# Submit Info #46235

Problem Lang User Status Time Memory
Partition Function pypy3 shakayami AC 9641 ms 203.80 MiB

ケース詳細
Name Status Time Memory
0_00 AC 51 ms 29.81 MiB
100000_00 AC 2090 ms 117.32 MiB
10000_00 AC 317 ms 41.30 MiB
1000_00 AC 119 ms 32.32 MiB
100_00 AC 75 ms 30.93 MiB
1_00 AC 51 ms 29.80 MiB
200000_00 AC 4199 ms 149.88 MiB
300000_00 AC 7661 ms 177.88 MiB
400000_00 AC 8627 ms 203.80 MiB
500000_00 AC 9641 ms 197.34 MiB
example_00 AC 52 ms 29.83 MiB

class FPS: 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) mod=998244353 Func=[0] def __init__(self,L): self.Func=[x%self.mod for x in L] def butterfly(self,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 r%=self.mod a[i+offset]=l+r a[i+offset]%=self.mod a[i+offset+p]=l-r a[i+offset+p]%=self.mod now*=self.sum_e[(~s & -~s).bit_length()-1] now%=self.mod return a def butterfly_inv(self,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 a[i+offset]%=self.mod a[i+offset+p]=(l-r)*inow a[i+offset+p]%=self.mod inow*=self.sum_ie[(~s & -~s).bit_length()-1] inow%=self.mod return a def __mul__(self,other): if type(other)==int: ret=[(x*other)%self.mod for x in self.Func] return FPS(ret) a=self.Func b=other.Func n=len(a);m=len(b) if not(a) or not(b): return FPS([]) if min(n,m)<=40: 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]%=self.mod return FPS(res) z=1<<((n+m-2).bit_length()) a=a+[0]*(z-n) b=b+[0]*(z-m) a=self.butterfly(a) b=self.butterfly(b) c=[0]*z for i in range(z): c[i]=(a[i]*b[i])%self.mod self.butterfly_inv(c) iz=pow(z,self.mod-2,self.mod) for i in range(n+m-1): c[i]=(c[i]*iz)%self.mod return FPS(c[:n+m-1]) def __imul__(self,other): self=self*other return self def __add__(self,other): res=[0 for i in range(max(len(self.Func),len(other.Func)))] for i,x in enumerate(self.Func): res[i]+=x res[i]%=self.mod for i,x in enumerate(other.Func): res[i]+=x res[i]%=self.mod return FPS(res) def __iadd__(self,other): self=(self+other) return self def __sub__(self,other): res=[0 for i in range(max(len(self.Func),len(other.Func)))] for i,x in enumerate(self.Func): res[i]+=x res[i]%=self.mod for i,x in enumerate(other.Func): res[i]-=x res[i]%=self.mod return FPS(res) def __isub__(self,other): self=self-other return self def inv(self,d=-1): n=len(self.Func) assert n!=0 and self.Func[0]!=0 if d==-1:d=n assert d>0 res=[pow(self.Func[0],self.mod-2,self.mod)] while(len(res)<d): m=len(res) f=[self.Func[i] for i in range(min(n,2*m))] r=res[:] if len(f)<2*m: f+=[0]*(2*m-len(f)) elif len(f)>2*m: f=f[:2*m] if len(r)<2*m: r+=[0]*(2*m-len(r)) elif len(r)>2*m: r=r[:2*m] f=self.butterfly(f) r=self.butterfly(r) for i in range(2*m): f[i]*=r[i] f[i]%=self.mod f=self.butterfly_inv(f) f=f[m:] if len(f)<2*m: f+=[0]*(2*m-len(f)) elif len(f)>2*m: f=f[:2*m] f=self.butterfly(f) for i in range(2*m): f[i]*=r[i] f[i]%=self.mod f=self.butterfly_inv(f) iz=pow(2*m,self.mod-2,self.mod) iz*=-iz iz%=self.mod for i in range(m): f[i]*=iz f[i]%=self.mod res+=f[:m] return FPS(res[:d]) def __truediv__(self,other): if type(other)==int: invother=pow(other,self.mod-2,self.mod) ret=[(x*invother)%self.mod for x in self.Func] return FPS(ret) assert (other.Func[0]!=0) return self*(other.inv()) def __itruediv__(self,other): self=self/other return self def __lshift__(self,d): n=len(self.Func) self.Func=[0]*d+self.Func return FPS(self.Func[:n]) def __ilshift__(self,d): self=self<<d return self def __rshift__(self,d): n=len(self.Func) self.Func=self.Func[min(n,d):] self.Func+=[0]*(n-len(self.Func)) return FPS(self.Func) def __irshift__(self,d): self=self>>d return self def __str__(self): return f'FPS({self.Func})' def diff(self): n=len(self.Func) ret=[0 for i in range(max(0,n-1))] for i in range(1,n): ret[i-1]=(self.Func[i]*i)%self.mod return FPS(ret) def integral(self): n=len(self.Func) ret=[0 for i in range(n+1)] for i in range(n): ret[i+1]=self.Func[i]*pow(i+1,self.mod-2,self.mod)%self.mod return FPS(ret) def log(self,deg=-1): assert self.Func[0]==1 n=len(self.Func) if deg==-1:deg=n return (self.diff()*self.inv()).integral() def mod_sqrt(self,a): p=self.mod assert 0<=a and a<p if a<2:return a if pow(a,(p-1)//2,p)!=1:return -1 b=1;one=1 while(pow(b,(p-1)>>1,p)==1): b+=one m=p-1;e=0 while(m%2==0): m>>=1 e+=1 x=pow(a,(m-1)>>1,p) y=(a*x*x)%p x*=a; x%=p z=pow(b,m,p) while(y!=1): j=0 t=y while(t!=one): j+=1 t*=t t%=p z=pow(z,1<<(e-j-1),p) x*=z x%=p z*=z z%=p y*=z y%=p e=j return x def sqrt(self,deg=-1): n=len(self.Func) if deg==-1:deg=n if n==0:return FPS([0 for i in range(deg)]) if self.Func[0]==0: for i in range(1,n): if self.Func[i]!=0: if i&1:return FPS([]) if deg-i//2<=0:break ret=(self>>i).sqrt(deg-i//2) if len(ret.Func)==0:return FPS([]) ret=ret<<(i//2) if len(ret.Func)<deg: ret.Func+=[0]*(deg-len(ret.Func)) return ret return FPS([0]*deg) sqr=self.mod_sqrt(self.Func[0]) if sqr==-1:return FPS([]) assert sqr*sqr%self.mod==self.Func[0] ret=FPS([sqr]) inv2=(self.mod+1)//2 i=1 while(i<deg): ret=(ret+FPS(self.Func[:i<<1])*ret.inv(i<<1))*inv2 i<<=1 return FPS(ret.Func[:deg]) def resize(self,deg): if len(self.Func)<deg: return FPS(self.Func+[0]*(deg-len(self.Func))) elif len(self.Func)>deg: return FPS(self.Func[:deg]) else: return self def exp(self,deg=-1): n=len(self.Func) assert n>0 and self.Func[0]==0 if deg==-1:deg=n ret=FPS([1]) i=1 while(i<deg): ret=ret*(self.resize(i<<2)+FPS([int(j==0) for j in range(i<<2)])-ret.log(i<<2)) ret=ret.resize(i<<2) i<<=1 return ret.resize(deg) def powfps(self,k,deg=-1): a=self.Func[:] n=len(self.Func) l=0 while(l<len(a) and not a[l]): l+=1 if l*k>=n: return FPS([0]*n) ic=pow(a[l],self.mod-2,self.mod) pc=pow(a[l],k,self.mod) a=FPS([(a[i]*ic)%self.mod for i in range(l,len(a))]).log() a*=k a=a.exp() a*=pc a=[0]*(l*k)+a.Func[:n-l*k] return FPS(a) N=int(input()) mod=998244353 X=[0 for i in range(N+1)] for k in range(1,N+1): for i in range(1,1+N//k): X[k*i]+=pow(i,mod-2,mod) ans=FPS(X).exp(N+1) print(*ans.Func)