class FFT(): def primitive_root_constexpr(self,m): if m==2:return 1 if m==167772161:return 3 if m==469762049:return 3 if m==754974721:return 11 if m==998244353:return 3 divs=[0]*20 divs[0]=2 cnt=1 x=(m-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,(m-1)//divs[i],m)==1: ok=False break if ok: return g g+=1 def bsf(self,x): res=0 while(x%2==0): res+=1 x//=2 return res rank2=0 root=[] iroot=[] rate2=[] irate2=[] rate3=[] irate3=[] def __init__(self,MOD): self.mod=MOD self.g=self.primitive_root_constexpr(self.mod) self.rank2=self.bsf(self.mod-1) self.root=[0 for i in range(self.rank2+1)] self.iroot=[0 for i in range(self.rank2+1)] self.rate2=[0 for i in range(self.rank2)] self.irate2=[0 for i in range(self.rank2)] self.rate3=[0 for i in range(self.rank2-1)] self.irate3=[0 for i in range(self.rank2-1)] self.root[self.rank2]=pow(self.g,(self.mod-1)>>self.rank2,self.mod) self.iroot[self.rank2]=pow(self.root[self.rank2],self.mod-2,self.mod) for i in range(self.rank2-1,-1,-1): self.root[i]=(self.root[i+1]**2)%self.mod self.iroot[i]=(self.iroot[i+1]**2)%self.mod prod=1;iprod=1 for i in range(self.rank2-1): self.rate2[i]=(self.root[i+2]*prod)%self.mod self.irate2[i]=(self.iroot[i+2]*iprod)%self.mod prod=(prod*self.iroot[i+2])%self.mod iprod=(iprod*self.root[i+2])%self.mod prod=1;iprod=1 for i in range(self.rank2-2): self.rate3[i]=(self.root[i+3]*prod)%self.mod self.irate3[i]=(self.iroot[i+3]*iprod)%self.mod prod=(prod*self.iroot[i+3])%self.mod iprod=(iprod*self.root[i+3])%self.mod def butterfly(self,a): n=len(a) h=(n-1).bit_length() LEN=0 while(LEN>d)&1: s[bit]+=1 g=[1] z=0 for d in range(N): if (bit>>d)&1: k,a=L[d][:] z+=pow(a,-1,mod) l=[0]*k for y in range(k): p=pow(a,y,mod) p*=u[y] p%=mod p=pow(p,-1,mod) l[y]=p g=Z.convolution(g,l) v[bit]=z h[bit]=g for bit in range(1,2**N): c=1 for k in range(N): if (bit>>k)&1: c+=0 else: c+=1 q=0 for b in range(2**N): if bit&b: continue e=Z.convolution(h[bit],h[b]) score=0 z=(v[bit]+v[b])%mod for y in range(len(e)): w=e[y]*u[y] w%=mod w*=pow(z,-(y+1),mod) w%=mod score+=w score%=mod if s[b]%2==0: q+=score else: q-=score for x in range(c,N+1): result[x]+=q result[x]%=mod result=result[1:] print(*result)