# 多项式基础操作

#include <bits/stdc++.h>
using namespace std;
typedef long long LL;
LL x=0,f=0;
char ch=getchar();
while (!isdigit(ch))
f|=ch=='-',ch=getchar();
while (isdigit(ch))
x=(x<<1)+(x<<3)+(ch^48),ch=getchar();
return f?-x:x;
}
const int N=1<<18,mod=998244353;
void Add(int &x,int y){
if ((x+=y)>=mod)
x-=mod;
}
void Del(int &x,int y){
if ((x-=y)<0)
x+=mod;
}
int del(int x,int y){
return x-y<0?x-y+mod:x-y;
}
int Pow(int x,int y){
int ans=1;
for (;y;y>>=1,x=(LL)x*x%mod)
if (y&1)
ans=(LL)ans*x%mod;
return ans;
}
int randint(){
return ((rand()&65535)<<15)^(rand()&65535);
}
namespace Rem2{
int INIT_TAG=0;
int t,w;
#define fi first
#define se second
void init(){
INIT_TAG=1;
srand('C'+'L'+'Y'+'A'+'K'+'I'+'O'+'I');
}
pair <int,int> Mul_pii(pair <int,int> A,pair <int,int> B){
static int a,b;
a=((LL)A.fi*B.fi+(LL)A.se*B.se%mod*w)%mod;
b=((LL)A.fi*B.se+(LL)A.se*B.fi)%mod;
return make_pair(a,b);
}
pair <int,int> Pow_pii(pair <int,int> x,int y){
pair <int,int> ans=make_pair(1,0);
for (;y;y>>=1,x=Mul_pii(x,x))
if (y&1)
ans=Mul_pii(ans,x);
return ans;
}
int Sqrt(int x){
if (!INIT_TAG)
init();
if (x==0)
return 0;
if (Pow(x,(mod-1)/2)!=1)
return -1;
do {
t=randint()%(mod-1)+1;
w=((LL)t*t+mod-x)%mod;
} while (Pow(w,(mod-1)/2)==1);
pair <int,int> res=Pow_pii(make_pair(t,1),(mod+1)/2);
return min(res.fi,mod-res.fi);
}
}
namespace Polynomial{
namespace Fast{
const int N=1<<18;
int n,Log[N+1],Fac[N+1],InvFac[N+1],Inv[N+1];
int ww[N*2],*Ew=ww,*w[N+1];
int iww[N*2],*Ei=iww,*iw[N+1];
int INIT_TAG=0;
void init(int _n){
INIT_TAG=1;
Log[1]=0,n=_n;
for (int i=2;i<=N;i++)
Log[i]=Log[i>>1]+1;
for (int i=Fac[0]=1;i<=N;i++)
Fac[i]=(LL)Fac[i-1]*i%mod;
InvFac[N]=Pow(Fac[N],mod-2);
for (int i=N;i>=1;i--)
InvFac[i-1]=(LL)InvFac[i]*i%mod;
for (int i=1;i<=N;i++)
Inv[i]=(LL)InvFac[i]*Fac[i-1]%mod;
for (int d=0;d<=Log[n];d++){
w[d]=Ew,iw[d]=Ei;
int n=1<<d;
w[d][0]=1,w[d][1]=Pow(3,(mod-1)/n);
for (int i=2;i<n;i++)
w[d][i]=(LL)w[d][i-1]*w[d][1]%mod;
iw[d][0]=1,iw[d][1]=Pow(w[d][1],mod-2);
for (int i=2;i<n;i++)
iw[d][i]=(LL)iw[d][i-1]*iw[d][1]%mod;
Ew+=n,Ei+=n;
}
}
int Rev[N+1],A[N+1],B[N+1];
void FFT(int a[],int n,int **w){
if (!INIT_TAG)
init(N);
for (int i=0;i<n;i++)
if (Rev[i]<i)
swap(a[i],a[Rev[i]]);
for (int t=1,d=1;d<n;t++,d<<=1)
for (int i=0;i<n;i+=(d<<1))
for (int j=0,*W=w[t];j<d;j++){
int tmp=(LL)(*W++)*a[i+j+d]%mod;
a[i+j+d]=del(a[i+j],tmp);
}
}
vector <int> Mul(vector <int> &a,vector <int> &b){
static vector <int> res;
res.clear();
LL Br=(LL)a.size()*b.size();
LL FF=(a.size()+b.size())*Log[a.size()+b.size()]*10+100;
if (Br<=FF){
for (int i=0;i<a.size()+b.size();i++)
res.push_back(0);
for (int i=0;i<a.size();i++)
for (int j=0;j<b.size();j++)
res[i+j]=((LL)a[i]*b[j]+res[i+j])%mod;
}
else {
int n=1,d=0;
for (;n<a.size()+b.size();n<<=1,d++);
for (int i=0;i<n;i++)
Rev[i]=(Rev[i>>1]>>1)|((i&1)<<(d-1)),A[i]=B[i]=0;
for (int i=0;i<a.size();i++)
A[i]=a[i];
for (int i=0;i<b.size();i++)
B[i]=b[i];
//                w[0]=1,w[1]=Pow(3,(mod-1)/n);
//                for (int i=2;i<n;i++)
//                    w[i]=(LL)w[i-1]*w[1]%mod;
FFT(A,n,w),FFT(B,n,w);
for (int i=0;i<n;i++)
A[i]=(LL)A[i]*B[i]%mod;
//                w[1]=Pow(w[1],mod-2);
//                for (int i=2;i<n;i++)
//                    w[i]=(LL)w[i-1]*w[1]%mod;
FFT(A,n,iw);
int inv=Pow(n,mod-2);
for (int i=0;i<n;i++)
res.push_back((int)((LL)inv*A[i]%mod));
}
while (!res.empty()&&!res.back())
res.pop_back();
return res;
}
vector <int> MulInv(vector <int> &a,vector <int> &b){
static vector <int> res;
res.clear();
int n=1,d=0;
for (;n<a.size()*2+b.size();n<<=1,d++);
for (int i=0;i<n;i++)
Rev[i]=(Rev[i>>1]>>1)|((i&1)<<(d-1)),A[i]=B[i]=0;
for (int i=0;i<a.size();i++)
A[i]=a[i];
for (int i=0;i<b.size();i++)
B[i]=b[i];
//            w[0]=1,w[1]=Pow(3,(mod-1)/n);
//            for (int i=2;i<n;i++)
//                w[i]=(LL)w[i-1]*w[1]%mod;
FFT(A,n,w),FFT(B,n,w);
for (int i=0;i<n;i++)
A[i]=(LL)A[i]*A[i]%mod*B[i]%mod;
//            w[1]=Pow(w[1],mod-2);
//            for (int i=2;i<n;i++)
//                w[i]=(LL)w[i-1]*w[1]%mod;
FFT(A,n,iw);
int inv=Pow(n,mod-2);
for (int i=0;i<n;i++)
res.push_back((int)((LL)inv*A[i]%mod));
while (!res.empty()&&!res.back())
res.pop_back();
return res;
}
}
struct Poly{
vector <int> v;
Poly(){
v.clear();
}
Poly(int x){
v.clear();
v.push_back(x);
}
Poly(vector <int> x){
v=x;
}
int operator ()(int x){
int ans=0,y=1;
for (int i=0;i<v.size();i++)
ans=((LL)v[i]*y+ans)%mod,y=(LL)y*x%mod;
return ans;
}
int size(){
return v.size();
}
void print(){
for (int i=0;i<v.size();i++)
printf("%d ",v[i]);
}
void print(int x){
for (int i=0;i<x;i++)
printf("%d ",i>=v.size()?0:v[i]);
}
void print(string s){
print(),cout << s;
}
void clear(){
v.clear();
}
void push_back(int x){
v.push_back(x);
}
void pop_back(){
v.pop_back();
}
int empty(){
return v.empty();
}
int back(){
return v.back();
}
int &operator [](int x){
return v[x];
}
void operator += (Poly A){
while (v.size()<A.size())
v.push_back(0);
for (int i=0;i<A.size();i++)
}
void operator -= (Poly &A){
while (v.size()<A.size())
v.push_back(0);
for (int i=0;i<A.size();i++)
Del(v[i],A[i]);
}
void operator *= (Poly &A);
void Derivation(){
for (int i=0;i<v.size()-1;i++)
v[i]=(LL)v[i+1]*(i+1)%mod;
v.pop_back();
}
void Integral(){
v.push_back(0);
for (int i=v.size()-2;i>=0;i--)
v[i+1]=(LL)v[i]*Fast :: Inv[i+1]%mod;
v[0]=0;
}
void operator *= (int x){
for (int i=0;i<v.size();i++)
v[i]=(LL)v[i]*x%mod;
}
}pp;
//struct Poly end-------------
Poly operator + (Poly A,Poly B){
pp.clear();
for (int i=0;i<max(A.size(),B.size());i++)
pp.push_back(0);
for (int i=0;i<A.size();i++)
for (int i=0;i<B.size();i++)
return pp;
}
Poly operator - (Poly A,Poly B){
pp.clear();
for (int i=0;i<max(A.size(),B.size());i++)
pp.push_back(0);
for (int i=0;i<A.size();i++)
for (int i=0;i<B.size();i++)
Del(pp[i],B[i]);
return pp;
}
Poly operator * (Poly A,Poly B){
return Poly(Fast :: Mul(A.v,B.v));
}
void Poly :: operator *= (Poly &A){
v=Fast :: Mul(v,A.v);
}
Poly operator * (Poly A,int x){
pp=A;
for (int i=0;i<A.size();i++)
pp[i]=(LL)pp[i]*x%mod;
return pp;
}
Poly Inverse(Poly a,int n);
Poly operator / (Poly A,Poly B){//Divide
int n=A.size(),m=B.size();
reverse(A.v.begin(),A.v.end());
reverse(B.v.begin(),B.v.end());
int k=n-m+1;
if (k<0)
return Poly(0);
while (A.size()>k)
A.pop_back();
while (B.size()>k)
B.pop_back();
A=A*Inverse(B,k);
while (A.size()>k)
A.pop_back();
reverse(A.v.begin(),A.v.end());
return A;
}
Poly operator % (Poly A,Poly B){//Modulo
while (!A.empty()&&!A.back())
A.pop_back();
while (!B.empty()&&!B.back())
B.pop_back();
A=A-A/B*B;
while (A.size()>=B.size())
A.pop_back();
while (!A.empty()&&!A.back())
A.pop_back();
return A;
}
Poly Derivation(Poly A){
for (int i=0;i<A.size()-1;i++)
A[i]=(LL)A[i+1]*(i+1)%mod;
A.pop_back();
return A;
}
Poly Integral(Poly A){
A.push_back(0);
for (int i=A.size()-2;i>=0;i--)
A[i+1]=(LL)A[i]*Fast :: Inv[i+1]%mod;
A[0]=0;
return A;
}
Poly Inverse(Poly a,int n){
static Poly A,B;
while (!a.empty()&&!a.back())
a.pop_back();
if (a.empty())
return a;
A.clear(),B.clear();
B.push_back(a[0]);
A.push_back(Pow(B[0],mod-2));
for (int t=1;t<n;){
for (int i=t;i<min(a.size(),(t<<1));i++)
B.push_back(a[i]);
t<<=1;
A=A*2-Poly(Fast :: MulInv(A.v,B.v));
while (A.size()>t)
A.pop_back();
}
while (A.size()>n)
A.pop_back();
return A;
}
Poly Sqrt(Poly a,int n){
static Poly A,B;
while (!a.empty()&&!a.back())
a.pop_back();
if (a.empty())
return a;
A.clear(),B.clear();
B.push_back(a[0]);
A.push_back(Rem2 :: Sqrt(B[0]));
for (int t=1;t<n;){
for (int i=t;i<min(a.size(),(t<<1));i++)
B.push_back(a[i]);
t<<=1;
A+=B*Inverse(A,t);
while (A.size()>t)
A.pop_back();
A*=499122177;
}
if (A[0]>mod-A[0])
for (int i=0;i<A.size();i++)
A[i]=(mod-A[i])%mod;
while (A.size()>n)
A.pop_back();
return A;
}
Poly Ln(Poly a,int n){
while (!a.empty()&&!a.back())
a.pop_back();
if (a.empty()||a[0]!=1)
return a;
a=Integral(Derivation(a)*Inverse(a,n));
while (a.size()>n)
a.pop_back();
return a;
}
Poly Exp(Poly a,int n){
static Poly A,B;
while (!a.empty()&&!a.back())
a.pop_back();
if (a.empty())
return Poly(1);
if (a[0]!=0)
return a;
A.clear(),B.clear();
B.push_back(1);
A.push_back(a[0]);
for (int t=1;t<n;){
for (int i=t;i<min(a.size(),(t<<1));i++)
A.push_back(a[i]);
t<<=1;
B=B*(Poly(1)+A-Ln(B,t));
while (B.size()>t)
B.pop_back();
}
while (B.size()>n)
B.pop_back();
return B;
}
Poly PolyPow(Poly x,int y,int n){
static Poly A,B;
int k0=0,kc,ivkc;
while (!x.empty()&&!x.back())
x.pop_back();
if (x.empty())
return x;
while (k0<x.size()&&x[k0]==0)
k0++;
kc=x[k0],ivkc=Pow(kc,mod-2);
A.clear();
for (int i=k0;i<x.size();i++)
A.push_back((int)((LL)x[i]*ivkc%mod));
A=Exp(Ln(A,n)*y,n);
B.clear();
if ((LL)k0*y>=n)
return B;
kc=Pow(kc,y),k0*=y;
for (int i=0;i<k0;i++)
B.push_back(0);
for (int i=0;i<min(A.size(),n-k0);i++)
B.push_back((int)((LL)A[i]*kc%mod));
while (B.size()>n)
B.pop_back();
return B;
}
namespace Qiuzhi{
Poly P[N<<2],f[N<<2],M;
vector <int> x,y;
int n;
void GetP(int rt,int L,int R){
if (L==R){
P[rt].clear();
P[rt].push_back((mod-x[L])%mod);
P[rt].push_back(1);
return;
}
int mid=(L+R)>>1,ls=rt<<1,rs=ls|1;
GetP(ls,L,mid);
GetP(rs,mid+1,R);
P[rt]=P[ls]*P[rs];
}
void qiuzhi(int rt,int L,int R){
if (f[rt].empty())
f[rt].push_back(0);
if (L==R)
return (void)(y[L]=f[rt][0]);
int mid=(L+R)>>1,ls=rt<<1,rs=ls|1;
f[ls]=f[rt]%P[ls];
f[rs]=f[rt]%P[rs];
qiuzhi(ls,L,mid);
qiuzhi(rs,mid+1,R);
}
vector <int> Get_Val(vector <int> A,Poly F){
n=A.size();
x.clear(),y.clear();
for (int i=0;i<n;i++){
x.push_back(A[i]);
y.push_back(0);
}
GetP(1,0,n-1);
f[1]=F;
qiuzhi(1,0,n-1);
return y;
}
}
namespace Chazhi{
Poly P[N<<2],M;
vector <int> x,y;
int n;
void GetP(int rt,int L,int R){
if (L==R){
P[rt].clear();
P[rt].push_back((mod-x[L])%mod);
P[rt].push_back(1);
return;
}
int mid=(L+R)>>1,ls=rt<<1,rs=ls|1;
GetP(ls,L,mid);
GetP(rs,mid+1,R);
P[rt]=P[ls]*P[rs];
}
Poly chazhi(int rt,int L,int R){
if (L==R)
return Poly(y[L]);
int mid=(L+R)>>1,ls=rt<<1,rs=ls|1;
return chazhi(ls,L,mid)*P[rs]+chazhi(rs,mid+1,R)*P[ls];
}
Poly Get_Poly(vector <int> A,vector <int> B){
n=A.size();
x=A;
int Product=1;
GetP(1,0,n-1);
M=Derivation(P[1]);
y=Qiuzhi :: Get_Val(A,M);
for (int i=0;i<y.size();i++)
y[i]=(LL)B[i]*Pow(y[i],mod-2)%mod;
return chazhi(1,0,n-1);
}
}
}// be careful about init!!!!!!
using namespace Polynomial;
Poly A,B;
vector <int> x,y;
int main(){
A.clear();
for (int i=0;i<n;i++)
B=Exp(Integral(Inverse(Sqrt(A,n),n)),n);
B=Poly(1)+Ln(Poly(2)+A-A(0)-B,n);
B=Derivation(PolyPow(B,k,n));
n--;
B.print(n);
return 0;
}
Polynomial

## UPD(2019-04-21): 补一个相对好写一些的LOJ#150板子。

#include <bits/stdc++.h>
#define clr(x) memset(x,0,sizeof (x))
#define clrint(x,n) memset(x,0,(n)<<2)
#define cpyint(a,b,n) memcpy(a,b,(n)<<2)
#define For(i,a,b) for (int i=a;i<=b;i++)
#define Fod(i,b,a) for (int i=b;i>=a;i--)
#define pb(x) push_back(x)
#define mp(x,y) make_pair(x,y)
#define fi first
#define se second
#define real __zzd001
#define _SEED_ ('C'+'L'+'Y'+'A'+'K'+'I'+'O'+'I')
#define outval(x) printf(#x" = %d\n",x)
#define outvec(x) printf("vec "#x" = ");for (auto _v : x)printf("%d ",_v);puts("")
#define outtag(x) puts("----------"#x"----------")
#define outarr(a,L,R) printf(#a"[%d...%d] = ",L,R);\
For(_v2,L,R)printf("%d ",a[_v2]);puts("");
using namespace std;
typedef long long LL;
typedef unsigned long long ULL;
typedef vector <int> vi;
LL x=0,f=0;
char ch=getchar();
while (!isdigit(ch))
f|=ch=='-',ch=getchar();
while (isdigit(ch))
x=(x<<1)+(x<<3)+(ch^48),ch=getchar();
return f?-x:x;
}
const int N=1<<19,mod=998244353,inv2=(mod+1)>>1;
const int YG=3;
int Pow(int x,int y){
int ans=1;
for (;y;y>>=1,x=(LL)x*x%mod)
if (y&1)
ans=(LL)ans*x%mod;
return ans;
}
void Add(int &x,int y){
if ((x+=y)>=mod)
x-=mod;
}
void Del(int &x,int y){
if ((x-=y)<0)
x+=mod;
}
return x>=mod?x-mod:x;
}
int Del(int x){
return x<0?x+mod:x;
}
namespace Math{
int Iv[N];
void prework(){
int n=N-1;
Iv[1]=1;
For(i,2,n)
Iv[i]=(LL)(mod-mod/i)*Iv[mod%i]%mod;
}
map <int,int> Map;
int ind(int x){
static int M,bas;
if (Map.empty()){
M=max((int)sqrt(mod),1);
bas=Pow(YG,M);
for (int i=1,v=YG;i<=M;i++,v=(LL)v*YG%mod)
Map[v]=i;
}
for (int i=M,v=(LL)bas*Pow(x,mod-2)%mod;i<=mod-1+M;i+=M,v=(LL)v*bas%mod)
if (Map[v])
return i-Map[v];
return -1;
}
}
namespace fft{
int w[N],R[N];
int Log[N+1];
void init(int n){
if (!Log[2]){
For(i,2,N)
Log[i]=Log[i>>1]+1;
}
int d=Log[n];
assert(n==(1<<d));
For(i,0,n-1)
R[i]=(R[i>>1]>>1)|((i&1)<<(d-1));
w[0]=1,w[1]=Pow(YG,(mod-1)/n);
For(i,2,n-1)
w[i]=(LL)w[i-1]*w[1]%mod;
}
void FFT(int *a,int n,int flag){
if (flag<0)
reverse(w+1,w+n);
For(i,0,n-1)
if (i<R[i])
swap(a[i],a[R[i]]);
for (int t=n>>1,d=1;d<n;d<<=1,t>>=1)
for (int i=0;i<n;i+=d<<1)
for (int j=0;j<d;j++){
int tmp=(LL)w[t*j]*a[i+j+d]%mod;
a[i+j+d]=Del(a[i+j]-tmp);
}
if (flag<0){
reverse(w+1,w+n);
int inv=Pow(n,mod-2);
For(i,0,n-1)
a[i]=(LL)a[i]*inv%mod;
}
}
void CirMul(int *a,int *b,int *c,int n){
init(n),FFT(a,n,1),FFT(b,n,1);
For(i,0,n-1)
c[i]=(LL)a[i]*b[i]%mod;
FFT(c,n,-1);
}
}
using fft::FFT;
using fft::CirMul;
int calc_up(int x){
int n=1;
while (n<=x)
n<<=1;
return n;
}
void Inv(int *a,int *b,int n){
static int f[N],g[N];
b[0]=Pow(a[0],mod-2);
int now=1;
while (now<n){
int len=now<<2;
For(i,0,len-1)
f[i]=g[i]=0;
cpyint(g,b,now),now<<=1,cpyint(f,a,min(n,now));
fft::init(len);
FFT(f,len,1),FFT(g,len,1);
For(i,0,len-1)
g[i]=(2LL*g[i]-(LL)f[i]*g[i]%mod*g[i]%mod+mod)%mod;
FFT(g,len,-1);
cpyint(b,g,min(n,now));
}
}
int Sqrt(int a){
int k=Math::ind(a);
assert(~k&1);
k=Pow(YG,k>>1);
return min(k,mod-k);
}
void Sqrt(int *a,int *b,int n){
static int f[N],g[N],h[N];
b[0]=Sqrt(a[0]);
int now=1;
while (now<n){
int len=now<<2;
For(i,0,len-1)
f[i]=g[i]=h[i]=0;
cpyint(f,b,now),now<<=1,Inv(f,h,now),cpyint(g,a,min(n,now));
CirMul(g,h,g,len);
For(i,0,len-1)
cpyint(b,f,min(n,now));
}
}
void Der(int *a,int n){
For(i,0,n-2)
a[i]=(LL)a[i+1]*(i+1)%mod;
a[n-1]=0;
}
void Int(int *a,int n){
if (!Math::Iv[1])
Math::prework();
Fod(i,n,1)
a[i]=(LL)a[i-1]*Math::Iv[i]%mod;
a[0]=0;
}
void Ln(int *a,int *b,int n){
static int f[N],g[N];
int len=calc_up(n*2);
For(i,0,len-1)
f[i]=g[i]=0;
cpyint(f,a,n),Inv(f,g,n),Der(f,n);
CirMul(f,g,f,len);
Int(f,n),cpyint(b,f,n);
}
void Exp(int *a,int *b,int n){
static int f[N],g[N],h[N];
b[0]=1;
int now=1;
while (now<n){
int len=now<<2;
For(i,0,len-1)
f[i]=g[i]=h[i]=0;
cpyint(f,b,now),now<<=1,Ln(f,g,now),cpyint(h,a,min(n,now));
For(i,0,now-1)
g[i]=Del(h[i]-g[i]);
CirMul(f,g,f,len),cpyint(b,f,min(n,now));
}
}
void Pow(int *a,int *b,int n,int k){
static int f[N];
clrint(b,n);
if (k==0)
return (void)(b[0]=1);
int fir=0;
for (;fir<n&&!a[fir];fir++);
if ((LL)fir*k>=n)
return;
int m=n-fir*k;
cpyint(f,a+fir,m);
int t=Pow(f[0],k),it=Pow(f[0],mod-2);
For(i,0,m-1)
f[i]=(LL)f[i]*it%mod;
Ln(f,f,m);
For(i,0,m-1)
f[i]=(LL)f[i]*k%mod;
Exp(f,b+fir*k,m);
For(i,fir*k,n-1)
b[i]=(LL)b[i]*t%mod;
}
int n,k;
int f[N],g[N],h[N];
int main(){
For(i,0,n-1)
Sqrt(f,g,n);
Inv(g,h,n);
Int(h,n);
Exp(h,g,n);
For(i,0,n-1)
g[i]=Del(f[i]-g[i]);
Ln(g,h,n);
Pow(h,g,n,k);
Der(g,n);
For(i,0,n-2)
printf("%d ",g[i]);
puts("");
return 0;
}
View Code

## UPD(2019-04-21晚)： 再加一个历时56min Rush出来的板子。感觉看起来比上面那个更好看。相比之下唯一的缺点就是要手动调用一个 prework() 函数。

#include <bits/stdc++.h>
#define clr(x) memset(x,0,sizeof x)
#define cpyint(a,b,n) memcpy(a,b,(n)<<2)
#define For(i,a,b) for (int i=a;i<=b;i++)
#define Fod(i,b,a) for (int i=b;i>=a;i--)
#define outval(x) printf(#x" = %d\n",x)
#define outtag(x) puts("-------------"#x"-------------");
#define outarr(a,L,R) printf(#a"[%d..%d] = ",L,R);\
For(_x,L,R)printf("%d ",a[_x]);puts("")
using namespace std;
typedef long long LL;
LL x=0,f=0;
char ch=getchar();
while (!isdigit(ch))
f|=ch=='-',ch=getchar();
while (isdigit(ch))
x=(x<<1)+(x<<3)+(ch^48),ch=getchar();
return f?-x:x;
}
const int N=1<<19,mod=998244353;
int Pow(int x,int y){
int ans=1;
for (;y;y>>=1,x=(LL)x*x%mod)
if (y&1)
ans=(LL)ans*x%mod;
return ans;
}
void Add(int &x,int y){
if ((x+=y)>=mod)
x-=mod;
}
void Del(int &x,int y){
if ((x-=y)<0)
x+=mod;
}
return x>=mod?x-mod:x;
}
int Del(int x){
return x<0?x+mod:x;
}
namespace fft{
int w[N],R[N];
void init(int n){
int d=0;
while ((1<<d)<n)
d++;
For(i,0,n-1)
R[i]=(R[i>>1]>>1)|((i&1)<<(d-1));
w[0]=1,w[1]=Pow(3,(mod-1)/n);
For(i,2,n-1)
w[i]=(LL)w[i-1]*w[1]%mod;
}
void FFT(int *a,int n,int flag){
if (flag<0)
reverse(w+1,w+n);
For(i,0,n-1)
if (i<R[i])
swap(a[i],a[R[i]]);
for (int t=n>>1,d=1;d<n;d<<=1,t>>=1)
for (int i=0;i<n;i+=d<<1)
for (int j=0;j<d;j++){
int tmp=(LL)w[t*j]*a[i+j+d]%mod;
a[i+j+d]=Del(a[i+j]-tmp);
}
if (flag<0){
reverse(w+1,w+n);
int inv=Pow(n,mod-2);
For(i,0,n-1)
a[i]=(LL)a[i]*inv%mod;
}
}
void Mul(int *a,int *b,int *c,int n){
init(n),FFT(a,n,1),FFT(b,n,1);
For(i,0,n-1)
c[i]=(LL)a[i]*b[i]%mod;
FFT(c,n,-1);
}
}
using fft::FFT;
using fft::Mul;
int Iv[N];
void prework(){
int n=N-1;
Iv[1]=1;
For(i,2,n)
Iv[i]=(LL)(mod-mod/i)*Iv[mod%i]%mod;
}
int Ind(int x){
static map <int,int> Map;
static int M,bas;
if (Map.empty()){
M=(int)sqrt(mod);
bas=Pow(3,M);
for (int i=1,v=3;i<=M;i++,v=(LL)v*3%mod)
Map[v]=i;
}
for (int i=M,v=(LL)bas*Pow(x,mod-2)%mod;i<=mod+M;i+=M,v=(LL)v*bas%mod)
if (Map[v])
return i-Map[v];
return -1;
}
int calup(int x){
int n=1;
while (n<x)
n<<=1;
return n;
}
void Inv(int *a,int *b,int n){
static int f[N],g[N];
b[0]=Pow(a[0],mod-2);
int now=1;
while (now<n){
int len=now<<2;
For(i,0,len-1)
f[i]=g[i]=0;
cpyint(g,b,now),now<<=1,cpyint(f,a,min(n,now));
fft::init(len),FFT(f,len,1),FFT(g,len,1);
For(i,0,len-1)
f[i]=(2LL*g[i]-(LL)f[i]*g[i]%mod*g[i]%mod+mod)%mod;
FFT(f,len,-1);
cpyint(b,f,min(n,now));
}
}
int Sqrt(int x){
int k=Ind(x);
assert(~k&1);
k=Pow(3,k>>1);
return min(k,mod-k);
}
void Sqrt(int *a,int *b,int n){
static int f[N],g[N],h[N];
b[0]=Sqrt(a[0]);
int now=1;
while (now<n){
int len=now<<2;
For(i,0,len-1)
f[i]=g[i]=h[i]=0;
cpyint(f,b,now),now<<=1,Inv(f,g,now),cpyint(h,a,min(n,now));
Mul(g,h,g,len);
For(i,0,len-1)
cpyint(b,f,min(n,now));
}
}
void Der(int *a,int n){
For(i,0,n-2)
a[i]=(LL)a[i+1]*(i+1)%mod;
a[n-1]=0;
}
void Int(int *a,int n){
Fod(i,n,1)
a[i]=(LL)a[i-1]*Iv[i]%mod;
a[0]=0;
}
void Ln(int *a,int *b,int n){
static int f[N],g[N];
int len=calup(n<<1);
For(i,0,len-1)
f[i]=g[i]=0;
cpyint(f,a,n),Inv(f,g,n),Der(f,n);
Mul(f,g,f,len);
Int(f,n),cpyint(b,f,n);
}
void Exp(int *a,int *b,int n){
static int f[N],g[N],h[N];
b[0]=1;
int now=1;
while (now<n){
int len=now<<2;
For(i,0,len-1)
f[i]=g[i]=h[i]=0;
cpyint(g,b,now),now<<=1,Ln(g,h,now),cpyint(f,a,min(n,now));
For(i,0,now-1)
Del(f[i],h[i]);
Mul(g,f,g,len);
cpyint(b,g,min(n,now));
}
}
void Pow(int *a,int *b,int n,int k){
static int f[N],g[N];
memset(b,0,sizeof(int)*n);
if (k==0)
return (void)(b[0]=1);
int fir=0;
for (;fir<n&&!a[fir];fir++);
if ((LL)fir*k>=n)
return;
int m=n-fir*k;
cpyint(f,a+fir,m);
int t=Pow(f[0],k),it=Pow(f[0],mod-2);
For(i,0,m-1)
f[i]=(LL)f[i]*it%mod;
Ln(f,g,m);
For(i,0,m-1)
g[i]=(LL)g[i]*k%mod;
Exp(g,f,m);
For(i,0,m-1)
f[i]=(LL)f[i]*t%mod;
cpyint(b+fir*k,f,m);
}
int n,k;
int a[N],b[N],c[N],d[N];
int main(){
prework();
For(i,0,n-1)
Sqrt(a,b,n);
Inv(b,c,n);
Int(c,n);
Exp(c,b,n);
For(i,0,n-1)
b[i]=Del(a[i]-b[i]);
Ln(b,c,n);
Pow(c,b,n,k);
Der(b,n);
n--;
For(i,0,n-1)
printf("%d ",b[i]);
puts("");
return 0;
}
View Code

posted @ 2018-12-30 14:32 -zhouzhendong- 阅读(...) 评论(...) 编辑 收藏