#line 1 "library/Template/template.hpp"
#include <bits/stdc++.h>
using namespace std;

#define rep(i,a,b) for(int i=(int)(a);i<(int)(b);i++)
#define ALL(v) (v).begin(),(v).end()
using ll=long long int;
const int inf = 0x3fffffff;
const ll INF = 0x1fffffffffffffff;
template<typename T>inline bool chmax(T& a,T b){if(a<b){a=b;return 1;}return 0;}
template<typename T>inline bool chmin(T& a,T b){if(a>b){a=b;return 1;}return 0;}
#line 2 "library/Utility/fastio.hpp"
#include <unistd.h>

class FastIO{
    static constexpr int L=1<<16;
    char rdbuf[L];
    int rdLeft=0,rdRight=0;
    inline void reload(){
        int len=rdRight-rdLeft;
        memmove(rdbuf,rdbuf+rdLeft,len);
        rdLeft=0,rdRight=len;
        rdRight+=fread(rdbuf+len,1,L-len,stdin);
    }
    inline bool skip(){
        for(;;){
            while(rdLeft!=rdRight and rdbuf[rdLeft]<=' ')rdLeft++;
            if(rdLeft==rdRight){
                reload();
                if(rdLeft==rdRight)return false;
            }
            else break;
        }
        return true;
    }
    template<typename T,enable_if_t<is_integral<T>::value,int> =0>inline bool _read(T& x){
        if(!skip())return false;
        if(rdLeft+20>=rdRight)reload();
        bool neg=false;
        if(rdbuf[rdLeft]=='-'){
            neg=true;
            rdLeft++;
        }
        x=0;
        while(rdbuf[rdLeft]>='0' and rdLeft<rdRight){
            x=x*10+(neg?-(rdbuf[rdLeft++]^48):(rdbuf[rdLeft++]^48));
        }
        return true;
    }
    template<typename T,enable_if_t<is_floating_point<T>::value,int> =0>inline bool _read(T& x){
        if(!skip())return false;
        if(rdLeft+20>=rdRight)reload();
        bool neg=false;
        if(rdbuf[rdLeft]=='-'){
            neg=true;
            rdLeft++;
        }
        x=0;
        while(rdbuf[rdLeft]>='0' and rdbuf[rdLeft]<='9' and rdLeft<rdRight){
            x=x*10+(rdbuf[rdLeft++]^48);
        }
        if(rdbuf[rdLeft]!='.')return true;
        rdLeft++;
        T base=.1;
        while(rdbuf[rdLeft]>='0' and rdbuf[rdLeft]<='9' and rdLeft<rdRight){
            x+=base*(rdbuf[rdLeft++]^48);
            base*=.1;
        }
        if(neg)x=-x;
        return true;
    }
    inline bool _read(char& x){
        if(!skip())return false;
        if(rdLeft+1>=rdRight)reload();
        x=rdbuf[rdLeft++];
        return true;
    }
    inline bool _read(string& x){
        if(!skip())return false;
        for(;;){
            int pos=rdLeft;
            while(pos<rdRight and rdbuf[pos]>' ')pos++;
            x.append(rdbuf+rdLeft,pos-rdLeft);
            if(rdLeft==pos)break;
            rdLeft=pos;
            if(rdLeft==rdRight)reload();
            else break;
        }
        return true;
    }
    template<typename T>inline bool _read(vector<T>& v){
        for(auto& x:v){
            if(!_read(x))return false;
        }
        return true;
    }

    char wtbuf[L],tmp[50];
    int wtRight=0;
    inline void flush(){
        fwrite(wtbuf,1,wtRight,stdout);
        wtRight=0;
    }
    inline void _write(const char& x){
        if(wtRight>L-32)flush();
        wtbuf[wtRight++]=x;
    }
    inline void _write(const string& x){
        for(auto& c:x)_write(c);
    }
    template<typename T,enable_if_t<is_integral<T>::value,int> =0>inline void _write(T x){
        if(wtRight>L-32)flush();
        if(x==0){
            _write('0');
            return;
        }
        else if(x<0){
            _write('-');
            if (__builtin_expect(x == std::numeric_limits<T>::min(), 0)) {
                switch (sizeof(x)) {
                case 2: _write("32768"); return;
                case 4: _write("2147483648"); return;
                case 8: _write("9223372036854775808"); return;
                }
            }
            x=-x;
        }
        int pos=0;
        while(x!=0){
            tmp[pos++]=char((x%10)|48);
            x/=10;
        }
        rep(i,0,pos)wtbuf[wtRight+i]=tmp[pos-1-i];
        wtRight+=pos;
    }
    template<typename T>inline void _write(const vector<T>& v){
        rep(i,0,v.size()){
            if(i)_write(' ');
            _write(v[i]);
        }
    }
public:
    FastIO(){}
    ~FastIO(){flush();}
    inline void read(){}
    template <typename Head, typename... Tail>inline void read(Head& head,Tail&... tail){
        assert(_read(head));
        read(tail...); 
    }
    template<bool ln=true,bool space=false>inline void write(){if(ln)_write('\n');}
    template <bool ln=true,bool space=false,typename Head, typename... Tail>inline void write(const Head& head,const Tail&... tail){
        if(space)_write(' ');
        _write(head);
        write<ln,true>(tail...); 
    }
};

/**
 * @brief Fast IO
 */
#line 3 "sol.cpp"

#line 2 "library/Math/modint.hpp"

template<int mod=1000000007>struct fp {
    int v; static int get_mod(){return mod;}
    int inv() const{
        int tmp,a=v,b=mod,x=1,y=0;
        while(b)tmp=a/b,a-=tmp*b,swap(a,b),x-=tmp*y,swap(x,y);
        if(x<0){x+=mod;} return x;
    }
    fp(ll x=0){init(x%mod+mod);}
    fp& init(ll x){v=(x<mod?x:x-mod); return *this;}
    fp operator-()const{return fp()-*this;}
    fp pow(ll t){assert(t>=0); fp res=1,b=*this; while(t){if(t&1)res*=b;b*=b;t>>=1;} return res;}
    fp& operator+=(const fp& x){return init(v+x.v);}
    fp& operator-=(const fp& x){return init(v+mod-x.v);}
    fp& operator*=(const fp& x){v=ll(v)*x.v%mod; return *this;}
    fp& operator/=(const fp& x){v=ll(v)*x.inv()%mod; return *this;}
    fp operator+(const fp& x)const{return fp(*this)+=x;}
    fp operator-(const fp& x)const{return fp(*this)-=x;}
    fp operator*(const fp& x)const{return fp(*this)*=x;}
    fp operator/(const fp& x)const{return fp(*this)/=x;}
    bool operator==(const fp& x)const{return v==x.v;}
    bool operator!=(const fp& x)const{return v!=x.v;}
    friend istream& operator>>(istream& is,fp& x){return is>>x.v;}
    friend ostream& operator<<(ostream& os,const fp& x){return os<<x.v;}
};
template<typename T>struct factorial {
    vector<T> Fact,Finv,Inv;
    factorial(int maxx){
        Fact.resize(maxx); Finv.resize(maxx); Inv.resize(maxx);
        Fact[0]=Fact[1]=Finv[0]=Finv[1]=Inv[1]=1;
        rep(i,2,maxx){Fact[i]=Fact[i-1]*i;} Finv[maxx-1]=Fact[maxx-1].inv();
        for(int i=maxx-1;i>=2;i--){Finv[i-1]=Finv[i]*i; Inv[i]=Finv[i]*Fact[i-1];}
    }
    T fact(int n,bool inv=0){if(n<0)return 0; return (inv?Finv[n]:Fact[n]);}
    T inv(int n){if(n<0)return 0; return Inv[n];}
    T nPr(int n,int r,bool inv=0){if(n<0||n<r||r<0)return 0; return fact(n,inv)*fact(n-r,inv^1);}
    T nCr(int n,int r,bool inv=0){if(n<0||n<r||r<0)return 0; return fact(n,inv)*fact(r,inv^1)*fact(n-r,inv^1);}
    T nHr(int n,int r,bool inv=0){return nCr(n+r-1,r,inv);}
};

/**
 * @brief Modint
 */
#line 2 "library/Convolution/ntt.hpp"

template<typename T,unsigned p=3>struct NTT{
    vector<T> rt,irt;
    NTT(int lg=21){
        unsigned m=T::get_mod()-1; T prt=p;
        rt.resize(lg); irt.resize(lg);
        rep(k,0,lg){
            rt[k]=-prt.pow(m>>(k+2));
            irt[k]=rt[k].inv();
        }
    }
    void ntt(vector<T>& f,bool inv=0){
        int n=f.size();
        if(inv){
            for(int m=1;m<n;m<<=1){ T w=1;
                for(int s=0,t=0;s<n;s+=m*2){
                    for(int i=s,j=s+m;i<s+m;i++,j++){
                        auto x=f[i],y=f[j];
                        f[i]=x+y; f[j]=(x-y)*w;
                    } w*=irt[__builtin_ctz(++t)];
                }
             } T mul=T(n).inv(); rep(i,0,n)f[i]*=mul;
        }else{
            for(int m=n;m>>=1;){ T w=1;
                for(int s=0,t=0;s<n;s+=m*2){
                    for(int i=s,j=s+m;i<s+m;i++,j++){
                        auto x=f[i],y=f[j]*w;
                        f[i]=x+y; f[j]=x-y;
                    } w*=rt[__builtin_ctz(++t)];
                }
            }
         }
    }
    vector<T> mult(const vector<T>& a,const vector<T>& b,bool same=0){
        if(a.empty() or b.empty())return vector<T>();
        int n=a.size()+b.size()-1,m=1<<__lg(n*2-1);
        vector<T> res(m); rep(i,0,a.size()){res[i]=a[i];} ntt(res);
        if(same)rep(i,0,m)res[i]*=res[i];
        else{
            vector<T> c(m); rep(i,0,b.size())c[i]=b[i];
            ntt(c); rep(i,0,m)res[i]*=c[i];
        } ntt(res,1); res.resize(n); return res;
    }
};

/**
 * @brief Number Theoretic Transform
 */
#line 2 "library/FPS/fps.hpp"

template<typename T>struct Poly:vector<T>{
    Poly(int n=0){this->assign(n,T());}
    Poly(const vector<T>& f){this->assign(ALL(f));}
    T eval(const T& x){
        T res;
        for(int i=this->size()-1;i>=0;i--)res*=x,res+=this->at(i);
        return res;
    }
    Poly rev()const{Poly res=*this; reverse(ALL(res)); return res;}
    void shrink(){while(!this->empty() and this->back()==0)this->pop_back();}
    vector<T> mult(const vector<T>& a,const vector<T>& b,bool same=0)const{
        if(a.empty() or b.empty())return vector<T>();
        int n=a.size()+b.size()-1,m=1<<__lg(n*2-1);
        vector<T> res(m);
        rep(i,0,a.size())res[i]=a[i];
        NTT(res,0);
        if(same)rep(i,0,m)res[i]*=res[i];
        else{
            vector<T> c(m);
            rep(i,0,b.size())c[i]=b[i];
            NTT(c,0);
            rep(i,0,m)res[i]*=c[i];
        }
        NTT(res,1);
        res.resize(n);
        return res;
    }
    Poly square()const{return Poly(mult(*this,*this,1));}
    Poly operator-()const{return Poly()-*this;}
    Poly operator+(const Poly& g)const{return Poly(*this)+=g;}
    Poly operator+(const T& g)const{return Poly(*this)+=g;}
    Poly operator-(const Poly& g)const{return Poly(*this)-=g;}
    Poly operator-(const T& g)const{return Poly(*this)-=g;}
    Poly operator*(const Poly& g)const{return Poly(*this)*=g;}
    Poly operator*(const T& g)const{return Poly(*this)*=g;}
    Poly operator/(const Poly& g)const{return Poly(*this)/=g;}
    Poly operator%(const Poly& g)const{return Poly(*this)%=g;}
    Poly& operator+=(const Poly& g){
        if(g.size()>this->size())this->resize(g.size());
        rep(i,0,g.size()){(*this)[i]+=g[i];} return *this;
    }
    Poly& operator+=(const T& g){
        if(this->empty())this->push_back(0);
        (*this)[0]+=g; return *this;
    }
    Poly& operator-=(const Poly& g){
        if(g.size()>this->size())this->resize(g.size());
        rep(i,0,g.size()){(*this)[i]-=g[i];} return *this;
    }
    Poly& operator-=(const T& g){
        if(this->empty())this->push_back(0);
        (*this)[0]-=g; return *this;
    }
    Poly& operator*=(const Poly& g){
        *this=mult(*this,g,0);
        return *this;
    }
    Poly& operator*=(const T& g){
        rep(i,0,this->size())(*this)[i]*=g;
        return *this;
    }
    Poly& operator/=(const Poly& g){
        if(g.size()>this->size()){
            this->clear(); return *this;
        }
        Poly g2=g;
        reverse(ALL(*this));
        reverse(ALL(g2));
        int n=this->size()-g2.size()+1;
        this->resize(n); g2.resize(n);
        *this*=g2.inv(); this->resize(n); 
        reverse(ALL(*this));
        shrink();
        return *this;
    }
    Poly& operator%=(const Poly& g){*this-=*this/g*g; shrink(); return *this;}
    Poly diff()const{
        Poly res(this->size()-1);
        rep(i,0,res.size())res[i]=(*this)[i+1]*(i+1);
        return res;
    }
    Poly inte()const{
        Poly res(this->size()+1);
        for(int i=res.size()-1;i;i--)res[i]=(*this)[i-1]/i;
        return res;
    }
    Poly log()const{
        assert(this->front()==1); const int n=this->size();
        Poly res=diff()*inv(); res=res.inte(); 
        res.resize(n); return res;
    }
    Poly shift(const int& c)const{
        const int n=this->size();
        Poly res=*this,g(n); g[0]=1; rep(i,1,n)g[i]=g[i-1]*c/i;
        vector<T> fact(n,1);
        rep(i,0,n){
            if(i)fact[i]=fact[i-1]*i;
            res[i]*=fact[i];
        }
        res=res.rev();
        res*=g;
        res.resize(n);
        res=res.rev();
        rep(i,0,n)res[i]/=fact[i];
        return res;
    }
    Poly inv()const{
        const int n=this->size();
        Poly res(1); res.front()=T(1)/this->front();
        for(int k=1;k<n;k<<=1){
            Poly f(k*2),g(k*2);
            rep(i,0,min(n,k*2))f[i]=(*this)[i];
            rep(i,0,k)g[i]=res[i];
            NTT(f,0);
            NTT(g,0);
            rep(i,0,k*2)f[i]*=g[i];
            NTT(f,1);
            rep(i,0,k){f[i]=0; f[i+k]=-f[i+k];}
            NTT(f,0);
            rep(i,0,k*2)f[i]*=g[i];
            NTT(f,1);
            rep(i,0,k)f[i]=res[i];
            swap(res,f);
        } res.resize(n); return res;
    }
    Poly exp()const{
        const int n=this->size();
        if(n==1)return Poly({T(1)});
        Poly b(2),c(1),z1,z2(2);
        b[0]=c[0]=z2[0]=z2[1]=1; b[1]=(*this)[1];
        for(int k=2;k<n;k<<=1){
            Poly y=b;
            y.resize(k*2);
            NTT(y,0);
            z1=z2;
            Poly z(k);
            rep(i,0,k)z[i]=y[i]*z1[i];
            NTT(z,1);
            rep(i,0,k>>1)z[i]=0;
            NTT(z,0);
            rep(i,0,k)z[i]*=-z1[i];
            NTT(z,1);
            c.insert(c.end(),z.begin()+(k>>1),z.end());
            z2=c;
            z2.resize(k*2);
            NTT(z2,0);
            Poly x=*this;
            x.resize(k);
            x=x.diff();x.resize(k);
            NTT(x,0);
            rep(i,0,k)x[i]*=y[i];
            NTT(x,1);
            Poly bb=b.diff();
            rep(i,0,k-1)x[i]-=bb[i];
            x.resize(k*2);
            rep(i,0,k-1){x[k+i]=x[i]; x[i]=0;}
            NTT(x,0);
            rep(i,0,k*2)x[i]*=z2[i];
            NTT(x,1);
            x.pop_back();
            x=x.inte();
            rep(i,k,min(n,k*2))x[i]+=(*this)[i];
            rep(i,0,k)x[i]=0;
            NTT(x,0);
            rep(i,0,k*2)x[i]*=y[i];
            NTT(x,1);
            b.insert(b.end(),x.begin()+k,x.end());
        } b.resize(n); return b;
    }
    Poly pow(ll t){
        if(t==0){
            Poly res(this->size()); res[0]=1;
            return res;
        }
        int n=this->size(),k=0; while(k<n and (*this)[k]==0)k++;
        Poly res(n); if(__int128_t(t)*k>=n)return res;
        n-=t*k; Poly g(n); T c=(*this)[k],ic=c.inv();
        rep(i,0,n)g[i]=(*this)[i+k]*ic;
        g=g.log(); for(auto& x:g)x*=t; g=g.exp();
        c=c.pow(t); rep(i,0,n)res[i+t*k]=g[i]*c; return res;
    }
    void NTT(vector<T>& a,bool inv)const;
};

/**
 * @brief Formal Power Series (NTT-friendly mod)
 */
#line 7 "sol.cpp"
using Fp=fp<998244353>;
NTT<Fp,3> ntt;
template<>void Poly<Fp>::NTT(vector<Fp>& v,bool inv)const{return ntt.ntt(v,inv);}

#line 2 "library/FPS/samplepointshift.hpp"

template<typename T>Poly<T> SamplePointsShift(vector<T>& ys,T c,int m=-1){
    ll n=ys.size()-1,C=c.v%T::get_mod();
    if(m==-1)m=n+1;
    factorial<T> fact(ys.size());
    if(C<=n){
        Poly<T> res;
        rep(i,C,n+1)res.push_back(ys[i]);
        if(int(res.size())>=m){
            res.resize(m);
            return res;
        }
        auto add=SamplePointsShift<T>(ys,n+1,m-res.size());
        for(int i=0;int(res.size())<m;i++){
            res.push_back(add[i]);
        }
        return res;
    }
    if(C+m>T::get_mod()){
        auto res=SamplePointsShift<T>(ys,c,T::get_mod()-c.v);
        auto add=SamplePointsShift<T>(ys,0,m-res.size());
        rep(i,0,add.size())res.push_back(add[i]);
        return res;
    }

    Poly<T> A(n+1),B(m+n);
    rep(i,0,n+1){
        A[i]=ys[i]*fact.fact(i,1)*fact.fact(n-i,1);
        if((n-i)&1)A[i]=-A[i];
    }
    rep(i,0,m+n)B[i]=Fp(1)/(c-n+i);
    auto AB=A*B;
    vector<Fp> res(m);
    Fp base=1;
    rep(x,0,n+1)base*=(c-x);
    rep(i,0,m){
        res[i]=AB[n+i]*base;
        base*=(c+i+1);
        base*=B[i];
    }
    return res;
}

/**
 * @brief Shift of Sampling Points of Polynomial
*/
#line 2 "library/Math/matrix.hpp"

template<class T>struct Matrix{
    int h,w; vector<vector<T>> val; T det;
    Matrix(){}
    Matrix(int n):h(n),w(n),val(vector<vector<T>>(n,vector<T>(n))){}
    Matrix(int n,int m):h(n),w(m),val(vector<vector<T>>(n,vector<T>(m))){}
    vector<T>& operator[](const int i){return val[i];}
    Matrix& operator+=(const Matrix& m){
        assert(h==m.h and w==m.w);
        rep(i,0,h)rep(j,0,w)val[i][j]+=m.val[i][j];
        return *this;
    }
    Matrix& operator-=(const Matrix& m){
        assert(h==m.h and w==m.w);
        rep(i,0,h)rep(j,0,w)val[i][j]-=m.val[i][j];
        return *this;
    }
    Matrix& operator*=(const Matrix& m){
        assert(w==m.h);
        Matrix<T> res(h,m.w);
        rep(i,0,h)rep(j,0,m.w)rep(k,0,w)res.val[i][j]+=val[i][k]*m.val[k][j];
        *this=res; return *this;
    }
    Matrix operator+(const Matrix& m)const{return Matrix(*this)+=m;}
    Matrix operator-(const Matrix& m)const{return Matrix(*this)-=m;}
    Matrix operator*(const Matrix& m)const{return Matrix(*this)*=m;}
    Matrix pow(ll k){
        Matrix<T> res(h,h),c=*this; rep(i,0,h)res.val[i][i]=1;
        while(k){if(k&1)res*=c; c*=c; k>>=1;} return res;
    }
    vector<int> gauss(int c=-1){
        if(val.empty())return {};
        if(c==-1)c=w;
        int cur=0; vector<int> res; det=1;
        rep(i,0,c){
            if(cur==h)break;
            rep(j,cur,h)if(val[j][i]!=0){
                swap(val[cur],val[j]);
                if(cur!=j)det*=-1;
                break;
            }
            det*=val[cur][i];
            if(val[cur][i]==0)continue;
            rep(j,0,h)if(j!=cur){
                T z=val[j][i]/val[cur][i];
                rep(k,i,w)val[j][k]-=val[cur][k]*z;
            }
            res.push_back(i);
            cur++;
        }
        return res;
    }
    Matrix inv(){
        assert(h==w);
        Matrix base(h,h*2),res(h,h);
        rep(i,0,h)rep(j,0,h)base[i][j]=val[i][j];
        rep(i,0,h)base[i][h+i]=1;
        base.gauss(h);
        rep(i,0,h)rep(j,0,h)res[i][j]=base[i][h+j]/base[i][i];
        return res;
    }
    bool operator==(const Matrix& m){
        assert(h==m.h and w==m.w);
        rep(i,0,h)rep(j,0,w)if(val[i][j]!=m.val[i][j])return false;
        return true;
    }
    bool operator!=(const Matrix& m){
        assert(h==m.h and w==m.w);
        rep(i,0,h)rep(j,0,w)if(val[i][j]==m.val[i][j])return false;
        return true;
    }
    friend istream& operator>>(istream& is,Matrix& m){
        rep(i,0,m.h)rep(j,0,m.w)is>>m[i][j];
        return is;
    }
    friend ostream& operator<<(ostream& os,Matrix& m){
        rep(i,0,m.h){
            rep(j,0,m.w)os<<m[i][j]<<(j==m.w-1 and i!=m.h-1?'\n':' ');
        }
        return os;
    }
};

/**
 * @brief Matrix
 */
#line 3 "library/Math/linearequation.hpp"

template<typename T>pair<vector<T>,Matrix<T>> LinearEquation(Matrix<T> a,vector<T> b){
   int h=a.h,w=a.w;
   rep(i,0,h)a[i].push_back(b[i]);
   a.w++;
   vector<int> idx=a.gauss(w);
   rep(i,idx.size(),h)if(a[i][w]!=0)return {{},{}};
   vector<T> res(w);
   rep(i,0,idx.size())res[idx[i]]=a[i][w]/a[i][idx[i]];
   Matrix<T> d(w,h+w);
   rep(i,0,h)rep(j,0,w)d[j][i]=a[i][j];
   rep(i,0,w)d[i][h+i]=1;
   int r=d.gauss(h).size();
   Matrix<T> basis(w-r,w);
   rep(i,r,w)basis[i-r]={d[i].begin()+h,d[i].end()};
   return {res,basis};
}

/**
 * @brief Linear Equation
 */
#line 5 "library/FPS/p-recursive.hpp"

template<typename T>Matrix<T> PrefixProdOfPolyMatrix(Matrix<Poly<T>>& m,ll K){
    using Mat=Matrix<T>;

    int n=m.val.size();
    int deg=1;
    rep(i,0,n)rep(j,0,n)chmax(deg,(int)m[i][j].size()-1);
    ll SQ=1;
    while(SQ*SQ*deg<K)SQ<<=1;
    T iSQ=T(SQ).inv();

    vector<Mat> G(deg+1);
    rep(k,0,deg+1){
        G[k]=Mat(n,n);
        rep(i,0,n)rep(j,0,n)G[k][i][j]=m[i][j].eval(SQ*k);
    }

    auto process=[&](vector<Mat>& base,T x)->vector<Mat>{
        int D=base.size();
        vector ret(D,Mat(n,n));
        rep(i,0,n)rep(j,0,n){
            vector<T> val(D);
            rep(k,0,D)val[k]=base[k][i][j];
            auto add=SamplePointsShift<T>(val,x);
            rep(k,0,D)ret[k][i][j]=add[k];
        }
        return ret;
    };
    
    for(ll w=1;w<SQ;w<<=1){
        auto G1=process(G,iSQ*w);
        auto G2=process(G,w*deg+1);
        auto G3=process(G,iSQ*w+w*deg+1);
        rep(i,0,w*deg+1)G1[i]*=G[i],G3[i]*=G2[i];
        G1.insert(G1.end(),ALL(G3));
        G1.pop_back();
        swap(G,G1);
    }
    
    Mat ret(n,n);
    rep(i,0,n)ret[i][i]=1;
    ll k=0;
    while(k*SQ+SQ<=K)ret=G[k++]*ret;
    k*=SQ;
    while(k<K){
        Mat mul(n,n);
        rep(i,0,n)rep(j,0,n)mul[i][j]=m[i][j].eval(k);
        ret=mul*ret;
        k++;
    }
    return ret;
}

// a_{n+i}*f_n(i)+...+a_i*f_0(i)=0
// {f_r}:dec order!!!
template<typename T>vector<Poly<T>> FindPRecursive(vector<T>& a,int d){
    int n=a.size();
    int k=(n+2)/(d+2)-1;
    if(k<=0)return {};
    int m=(d+1)*(k+1);
    Matrix<T> mat(m-1,m);
    rep(i,0,m-1)rep(j,0,k+1){
        T base=1;
        rep(deg,0,d+1){
            mat[i][(d+1)*j+deg]=a[i+j]*base;
            base*=(i+j);
        }
    }
    auto basis=LinearEquation(mat,vector<T>(m-1)).second;
    if(basis.val.empty())return {};
    auto c=basis[0];
    vector<Poly<T>> ret;
    for(int i=0;i*(d+1)<(int)c.size();i++){
        Poly<T> add,base({T(i),T(1)});
        for(int j=d;j>=0;j--){
            add*=base;
            if(c[i*(d+1)+j]!=0)add+=c[i*(d+1)+j];
        }
        ret.push_back(add);
    }
    while(ret.back().empty())ret.pop_back();
    reverse(ALL(ret));
    return ret;
}

template<typename T>T KthtermOfPRecursive(vector<T>& a,vector<Poly<T>>& fs,ll k){
    int n=fs.size()-1;
    assert(int(a.size())>=n);
    if(k<int(a.size()))return a[k];

    Matrix<Poly<T>> m(n),den(1);
    Matrix<T> base(n);
    rep(i,0,n)m[0][i]=-fs[i+1];
    rep(i,1,n)m[i][i-1]=fs[0];
    den[0][0]=fs[0];
    rep(i,0,n)base[i][0]=a[n-1-i];
    T ret=(PrefixProdOfPolyMatrix(m,k-n+1)*base)[0][0];
    ret/=PrefixProdOfPolyMatrix(den,k-n+1)[0][0];
    return ret;
}

template<typename T>T KthtermEsper(vector<T>& a,ll k){
    if(k<(int)a.size())return a[k];
    int n=a.size()-1;
    vector<Fp> b=a;
    b.pop_back();

    for(int d=0;;d++){
        if((n+2)/(d+2)<=1)break;
        auto fs=FindPRecursive(b,d);
        if(KthtermOfPRecursive(b,fs,n)==a.back()){
            return KthtermOfPRecursive(a,fs,k);
        }
    }
    cerr<<"esper Failed"<<'\n';
    assert(0);
}

/**
 * @brief P-recursive
*/
#line 2 "library/FPS/multieval.hpp"

template<typename T>struct MultiEval{
    int m,n; vector<Poly<T>> t;
    MultiEval(vector<T>& v){
        m=v.size(),n=1; while(n<m)n<<=1;
        t.resize(n<<1);
        rep(i,0,n){
            T w=(i<m?v[i]:0);
            t[n+i]=Poly<T>({-w,T(1)});
        }
        for(int i=n-1;i;i--)t[i]=t[i*2]*t[i*2+1];
    }
    vector<T> run(const vector<T>& f){
        if(f.empty())return vector<T>(m);
        vector<Poly<T>> c(n*2);
        auto v=t[1].rev();
        v.resize(f.size());
        v=v.inv().rev()*Poly<T>(f);
        v.erase(v.begin(),v.begin()+f.size()-1);
        v.resize(n); reverse(ALL(v)); c[1]=v;
        rep(i,1,n){
            int d=c[i].size();
            rep(k,0,2){
                auto add=t[i*2+(k^1)];
                add.resize(d/2+1);
                add=add.rev();
                add*=c[i];
                add.resize(d);
                c[i*2+k]=vector<T>(add.begin()+d/2,add.end());
            }
        }
        vector<T> res(m); rep(i,0,m)res[i]=c[n+i][0];
        return res;
    }
    vector<T> build(vector<T>& ys){
        auto w=t[1].rev();
        w.resize(m+1);
        auto vs=run(w.rev().diff());
        rep(i,0,m)ys[i]/=vs[i];
        vector<Poly<T>> c(n*2);
        rep(i,0,n){
            if(i<m)c[n+i]=Poly<T>({ys[i]});
            else c[n+i]=Poly<T>({T()});
        }
        for(int i=n-1;i;i--)c[i]=c[i*2]*t[i*2+1]+c[i*2+1]*t[i*2];
        c[1]=vector<T>(c[1].begin()+(n-m),c[1].end());
        c[1].resize(m);
       return c[1];
    }
};

/**
 * @brief Multipoint Evaluation
 */
#line 13 "sol.cpp"

FastIO io;
void solve1(int t){
    vector<ll> n(t),k(t);
    rep(i,0,t)io.read(n[i],k[i]);

    int m=1<<17;
    vector<Poly<Fp>> subprod(m*2,Poly<Fp>({Fp(1)}));
    using P=pair<ll,ll>;
    vector que(m,vector<P>());
    rep(i,0,t){
        que[k[i]].push_back({n[i],i});
    }
    rep(k,0,m)if(que[k].size()){
        deque<Poly<Fp>> deq;
        for(auto& [N,_]:que[k])deq.push_back(Poly<Fp>({Fp(-N),Fp(1)}));
        while(deq.size()>1){
            auto A=deq.front();
            deq.pop_front();
            auto B=deq.front();
            deq.pop_front();
            deq.push_back(A*B);
        }
        subprod[m+k]=deq.front();
    }
    for(int i=m-1;i;i--)subprod[i]=subprod[i*2]*subprod[i*2+1];

    vector<Fp> ret(t);
    vector mat(m*2,Matrix<Poly<Fp>>(2)),rui(m*2,Matrix<Poly<Fp>>(2));
    auto dfs=[&](auto& dfs,int L,int R,int id)->void{
        if(R-L==1){ 
            if(que[L].size()){
                vector<Fp> xs;
                for(auto& [x,_]:que[L])xs.push_back(x);
                MultiEval<Fp> buf(xs);
                auto ys=buf.run(mat[id][0][0]%subprod[id]);
                rep(i,0,que[L].size())ret[que[L][i].second]=ys[i];
            }

            rui[id][0][0]=Poly<Fp>({Fp(-2*L),Fp(2)});
            rui[id][0][1]=Poly<Fp>({Fp(-L)*(L-1)/2,Fp(L)});
            rui[id][1][0]=Poly<Fp>({Fp(1)});
            return;
        }
        int mid=(L+R)>>1;
        rep(i,0,2)rep(j,0,2)mat[id*2][i][j]=mat[id][i][j]%subprod[id];
        dfs(dfs,L,mid,id*2);
        mat[id*2+1]=rui[id*2]*mat[id*2];
        dfs(dfs,mid,R,id*2+1);
        rui[id]=rui[id*2+1]*rui[id*2];
        return;
    };

    mat[1][0][0]=mat[1][1][1]=Poly<Fp>({Fp(1)});
    dfs(dfs,0,m,1);
    rep(i,0,t)io.write(ret[i].v);
}

void solve2(int t){
    while(t--){
        ll n,k;
        io.read(n,k);
        if(k>=Fp::get_mod())io.write(0);
        else{
            vector<Fp> a(2);
            a[0]=1,a[1]=n*2;
            vector<Poly<Fp>> fs(3);
            fs[0]=Poly<Fp>({Fp(1)});
            fs[1]=Poly<Fp>({-n*2+2,2});
            fs[2]=Poly<Fp>({-n,Fp(1-n*2)/2,Fp(1)/2});
            Fp ret=KthtermOfPRecursive(a,fs,k);
            io.write(ret.v);
        }
    }
}

int main(){
    int t;
    io.read(t);

    if(t>5)solve1(t);
    else solve2(t);
    return 0;
}