Polynomial

#include<bits/stdc++.h>using namespace std;const int mo=998244353;
const int maxn=1<<20;int add(int x,int y){return (x+y>=mo)?x+y-mo:x+y;
}int sub(int x,int y){return (x-y<0)?x-y+mo:x-y;
}int mul(int x,int y){return 1ll*x*y%mo;
}#define gc getchar
int rd(){int f=1,r=0;char ch=gc();while(!isdigit(ch)){ if(ch=='-') f=-1;ch=gc();}while(isdigit(ch)){ r=(r<<1)+(r<<3)+(ch^48);ch=gc();}return f*r;
}int ksm(int x,int y){int rs=1;while(y){if(y&1) rs=1ll*rs*x%mo;x=1ll*x*x%mo;y>>=1;}return rs;
}int rev[maxn];	void init_rev(int len){for(int i=0;i<len;++i){rev[i]=rev[i>>1]>>1;if(i&1) rev[i]|=len>>1;}
}namespace Polynomial{struct poly{int a[maxn];poly(){memset(a,0,sizeof(a));};int& operator[](int x){return a[x];}int operator[](int x)const{return a[x];}void operator=(const poly &t){memcpy(a,t.a,sizeof(a));return;}void slice(int len,int k){for(int i=len;i<k;++i) a[i]=0;}void NTT(int len,int rv){for(int i=0;i<len;++i) if(i<rev[i]) swap(a[i],a[rev[i]]);for(int h=2;h<=len;h<<=1){int wn=ksm(3,(mo-1)/h);for(int i=0;i<len;i+=h){int w=1;for(int k=i;k<i+h/2;++k){int u=a[k],v=mul(w,a[k+h/2]);a[k]=add(u,v);a[k+h/2]=sub(u,v);w=mul(w,wn);}}}if(rv==-1){reverse(a+1,a+len);int inv=ksm(len,mo-2);for(int i=0;i<len;++i) a[i]=mul(a[i],inv);}}poly inv(int len)const{poly g,g0,d;g[0]=ksm(a[0],mo-2);for(int lim=2;(lim>>1)<len;lim<<=1){g0=g,d=*this;d.slice(lim,len);int k=lim<<1;init_rev(k);g0.NTT(k,1),d.NTT(k,1);for(int i=0;i<k;++i) g0[i]=mul(g0[i],sub(2,mul(g0[i],d[i])));g0.NTT(k,-1);g0.slice(lim,k);g=g0;}return g;}poly der(int len)const{poly g=*this;for(int i=0;i<len;++i) g[i]=mul(g[i+1],i+1);return g;}poly integ(int len)const{poly g=*this;for(int i=len-1;i;--i) g[i]=mul(g[i-1],ksm(i,mo-2));g[0]=0;return g;}poly ln(int len)const{poly d=this->der(len),iv=this->inv(len),rs;int k=len<<1;init_rev(k);d.NTT(k,1),iv.NTT(k,1);for(int i=0;i<k;++i) rs[i]=mul(d[i],iv[i]);rs.NTT(k,-1);rs=rs.integ(k);rs.slice(len,k);return rs;}poly Exp(int len)const{poly g,g0,lng,d;g[0]=1;int k;for(int lim=2;(lim>>1)<len;lim<<=1){k=lim<<1;g0=g,lng=g.ln(k),d=*this;d.slice(lim,k);lng.slice(lim,k);init_rev(k);g0.NTT(k,1),lng.NTT(k,1),d.NTT(k,1);for(int i=0;i<k;++i) g[i]=mul(g0[i],add(sub(1,lng[i]),d[i]));g.NTT(k,-1);g.slice(lim,k);}g.slice(len,k);return g;}poly Mul(int len,int k)const{poly rs=*this;for(int i=0;i<len;++i) rs[i]=mul(rs[i],k);return rs;}poly pow(int len,int k)const{poly rs=this->ln(len);rs=rs.Mul(len,k);rs=rs.Exp(len);return rs;}poly rv(int len)const{poly rs=*this;reverse(rs.a,rs.a+len);return rs;}pair<poly,poly> modulo(int n,int m,const poly g)const{poly rf=this->rv(n+1),rg=g.rv(m+1),q,r;rf.slice(n-m+1,n+1),rg.slice(n-m+1,m+1);int k=1;while(k<=(n-m+1)) k<<=1;rg=rg.inv(k);while(k<=(n-m+1)*2) k<<=1;init_rev(k);rf.NTT(k,1),rg.NTT(k,1);for(int i=0;i<k;++i) q[i]=mul(rf[i],rg[i]);q.NTT(k,-1);q.slice(n-m+1,k);q=q.rv(n-m+1);poly f=*this,G=g;k=1;while(k<=2*max(n+1,m+1)) k<<=1;init_rev(k);f.NTT(k,1),G.NTT(k,1),q.NTT(k,1);for(int i=0;i<k;++i) r[i]=sub(f[i],mul(q[i],G[i]));r.NTT(k,-1),q.NTT(k,-1);q.slice(n-m+1,k);r.slice(m,k);return make_pair(q,r);}};
}
using namespace Polynomial;