import sys from collections import deque readline=sys.stdin.readline def NTT(polynomial0,polynomial1): if len(polynomial0)*len(polynomial1)<=60: poly=[0]*(len(polynomial0)+len(polynomial1)-1) for i in range(len(polynomial0)): for j in range(len(polynomial1)): poly[i+j]+=polynomial0[i]*polynomial1[j]%mod poly[i+j]%=mod return poly if mod==998244353: prim_root=3 prim_root_inve=332748118 else: prim_root=Primitive_Root(mod) prim_root_inve=MOD(mod).Pow(prim_root,-1) def DFT(polynomial,n,inverse=False): if inverse: for bit in range(1,n+1): a=1<>bit,mod) U=[1] for _ in range(a): U.append(U[-1]*x%mod) for i in range(1<>bit,mod) U=[1] for _ in range(a): U.append(U[-1]*x%mod) for i in range(1<self.max_degree+1: self.polynomial=polynomial[:self.max_degree+1] else: self.polynomial=polynomial mod=mod self.eps=eps def __eq__(self,other): if type(other)!=Polynomial: return False if len(self.polynomial)!=len(other.polynomial): return False for i in range(len(self.polynomial)): if self.epsself.max_degree+1: prod=prod[:self.max_degree+1] while prod and abs(prod[-1])<=self.eps: prod.pop() prod=Polynomial(prod,max_degree=self.max_degree,eps=self.eps,mod=mod) return prod def __truediv__(self,other): if type(other)==Polynomial: assert other.polynomial for n in range(len(other.polynomial)): if self.epsn for i in range(n): assert abs(self.polynomial[i])<=self.eps self_polynomial=self.polynomial[n:] other_polynomial=other.polynomial[n:] if mod: inve=MOD(mod).Pow(other_polynomial[0],-1) else: inve=1/other_polynomial[0] quot=[] for i in range(len(self_polynomial)-len(other_polynomial)+1): if mod: quot.append(self_polynomial[i]*inve%mod) else: quot.append(self_polynomial[i]*inve) for j in range(len(other_polynomial)): self_polynomial[i+j]-=other_polynomial[j]*quot[-1] if mod: self_polynomial[i+j]%=mod for i in range(max(0,len(self_polynomial)-len(other_polynomial)+1),len(self_polynomial)): if self.eps>bit,mod) U=[1] for _ in range(a): U.append(U[-1]*x%mod) for i in range(1<>bit,mod) U=[1] for _ in range(a): U.append(U[-1]*x%mod) for i in range(1<=2: f0=queue.pop() f1=queue.pop() f=NTT(f0,f1)[:M+1] queue.appendleft(f) ans=0 f=Polynomial(queue[0],max_degree=M,mod=mod) f=-(f.log()) ans_lst=[f[i]*i%mod for i in range(1,M+1)] print(*ans_lst)