#include using namespace std; template inline void chmin(T1 &a,T2 b){if(a>b) a=b;} template inline void chmax(T1 &a,T2 b){if(a struct Mint{ static constexpr T mod = MOD; T v; Mint():v(0){} Mint(signed v):v(v){} Mint(long long t){v=t%MOD;if(v<0) v+=MOD;} Mint pow(long long k){ Mint res(1),tmp(v); while(k){ if(k&1) res*=tmp; tmp*=tmp; k>>=1; } return res; } static Mint add_identity(){return Mint(0);} static Mint mul_identity(){return Mint(1);} Mint inv(){return pow(MOD-2);} Mint& operator+=(Mint a){v+=a.v;if(v>=MOD)v-=MOD;return *this;} Mint& operator-=(Mint a){v+=MOD-a.v;if(v>=MOD)v-=MOD;return *this;} Mint& operator*=(Mint a){v=1LL*v*a.v%MOD;return *this;} Mint& operator/=(Mint a){return (*this)*=a.inv();} Mint operator+(Mint a) const{return Mint(v)+=a;} Mint operator-(Mint a) const{return Mint(v)-=a;} Mint operator*(Mint a) const{return Mint(v)*=a;} Mint operator/(Mint a) const{return Mint(v)/=a;} Mint operator-() const{return v?Mint(MOD-v):Mint(v);} bool operator==(const Mint a)const{return v==a.v;} bool operator!=(const Mint a)const{return v!=a.v;} bool operator <(const Mint a)const{return v constexpr T Mint::mod; template ostream& operator<<(ostream &os,Mint m){os< rts={{0,0},{1,0}}; vector rev={0,1}; const dbl PI=asinl(1)*2; void ensure_base(int nbase){ if(nbase<=base) return; rev.resize(1<>1]>>1)+((i&1)<<(nbase-1)); rts.resize(1< &as){ int n=as.size(); assert((n&(n-1))==0); int zeros=__builtin_ctz(n); ensure_base(zeros); int shift=base-zeros; for(int i=0;i>shift)) swap(as[i],as[rev[i]>>shift]); for(int k=1;k vector multiply(vector &as,vector &bs){ int need=as.size()+bs.size()-1; int nbase=0; while((1< fa(sz); for(int i=0;i>1);i++){ int j=(sz-i)&(sz-1); num z=(fa[j]*fa[j]-conj(fa[i]*fa[i]))*r; if(i!=j) fa[j]=(fa[i]*fa[i]-conj(fa[j]*fa[j]))*r; fa[i]=z; } fft(fa); vector res(need); for(int i=0;i struct ArbitraryMod{ using dbl=FFT::dbl; using num=FFT::num; vector multiply(vector as,vector bs){ int need=as.size()+bs.size()-1; int sz=1; while(sz fa(sz),fb(sz); for(int i=0;i<(int)as.size();i++) fa[i]=num(as[i].v&((1<<15)-1),as[i].v>>15); for(int i=0;i<(int)bs.size();i++) fb[i]=num(bs[i].v&((1<<15)-1),bs[i].v>>15); fft(fa);fft(fb); dbl ratio=0.25/sz; num r2(0,-1),r3(ratio,0),r4(0,-ratio),r5(0,1); for(int i=0;i<=(sz>>1);i++){ int j=(sz-i)&(sz-1); num a1=(fa[i]+conj(fa[j])); num a2=(fa[i]-conj(fa[j]))*r2; num b1=(fb[i]+conj(fb[j]))*r3; num b2=(fb[i]-conj(fb[j]))*r4; if(i!=j){ num c1=(fa[j]+conj(fa[i])); num c2=(fa[j]-conj(fa[i]))*r2; num d1=(fb[j]+conj(fb[i]))*r3; num d2=(fb[j]-conj(fb[i]))*r4; fa[i]=c1*d1+c2*d2*r5; fb[i]=c1*d2+c2*d1; } fa[j]=a1*b1+a2*b2*r5; fb[j]=a1*b2+a2*b1; } fft(fa);fft(fb); vector cs(need); using ll = long long; for(int i=0;i struct Rint{ static T mod; static void set_mod(T nmod){mod=nmod;} T v; Rint():v(0){} Rint(signed v):v(v){} Rint(long long t){v=t%mod;if(v<0) v+=mod;} Rint pow(long long k){ Rint res(1),tmp(v); while(k){ if(k&1) res*=tmp; tmp*=tmp; k>>=1; } return res; } static Rint add_identity(){return Rint(0);} static Rint mul_identity(){return Rint(1);} Rint inv(){return pow(mod-2);} Rint& operator+=(Rint a){v+=a.v;if(v>=mod)v-=mod;return *this;} Rint& operator-=(Rint a){v+=mod-a.v;if(v>=mod)v-=mod;return *this;} Rint& operator*=(Rint a){v=1LL*v*a.v%mod;return *this;} Rint& operator/=(Rint a){return (*this)*=a.inv();} Rint operator+(Rint a) const{return Rint(v)+=a;} Rint operator-(Rint a) const{return Rint(v)-=a;} Rint operator*(Rint a) const{return Rint(v)*=a;} Rint operator/(Rint a) const{return Rint(v)/=a;} Rint operator-() const{return v?Rint(mod-v):Rint(v);} bool operator==(const Rint a)const{return v==a.v;} bool operator!=(const Rint a)const{return v!=a.v;} bool operator <(const Rint a)const{return v T Rint::mod; template ostream& operator<<(ostream &os,Rint m){os<>p>>n>>k>>b; vector as(n); for(int i=0;i>as[i]; using R = Rint; R::set_mod(p); vector ps(p); for(int i=0;i; ArbitraryMod arb; vector dp(p,0); dp[0]=1; for(int i=0;i ad(p,0); for(int j=0;j