namespace mypoly{
const int MOD=998244353;
const int g=3;
int qmul(int x, int y){return 1ll*x*y-1ll*x*y/MOD*MOD;}
int qadd(int x, int y){return x+y>=MOD?x+y-MOD:x+y;}
int G[21][(1<<20)+1],R[21][(1<<20)+1],inver[(1<<20)+1];
int quick(int k1,int k2){
int k3=1;for(;k2;k2>>=1,k1=1LL*k1*k1%MOD)if(k2&1)k3=1LL*k3*k1%MOD;return k3;
}
int inv(int A){return quick(A,MOD-2);}
struct POLY{
int len;
int rev[1<<20];
POLY(){
rb(i,1,(1<<20)) inver[i]=inv(i);
rb(i,1,20){
G[i][0]=1;
R[i][0]=1;
int tmp2=inv(quick(g,(MOD-1)>>i));
int tmp=quick(g,(MOD-1)>>i);
rb(j,1,(1<<i)){
G[i][j]=qmul(G[i][j-1],tmp);
R[i][j]=qmul(R[i][j-1],tmp2);
}
}
}
void butterfly(vector<int> & v){
rep(i,len){
rev[i]=rev[i>>1]>>1;
if(i&1) rev[i]|=len>>1;
}
rep(i,len) if(rev[i]>i) swap(v[i],v[rev[i]]);
}
vector<int> ntt(vector<int> v){
butterfly(v);
vector<int> nex;
int lg=1;
for( int l=2;l<=len;l<<=1,++lg){
nex.clear();
nex.resize(len);
for( int j=0;j<len;j+=l){
for( int k=0;k<l/2;++k){
int A,B;
A=v[j+k];
B=v[j+l/2+k];
B=qmul(B,G[lg][k]);
nex[j+k]=qadd(A,B);
nex[j+k+l/2]=qadd(A,MOD-B);
}
}
v=nex;
}
return v;
}
vector<int> intt(vector<int> v){
butterfly(v);
vector<int> nex;
int lg=1;
for(int l=2;l<=len;l<<=1,++lg){
nex.clear();
nex.resize(len);
for(int j=0;j<len;j+=l){
for(int k=0;k<l/2;++k){
int A,B;
A=v[j+k];
B=v[j+l/2+k];
B=qmul(R[lg][k],B);
nex[j+k]=qadd(A,B);
nex[j+k+l/2]=qadd(A,MOD-B);
}
}
v=nex;
}
return v;
}
void getlen(int x){
len=1;
while(len<x){
len<<=1;
}
}
vector<int> mul(vector<int> A,vector<int> B){
if(A.size()+B.size()<=25){
vector<int> ret(A.size()+B.size()-1);
rep(i,A.size()) rep(j,B.size()) ret[i+j]=qadd(ret[i+j],qmul(A[i],B[j]));
return ret;
}
getlen(A.size()+B.size());
A.resize(len);
B.resize(len);
A=ntt(A);
B=ntt(B);
rep(i,len) A[i]=qmul(A[i],B[i]);
A=intt(A);
int iv=inver[len];
rep(i,len){
A[i]=qmul(A[i],iv);
}
while(!A.empty()&&A.back()==0) A.pop_back();
return A;
}
vector<int> inverse(vector<int> A,int n){
//计算% x^n 的逆元
vector<int> ret(n);
if(n==1){
ret[0]=quick(A[0],MOD-2);
}
else{
vector<int> oth=inverse(A,(n+1)>>1);
ret=oth;
ret.resize(n);
rep(i,n) ret[i]=(ret[i]+ret[i])%MOD;
getlen((oth.size()<<1)+A.size());
oth.resize(len);
A.resize(len);
oth=ntt(oth);
A=ntt(A);
rep(i,len) oth[i]=qmul(qmul(oth[i],oth[i]),A[i]);
oth=intt(oth);
oth.resize(n);
int iv=inver[len];
rep(i,n){
oth[i]=qmul(oth[i],iv);
}
rep(i,n) ret[i]=qadd(ret[i],MOD-oth[i]);
}
return ret;
}
}poly;
vector<int> operator * (vector<int> A,vector<int> B){
return poly.mul(A,B);
}
vector<int> operator + (vector<int> A,vector<int> B){
int Sz=max(A.size(),B.size());
A.resize(Sz);
rep(i,B.size()) A[i]=qadd(A[i],B[i]);
return A;
}
vector<int> operator - (vector<int> A,vector<int> B){
int Sz=max(A.size(),B.size());
A.resize(Sz);
rep(i,B.size()) A[i]=qadd(A[i],MOD-B[i]);
return A;
}
vector<int> operator / (vector<int> A,vector<int> B){// use poly.inverse , don't use it !!
return A*poly.inverse(B,A.size()-B.size()+1);
}
vector<int> operator % (vector<int> A,vector<int> B){
while(A.size()!=1&&A.back()==0) A.POB();
while(B.size()!=1&&B.back()==0) B.POB();
if(B.size()>A.size()) return A;
vector<int> rem,mod;
int n,m;
n=A.size()-1;
m=B.size()-1;
reverse(ALL(A));
reverse(ALL(B));
rem=A/B;
reverse(ALL(A));
reverse(ALL(B));
rem.resize(n-m+1);
reverse(ALL(rem));
mod=A-rem*B;
mod.resize(m);
return mod;
}
vector<int> D(vector<int> A){//导数
while(A.size()!=1&&A.back()==0) A.POB();
vector<int> ret(A.size()-1);
rep(i,ret.size()) ret[i]=1ll*(i+1)*A[i+1]%MOD;
if(ret.empty()) return vector<int> (1,0);
return ret;
}
vector<int> I(vector<int> A){//积分
while(A.size()!=1&&A.back()==0) A.POB();
vector<int> ret(A.size()+1,0);
rep(i,A.size()) ret[i+1]=1ll*A[i]*inver[i+1]%MOD;
while(ret.size()!=1&&ret.back()==0) ret.POB();
return ret;
}
vector<int> poly_ln(vector<int> A,int n){// ln(A) % x^n (A[0]=0)
auto tmp=I(D(A)*poly.inverse(A,n));
if(tmp.size()>n) tmp.resize(n);
while(tmp.size()!=1&&tmp.back()==0) tmp.POB();
return tmp;
}
vector<int> poly_exp(vector<int> A,int n){// exp(A) % x^n (A[0]=0)
if(n==1){
return vector<int> (1,1);
}
vector<int> G0=poly_exp(A,(n+1)/2);
vector<int> G;
G=(G0*((vector<int>{1})-poly_ln(G0,n)+A));
if(G.size()>n) G.resize(n);
while(G.size()!=1&&G.back()==0) G.POB();
return G;
}
class MC{//多点求值
vector<vector<int> > RAM;
vector<vector<int> > SIN;
vector<int> Lc;
vector<int> Rc;
vector<int> ret;
vector<int> x_;
void fendge1(int l,int r,int& cnt){
if(l==r-1){
Lc.PB(0);
Rc.PB(0);
RAM.PB(SIN[l]);
return ;
}
RAM.PB(vector<int> (0));
Lc.PB(0);
Rc.PB(0);
int now=cnt;
int mid=(l+r)>>1;
int L=++cnt;
fendge1(l,mid,cnt);
int R=++cnt;
fendge1(mid,r,cnt);
Lc[now]=L;
Rc[now]=R;
RAM[now]=RAM[L]*RAM[R];
}
void fendge2(int l,int r,int cnt,vector<int> p){
p=p%RAM[cnt];
if(r-l<=300){
rb(i,l,r-1){
int T=1;
rep(j,p.size()){
ret[i]=qadd(ret[i],qmul(T,p[j]));
T=qmul(T,x_[i]);
}
}
return ;
}
int mid=(l+r)>>1;
fendge2(l,mid,Lc[cnt],p);
fendge2(mid,r,Rc[cnt],p);
}
public:
vector<int> init(vector<int> p,vector<int> x){
x_=x;
Lc.clear();
Rc.clear();
RAM.clear();
SIN.clear();
ret.clear();
ret=vector<int>(x.size(),0);
rep(i,x.size()){
SIN.PB(vector<int>{(MOD-x[i]),1});
}
int cnt=0;
fendge1(0,x.size(),cnt);
fendge2(0,x.size(),0,p);
return ret;
}
}mc;
vector<int> multiple_calculation(vector<int> p,vector<int> x){
return mc.init(p,x);
}
class ITP{
vector<int> u;
vector<int> v;
vector<int> fm;
vector<int> fendge(int l,int r){
if(l==r-1){return vector<int> {(MOD-u[l]),1};}
int mid=(l+r)>>1;
return fendge(l,mid)*fendge(mid,r);
}
pair<vector<int>,vector<int> > fendge2(int l,int r){
if(l==r-1){
return {vector<int> {(MOD-u[l]),1},vector<int> {fm[l]}};
}
int mid=(l+r)>>1;
pair<vector<int>,vector<int> > L,R;
L=fendge2(l,mid);
R=fendge2(mid,r);
return {L.FIR*R.FIR,L.FIR*R.SEC+R.FIR*L.SEC};
}
public:
vector<int> solve(vector<mp> x){
u.clear();
v.clear();
int n=x.size();
for(auto it:x) u.PB(it.FIR),v.PB(it.SEC);
vector<int> g=fendge(0,u.size());
fm=multiple_calculation(D(g),u);
rep(i,n){
fm[i]=qmul(v[i],inv(fm[i]));
}
return fendge2(0,n).SEC;
}
}itp;
vector<int> interpolation(vector<mp> x){
return itp.solve(x);
}
}
