * k) + tmp.f[:deg - p * k] times = pow(a, k, FPS.mod) return FPS([x * times % FPS.mod for x in tmp]) def __ipow__(self, k): return self.__pow__(k) def cipolla(self, a): if FPS.mod == 2: return a elif a == 0: return 0 elif pow(a, (FPS.mod - 1) // 2, FPS.mod) != 1: return -1 b = 0 while pow((b * b + FPS.mod - a) % FPS.mod, (FPS.mod - 1) // 2, FPS.mod) == 1: b += 1 base = b * b + FPS.mod - a def multi(a0, b0, a1, b1): return (a0 * a1 + (b0 * b1 % FPS.mod) * base) % FPS.mod, (a0 * b1 + b0 * a1) % FPS.mod def pow_(a, b, n): if n == 0: return 1, 0 a_, b_ = pow_(*multi(a, b, a, b), n // 2) if n % 2 == 1: a_, b_ = multi(a_, b_, a, b) return a_, b_ return pow_(b, 1, (FPS.mod + 1) // 2)[0] def sqrt(self, deg=None): if deg is None: deg = len(self) if len(self) == 0: return FPS([0] * deg) if self[0] == 0: for i in range(1, len(self)): if self[i] != 0: if i & 1: return FPS([]) if deg <= i // 2: break ret = FPS(self.f[i:]).sqrt(deg - i // 2) if len(ret) == 0: return FPS([]) ret.f = [0] * (i // 2) + ret.f if len(ret) < deg: ret.f += [0] * (deg - len(ret)) return ret return FPS([0] * deg) sq = self.cipolla(self[0]) if sq == -1: return FPS([]) inv2 = (FPS.mod + 1) // 2 g = FPS([sq]) l = 1 while l < deg: l *= 2 tmp = FPS(self.f[:l]) * g.inv(deg=l) g += tmp g *= inv2 del g.f[deg:] return g def taylorshift(self, a): deg = len(self) f = self.f[:] self.extend_fact(deg) for i in range(deg): f[i] *= FPS.fact[i] f[i] %= FPS.mod f = f[::-1] g = [0] * deg g[0] = 1 for i in range(1, deg): g[i] = (g[i - 1] * a % FPS.mod) * (FPS.fact[i - 1] * FPS.invfact[i] % FPS.mod) % FPS.mod f = FPS.fft.convolve(f, g) del f[deg:] f = f[::-1] for i in range(deg): f[i] *= FPS.invfact[i] f[i] %= FPS.mod return FPS(f) def Extended_Euclid(n,m): stack=[] while m: stack.append((n,m)) n,m=m,n%m if n>=0: x,y=1,0 else: x,y=-1,0 for i in range(len(stack)-1,-1,-1): n,m=stack[i] x,y=y,x-(n//m)*y return x,y class MOD: def __init__(self,p,e=None): self.p=p self.e=e if self.e==None: self.mod=self.p else: self.mod=self.p**self.e def Pow(self,a,n): a%=self.mod if n>=0: return pow(a,n,self.mod) else: assert math.gcd(a,self.mod)==1 x=Extended_Euclid(a,self.mod)[0] return pow(x,-n,self.mod) def Build_Fact(self,N): assert N>=0 self.factorial=[1] if self.e==None: for i in range(1,N+1): self.factorial.append(self.factorial[-1]*i%self.mod) else: self.cnt=[0]*(N+1) for i in range(1,N+1): self.cnt[i]=self.cnt[i-1] ii=i while ii%self.p==0: ii//=self.p self.cnt[i]+=1 self.factorial.append(self.factorial[-1]*ii%self.mod) self.factorial_inve=[None]*(N+1) self.factorial_inve[-1]=self.Pow(self.factorial[-1],-1) for i in range(N-1,-1,-1): ii=i+1 while ii%self.p==0: ii//=self.p self.factorial_inve[i]=(self.factorial_inve[i+1]*ii)%self.mod def Fact(self,N): if N<0: return 0 retu=self.factorial[N] if self.e!=None and self.cnt[N]: retu*=pow(self.p,self.cnt[N],self.mod)%self.mod retu%=self.mod return retu def Fact_Inve(self,N): if self.e!=None and self.cnt[N]: return None return self.factorial_inve[N] def Comb(self,N,K,divisible_count=False): if K<0 or K>N: return 0 retu=self.factorial[N]*self.factorial_inve[K]%self.mod*self.factorial_inve[N-K]%self.mod if self.e!=None: cnt=self.cnt[N]-self.cnt[N-K]-self.cnt[K] if divisible_count: return retu,cnt else: retu*=pow(self.p,cnt,self.mod) retu%=self.mod return retu N,M,K=map(int,readline().split()) mod=998244353 MD=MOD(mod) MD.Build_Fact(N) poly=[None]*(N-K+1) for i in range(N-K+1): poly[i]=MD.Fact_Inve(i+1) P=FPS(poly) P=P.log(deg=N-K+1) for i in range(N-K+1): P.f[i]*=K P.f[i]%=mod P=P.exp(deg=N-K+1) ans=0 for n in range(K,N+1): ans+=P[n-K]*MD.Pow(M,N-n)%mod*MD.Fact_Inve(N-n)%mod ans*=MD.Comb(M,K)*MD.Fact(N)%mod ans%=mod print(ans)