#line 2 "nachia\\fps\\formal-power-series-struct.hpp"
#include <vector>
#include <algorithm>
#include <string>
#include <cassert>
#include <iostream>
#line 3 "nachia\\math-modulo\\modulo-primitive-root.hpp"
#include <utility>

namespace nachia{

template<unsigned int MOD>
struct PrimitiveRoot{
    static constexpr unsigned long long powm(unsigned long long a, unsigned long long i) {
        unsigned long long res = 1, aa = a;
        while(i){
            if(i & 1) res = res * aa % MOD;
            aa = aa * aa % MOD;
            i /= 2;
        }
        return res;
    }
    static constexpr bool ExamineVal(unsigned int g){
        unsigned int t = MOD - 1;
        for(unsigned long long d=2; d*d<=t; d++) if(t % d == 0){
            if(powm(g, (MOD - 1) / d) == 1) return false;
            while(t % d == 0) t /= d;
        }
        if(t != 1) if(powm(g, (MOD - 1) / t) == 1) return false;
        return true;
    }
    static constexpr unsigned int GetVal(){
        for(unsigned int x=2; x<MOD; x++) if(ExamineVal(x)) return x;
        return 0;
    }
    static const unsigned int val = GetVal();
};

}
#line 3 "nachia\\math\\combination.hpp"

namespace nachia{

template<class Modint>
class Comb{
private:
    std::vector<Modint> F;
    std::vector<Modint> iF;
public:
    void extend(int newN){
        int prevN = (int)F.size() - 1;
        if(prevN >= newN) return;
        F.resize(newN+1);
        iF.resize(newN+1);
        for(int i=prevN+1; i<=newN; i++) F[i] = F[i-1] * Modint::raw(i);
        iF[newN] = F[newN].inv();
        for(int i=newN; i>prevN; i--) iF[i-1] = iF[i] * Modint::raw(i);
    }
    Comb(int n = 1){
        F.assign(2, Modint(1));
        iF.assign(2, Modint(1));
        extend(n);
    }
    Modint factorial(int n) const { return F[n]; }
    Modint invFactorial(int n) const { return iF[n]; }
    Modint invOf(int n) const { return iF[n] * F[n-1]; }
    Modint comb(int n, int r) const {
        if(n < 0 || n < r || r < 0) return Modint(0);
        return F[n] * iF[r] * iF[n-r];
    }
    Modint invComb(int n, int r) const {
        if(n < 0 || n < r || r < 0) return Modint(0);
        return iF[n] * F[r] * F[n-r];
    }
    Modint perm(int n, int r) const {
        if(n < 0 || n < r || r < 0) return Modint(0);
        return F[n] * iF[n-r];
    }
    Modint invPerm(int n, int r) const {
        if(n < 0 || n < r || r < 0) return Modint(0);
        return iF[n] * F[n-r];
    }
    Modint operator()(int n, int r) const { return comb(n,r); }
};

} // namespace nachia
#line 1 "nachia\\fps\\ntt-modint.hpp"

#line 3 "nachia\\fps\\ntt-modint.hpp"
#include <iterator>
#line 6 "nachia\\fps\\ntt-modint.hpp"

namespace nachia{

template<class RandomAccessIterator>
void Ntt(RandomAccessIterator a, int N) {
    using Modint = typename std::iterator_traits<RandomAccessIterator>::value_type;
    assert(1 <= N && N == (N&-N));
    constexpr unsigned int MOD = Modint::mod();
    Modint Zeta = Modint(nachia::PrimitiveRoot<MOD>::GetVal());
    Modint One = Modint(1);
    static std::vector<Modint> rq = { Zeta.pow((MOD - 1) >> 2) };
    while(1 << (rq.size()+1) < N) rq.push_back(Zeta.pow((MOD - 1) / 2 + ((MOD - 1) >> (rq.size()+2)) * 3));
    for (int i = 1; i < N; i <<= 1) {
        auto q = One;
        int maxk = N / i / 2;
        for (int j = 0; j < i; j++) {
            int off = j * maxk * 2;
            for (int k = off; k < off + maxk; k++) {
                Modint l = a[k], r = a[k + maxk] * q;
                a[k] = l + r;
                a[k + maxk] = l - r;
            }
            if(j+1 != i) for(int d=0; ; d++) if(!(j&(1<<d))){ q = q * rq[d]; break; }
        }
    }
    for (int i = 0, j = 0; j < N; j++) {
        if (i < j) std::swap(a[i], a[j]);
        for (int k = N >> 1; k > (i ^= k); k >>= 1);
    }
}

template<class RandomAccessIterator>
void INtt(RandomAccessIterator a, int N) {
    using Modint = typename std::iterator_traits<RandomAccessIterator>::value_type;
    assert(1 <= N && N == (N&-N));
    Ntt(a, N);
    std::reverse(a + 1, a + N);
    Modint invN = Modint(1), inv2 = Modint(Modint::mod() / 2 + 1);
    for(int i=1; i<N; i<<=1) invN *= inv2;
    for(int i=0; i<N; i++) a[i] *= invN;
}

} // namespace nachia
#line 10 "nachia\\fps\\formal-power-series-struct.hpp"

namespace nachia {

template<class Elem>
struct FormalPowerSeriesNTT {
public:
    using MyType = FormalPowerSeriesNTT;
    static constexpr unsigned int MOD = Elem::mod();
private:
    using u32 = unsigned int;
    static const u32 zeta = nachia::PrimitiveRoot<MOD>::GetVal();
    static Elem ZeroElem() noexcept { return Elem(0); }
    static Elem OneElem() noexcept { return Elem(1); }
    static Comb<Elem> comb;
    std::vector<Elem> a;
public:

    unsigned int size() const noexcept { return a.size(); }
    Elem& operator[](unsigned int x) noexcept { return a[x]; }
    const Elem& operator[](unsigned int x) const noexcept { return a[x]; }
    Elem get_coeff(unsigned int x) const{ return (x < size()) ? a[x] : ZeroElem(); }
    static Comb<Elem>& GetComb() { return comb; }

    MyType& removeLeadingZeros(){
        unsigned int newsz = size();
        while(newsz && a[newsz-1].val() == 0) newsz--;
        a.resize(newsz);
        if(a.capacity() / 4 > newsz) a.shrink_to_fit();
        return *this;
    }

    FormalPowerSeriesNTT(){ a = {  }; }
    FormalPowerSeriesNTT(unsigned int new_size) : a(new_size, ZeroElem()) {}
    FormalPowerSeriesNTT(std::vector<Elem>&& src) : a(std::move(src)) {}
    FormalPowerSeriesNTT(const std::vector<Elem>& src) : a(src) {}
    
    MyType& ntt() {
        int N = 1; while (N < (int)size()) N *= 2;
        a.resize(N, ZeroElem());
        Ntt(a.begin(), N);
        return *this;
    }
    MyType& intt() {
        INtt(a.begin(), a.size());
        return *this;
    }

    // returns [ a[l], a[l+1], a[l+2], ... , a[r-1] ]
    // a[i] = 0 ( i < 0 OR size() <= i )
    MyType getSlice(int l, int r) const {
        if(l >= r) return MyType();
        MyType res(r - l);
        for(int i=l; i<r; i++) res[i-l] = (0 <= i && i < (int)size()) ? a[i] : ZeroElem();
        return res;
    }

    // upper < 0  ->  upper = lower
    MyType& capSize(int lower, int upper = -1) {
        if(upper < 0) upper = lower;
        if(upper <= (int)size()) a.resize(upper);
        if((int)size() <= lower) a.resize(lower, ZeroElem());
        return *this;
    }

    static MyType convolution(const MyType& a, const MyType& b){
        if(a.size() <= 30 || b.size() <= 30){
            if(a.size() > 30) return convolution(b,a);
            if(a.size() == 0 || b.size() == 0) return std::vector<Elem>{ ZeroElem() };
            std::vector<Elem> res(a.size() + b.size() - 1);
            for(std::size_t i=0; i<a.size(); i++){
                for(std::size_t j=0; j<b.size(); j++) res[i+j] += a[i] * b[j];
            }
            return res;
        }
        int z = a.size() + b.size() - 1;
        int Z = 1; while(Z < z) Z *= 2;
        MyType ax = a.getSlice(0, Z);
        MyType bx = b.getSlice(0, Z);
        ax.ntt();
        bx.ntt();
        for(int i=0; i<Z; i++) ax[i] *= bx[i];
        ax.intt();
        return ax.getSlice(0, z);
    }

    static MyType back_half_convolution(unsigned int sz, const MyType& smaller, const MyType& larger){
        assert(smaller.size() <= sz);
        assert(larger.size() <= sz*2);
        if(sz <= 5) return convolution(smaller, larger).getSlice(sz, sz*2);
        int z = sz*2;
        int Z = 1; while(Z < z) Z *= 2;
        MyType ax = smaller.getSlice(0, Z).ntt();
        MyType bx = larger.getSlice(0, Z).ntt();
        for(int i=0; i<Z; i++) ax[i] *= bx[i];
        ax.intt();
        return ax.getSlice(sz, sz*2);
    }
    
    //   1
    // ----- = 1 + f + f^2 + f^3 + ...
    //  1-f
    MyType power_sum(unsigned int sz){
        if (sz == 0) { return {}; }
        if (sz == 1) { return MyType(std::vector<Elem>{ OneElem() }); }
        u32 N = 1; while (N < sz) N *= 2;
        u32 hN = N / 2;
        MyType hInv = power_sum(hN);
        MyType tgA = getSlice(0, N).ntt();
        MyType htInv = hInv.getSlice(0, N);
        htInv.ntt();
        MyType R = MyType(N);
        for(u32 i=0; i<N; i++) R[i] = tgA[i] * htInv[i];
        R = R.intt().getSlice(hN, N + hN).ntt();
        for(u32 i=0; i<N; i++) R[i] *= htInv[i];
        R.intt();
        hInv.capSize(sz, sz);
        for(u32 i=hN; i<sz; i++) hInv[i] = R[i - hN];
        return hInv;
    }

    MyType inv(unsigned int sz){
        Elem iA0 = a[0].inv();
        MyType xA(std::min(sz, size()));
        for(u32 i=0; i<xA.size(); i++) xA[i] = -a[i] * iA0;
        xA[0] = 0;
        xA = xA.power_sum(sz);
        for(u32 i=0; i<xA.size(); i++) xA[i] *= iA0;
        return xA;
    }
    
    MyType& difference(){
        if(size() == 0) return *this;
        for(u32 i=0; i+1<size(); i++) a[i] = a[i+1] * Elem(i+1);
        capSize(0, size() - 1);
        return *this;
    }
    MyType& integral(){
        if(size() == 0){
            a.push_back(ZeroElem());
            return *this;
        }
        capSize(size()+1);
        comb.extend(size());
        for(u32 i=size()-1; i>=1; i--) a[i] = a[i-1] * Elem(comb.invOf(i));
        a[0] = ZeroElem();
        return *this;
    }
    MyType copied() const { return MyType(*this); }
    
    MyType log(unsigned int sz){
        assert(sz != 0);
        assert(a[0].val() == 1);
        return convolution(inv(sz), copied().difference()).capSize(sz-1,sz-1).integral();
    }

    MyType exp(unsigned int sz){
        MyType res = MyType(std::vector<Elem>{ OneElem() });
        while(res.size() < sz){
            auto z = res.size();
            auto tmp = res.log(z*2);
            tmp[0] = -OneElem();
            for(u32 i=0; i<z*2 && i<size(); i++) tmp[i] = a[i] - tmp[i];
            tmp = back_half_convolution(z, res, tmp);
            res.capSize(std::min(sz, z*2), z);
            for(u32 i=z; i<res.size(); i++) res[i] = tmp[i-z];
        }
        return res;
    }

    MyType& reverse(){ std::reverse(a.begin(), a.end()); return *this; }
    
    MyType pow(unsigned long long k){
        int n = size();
        if(k == 0){
            auto res = MyType(n);
            res[0] = 1;
            return res;
        }
        int ctz = 0;
        for(int i=0; i<n; i++) if(a[i].val() == 0) ctz = i+1; else break;
        if((unsigned long long)ctz >= (n-1) / k + 1) return MyType(n);
        auto res = *this;
        for(int i=0; i<n-ctz; i++) res[i] = res[i+ctz];
        Elem A0 = res[0], iA0 = A0.inv(), pA0 = A0.pow(k);
        for(int i=0; i<n; i++) res[i] *= iA0;
        res = res.log(n);
        for(int i=0; i<n; i++) res[i] *= k;
        res = res.exp(n);
        for(int i=0; i<n; i++) res[i] *= pA0;
        ctz *= k;
        for(int i=n-1; i>=ctz; i--) res[i] = res[i-ctz];
        for(int i=0; i<ctz; i++) res[i] = 0;
        return res;
    }

    auto begin(){ return a.begin(); }
    auto end(){ return a.end(); }
    auto begin() const { return a.begin(); }
    auto end() const { return a.end(); }

    std::string to_string() const {
        std::string res = "[";
        for(auto x : a){ res += " "; res += std::to_string(*x); }
        res += " ]";
        return res;
    }

    std::vector<Elem> get_vector_moved(){
        std::vector<Elem> res = std::move(a);
        a.clear();
        return std::move(a);
    }

    MyType ax_plus_b(Elem a, Elem b) const {
        auto buf = MyType(size() + 1);
        for(u32 i=0; i<size(); i++) buf[i] += this->a[i] * b;
        for(u32 i=0; i<size(); i++) buf[i+1] += this->a[i] * a;
        return buf;
    }

    MyType operator+(const MyType& r) const {
        auto sz = std::max(this->size(), r.size());
        MyType res(sz);
        for(u32 i=0; i<this->size(); i++) res[i] += this->operator[](i);
        for(u32 i=0; i<r.size(); i++) res[i] += r[i];
        return res;
    }
    
    MyType operator-(const MyType& r) const {
        auto sz = std::max(this->size(), r.size());
        MyType res(sz);
        for(u32 i=0; i<this->size(); i++) res[i] += this->operator[](i);
        for(u32 i=0; i<r.size(); i++) res[i] -= r[i];
        return res;
    }

    MyType operator*(const MyType& r) const { return convolution(*this, r); }
    MyType& operator*=(const MyType& r){ (*this) = (*this) * r; return *this; }
    MyType& operator*=(Elem m){ for(size_t i=0; i<a.size(); i++) a[i] *= m; return *this; }
    MyType operator*(Elem m) const { MyType b = *this; b *= m; return b; }

    Elem eval(Elem x) const {
        int z = size();
        Elem res = 0;
        for(int i=z-1; i>=0; i--) res = res * x + a[i];
        return res;
    }
};

template<class Elem> Comb<Elem> FormalPowerSeriesNTT<Elem>::comb;

} // namespace nachia

#line 2 "nachia\\math\\ext-gcd.hpp"

#line 6 "nachia\\math\\ext-gcd.hpp"
namespace nachia{

// ax + by = gcd(a,b)
std::pair<long long, long long> ExtGcd(long long a, long long b){
    long long x = 1, y = 0;
    while(b){
        long long u = a / b;
        std::swap(a-=b*u, b);
        std::swap(x-=y*u, y);
    }
    return std::make_pair(x, y);
}

} // namespace nachia
#line 5 "nachia\\math-modulo\\static-modint.hpp"

namespace nachia{

template<unsigned int MOD>
struct StaticModint{
private:
    using u64 = unsigned long long;
    unsigned int x;
public:

    using my_type = StaticModint;
    template< class Elem >
    static Elem safe_mod(Elem x){
        if(x < 0){
            if(0 <= x+MOD) return x + MOD;
            return MOD - ((-(x+MOD)-1) % MOD + 1);
        }
        return x % MOD;
    }

    StaticModint() : x(0){}
    StaticModint(const my_type& a) : x(a.x){}
    StaticModint& operator=(const my_type&) = default;
    template< class Elem >
    StaticModint(Elem v) : x(safe_mod(v)){}
    unsigned int operator*() const noexcept { return x; }
    my_type& operator+=(const my_type& r) noexcept { auto t = x + r.x; if(t >= MOD) t -= MOD; x = t; return *this; }
    my_type operator+(const my_type& r) const noexcept { my_type res = *this; return res += r; }
    my_type& operator-=(const my_type& r) noexcept { auto t = x + MOD - r.x; if(t >= MOD) t -= MOD; x = t; return *this; }
    my_type operator-(const my_type& r) const noexcept { my_type res = *this; return res -= r; }
    my_type operator-() const noexcept { my_type res = *this; res.x = ((res.x == 0) ? 0 : (MOD - res.x)); return res; }
    my_type& operator*=(const my_type& r)noexcept { x = (u64)x * r.x % MOD; return *this; }
    my_type operator*(const my_type& r) const noexcept { my_type res = *this; return res *= r; }
    my_type pow(unsigned long long i) const noexcept {
        my_type a = *this, res = 1;
        while(i){ if(i & 1){ res *= a; } a *= a; i >>= 1; }
        return res;
    }
    my_type inv() const { return my_type(ExtGcd(x, MOD).first); }
    unsigned int val() const noexcept { return x; }
    static constexpr unsigned int mod() { return MOD; }
    static my_type raw(unsigned int val) noexcept { auto res = my_type(); res.x = val; return res; }
    my_type& operator/=(const my_type& r){ return operator*=(r.inv()); }
    my_type operator/(const my_type& r) const { return operator*(r.inv()); }
};

}
#line 4 "nachia\\fps\\shift-of-sampling-points.hpp"

namespace nachia {

template <class Elem>
std::vector<Elem> ShiftOfSamplingPointsOfPolynomial(std::vector<Elem> points, Elem sh, int count=-1){
    using Fps = FormalPowerSeriesNTT<Elem>;
    int n = points.size();
    int m = (count < 0) ? n : count;
    if(m == 0){ return {}; }
    if(n == 0){ return std::vector<Elem>(m); }
    int z = std::max(n, m);
    Fps iF(z);
    Fps F(z);
    F[0] = 1;
    for(int i=1; i<z; i++) F[i] = F[i-1] * Elem::raw(i);
    iF[z-1] = F[z-1].inv();
    for(int i=z-1; i>=1; i--) iF[i-1] = iF[i] * Elem::raw(i);
    Fps P(n);
    for(int i=0; i<n; i++) P[i] = points[i] * iF[i];
    Fps iFI(n);
    for(int i=0; i<n; i++) iFI[i] = (i%2) ? -iF[i] : iF[i];
    P = (P * iFI).capSize(n);
    Elem q = 1;
    for(int i=1; i<n; i++) iFI[i] = iF[i] * (q *= (sh - Elem::raw(i-1)));
    for(int i=0; i<n; i++) P[i] *= F[i];
    P.reverse();
    P = (P * iFI).capSize(n);
    P.reverse();
    for(int i=0; i<n; i++) P[i] *= iF[i];
    P = P * iF;
    std::vector<Elem> res(m);
    res[0] = P[0];
    for(int i=1; i<m; i++) res[i] = P[i] * F[i];
    return res;
}

} // namespace nachia
#line 5 "nachia\\linear\\simple-matrix.hpp"

namespace nachia{

template<class Elem>
struct SimpleMatrix{
private:
    int h;
    int w;
    std::vector<Elem> elems;

public:
    
    SimpleMatrix(int new_h=0, int new_w=0){ h = new_h; w = new_w; elems.assign(h * w, 0); }
    SimpleMatrix(SimpleMatrix const&) = default;
    int numRow() const { return h; }
    int numColumn() const { return w; }
    int height() const { return numRow(); }
    int width() const { return numColumn(); }
    typename std::vector<Elem>::iterator operator[](int y){ return elems.begin() + (y*w); }
    typename std::vector<Elem>::const_iterator operator[](int y) const { return elems.begin() + (y*w); }
    static SimpleMatrix Identity(int idx, Elem One){ auto res = SimpleMatrix(idx, idx); for(int i=0; i<idx; i++) res[i][i] = One; return res; }
    void swapColumns(int x1, int x2){
        assert(0 <= x1 && x1 < numColumn());
        assert(0 <= x2 && x2 < numColumn());
        for(int y=0; y<numRow(); y++) std::swap((*this)[y][x1], (*this)[y][x2]);
    }
    void swapRows(int y1, int y2){
        assert(0 <= y1 && y1 < numRow());
        assert(0 <= y2 && y2 < numRow());
        for(int x=0; x<numColumn(); x++) std::swap((*this)[y1][x], (*this)[y2][x]);
    }
    SimpleMatrix operator*(const SimpleMatrix& r) const {
        assert(width() == r.height());
        auto res = SimpleMatrix(h, r.w);
        for(int i=0; i<h; i++) for(int j=0; j<w; j++) for(int k=0; k<r.w; k++) res[i][k] = res[i][k] + (*this)[i][j] * r[j][k];
        return res;
    }
    SimpleMatrix pow(unsigned long long i){
        auto a = *this;
        auto res = Identity(height());
        while(i){
            if(i % 2 == 1) res = res * a;
            a = a * a;
            i /= 2;
        }
        return res;
    }
};

} // namespace nachia
#line 5 "nachia\\fps\\p-recursive-matrix-product.hpp"

namespace nachia{

template<class Elem>
SimpleMatrix<Elem> PRecursiveMatrixProduct(
    SimpleMatrix<FormalPowerSeriesNTT<Elem>> p,
    unsigned long long idx
){
    using u64 = unsigned long long;
    int h = p.height();
    std::vector<std::vector<std::vector<Elem>>> res;
    res.resize(h);
    for(auto& a : res) a.resize(h);
    u64 a = 1, b = 1;
    for(int i=0; i<h; i++) for(int j=0; j<h; j++) while(b < p[i][j].size()) b <<= 1;
    u64 maxA = 1, maxB = b;
    while(maxA * maxB <= idx){ maxB <<= 1; maxA <<= 1; }
    for(int i=0; i<h; i++) for(int j=0; j<h; j++){
        res[i][j].resize(b);
        for(u64 k=0; k<b; k++) res[i][j][k] = p[i][j].eval(Elem(maxA) * Elem(k));
    }
    auto ExtendA = [&](){
        for(int i=0; i<h; i++) for(int j=0; j<h; j++){
            auto tmp = ShiftOfSamplingPointsOfPolynomial<Elem>(res[i][j], Elem(b));
            std::copy(tmp.begin(), tmp.end(), std::back_inserter(res[i][j]));
        }
        b *= 2;
    };
    auto ExtendB = [&](){
        std::vector<std::vector<std::vector<Elem>>> resbuf;
        resbuf.assign(h, std::vector<std::vector<Elem>>(h, std::vector<Elem>(b)));
        for(int i=0; i<h; i++) for(int j=0; j<h; j++){
            auto hpq = ShiftOfSamplingPointsOfPolynomial<Elem>(res[i][j], Elem(a) / Elem(maxA));
            for(int k=0; k<h; k++){
                auto resbeg = res[j][k].begin();
                auto destbeg = resbuf[i][k].begin();
                for(u64 id=0; id<b; id++) destbeg[id] += hpq[id] * resbeg[id];
            }
        }
        std::swap(res, resbuf);
        a *= 2;
    };
    auto EvalP = [p, h](Elem val) -> SimpleMatrix<Elem> {
        SimpleMatrix<Elem> res(h, h);
        for(int y=0; y<h; y++) for(int x=0; x<h; x++) res[y][x] = p[y][x].eval(val);
        return res;
    };
    auto EvalL = [&res, h](u64 idx) -> SimpleMatrix<Elem> {
        SimpleMatrix<Elem> g(h, h);
        for(int y=0; y<h; y++) for(int x=0; x<h; x++) g[y][x] = res[y][x][idx];
        return g;
    };
    while(b < maxB){ ExtendA(); ExtendB(); }
    u64 pos = 0;
    SimpleMatrix<Elem> ans = SimpleMatrix<Elem>::Identity(h, Elem::raw(1));
    while(pos + maxA <= idx){ ans = EvalL(pos / maxA) * ans; pos += maxA; }
    while(pos < idx){ ans = EvalP(pos++) * ans; }
    return ans;
}

} // namespace nachia
#line 4 "nachia\\fps\\polinomial-division.hpp"

namespace nachia{

// return polynomials have no leading zeros
template<class Elem>
std::pair<FormalPowerSeriesNTT<Elem>, FormalPowerSeriesNTT<Elem>> PolynomialDivision(
    FormalPowerSeriesNTT<Elem> A,
    FormalPowerSeriesNTT<Elem> D,
    bool do_get_remainder = true
){
    using Fps = FormalPowerSeriesNTT<Elem>;
    auto dsize = D.size();
    while(dsize != 0 && D[dsize-1].val() == 0) dsize--;
    assert(dsize != 0);
    if(A.size() == 0){ return std::make_pair(Fps(), Fps()); }
    if(A.size() < dsize){ return std::make_pair(Fps(), std::move(A)); }
    
    std::reverse(D.begin(), D.begin() + dsize);
    std::reverse(A.begin(), A.end());

    int n = A.size();
    unsigned int divSize = n - dsize + 1;
    auto invD = D.inv(divSize);

    auto tmp = (A.getSlice(0, divSize) * invD).getSlice(0, divSize);
    Fps ans1(divSize);
    for(unsigned int i=0; i<divSize; i++) ans1[divSize-1-i] = tmp[i];
    if(!do_get_remainder || dsize == 1) return std::make_pair(std::move(ans1), Fps());
    tmp = tmp * D;
    Fps ans2(dsize - 1);
    for(unsigned int i=0; i<dsize-1; i++) ans2[i] = A[n-1-i] - tmp[n-1-i];
    auto ans2sz = ans2.size();
    while(ans2sz != 0 && ans2[ans2sz-1].val() == 0) ans2sz--;
    return std::make_pair(std::move(ans1), ans2.getSlice(0, ans2sz));
}

} // namespace nachia
#line 2 "nachia\\misc\\fastio.hpp"
#include <cstdio>
#include <cctype>
#include <cstdint>
#line 6 "nachia\\misc\\fastio.hpp"

namespace nachia{

struct CInStream{
private:
	static const unsigned int INPUT_BUF_SIZE = 1 << 17;
	unsigned int p = INPUT_BUF_SIZE;
	static char Q[INPUT_BUF_SIZE];
public:
	using MyType = CInStream;
	char seekChar(){
		if(p == INPUT_BUF_SIZE){
			size_t len = fread(Q, 1, INPUT_BUF_SIZE, stdin);
			if(len != INPUT_BUF_SIZE) Q[len] = '\0';
			p = 0;
		}
		return Q[p];
	}
	void skipSpace(){ while(isspace(seekChar())) p++; }
	uint32_t nextU32(){
		skipSpace();
		uint32_t buf = 0;
		while(true){
			char tmp = seekChar();
			if('9' < tmp || tmp < '0') break;
			buf = buf * 10 + (tmp - '0');
			p++;
		}
		return buf;
	}
	int32_t nextI32(){
		skipSpace();
		if(seekChar() == '-'){ p++; return (int32_t)(-nextU32()); }
		return (int32_t)nextU32();
	}
	uint64_t nextU64(){
		skipSpace();
		uint64_t buf = 0;
		while(true){
			char tmp = seekChar();
			if('9' < tmp || tmp < '0') break;
			buf = buf * 10 + (tmp - '0');
			p++;
		}
		return buf;
	}
	int64_t nextI64(){
		skipSpace();
		if(seekChar() == '-'){ p++; return (int64_t)(-nextU64()); }
		return (int64_t)nextU64();
	}
	char nextChar(){ skipSpace(); char buf = seekChar(); p++; return buf; }
	std::string nextToken(){
		skipSpace();
		std::string buf;
		while(true){
			char ch = seekChar();
			if(isspace(ch) || ch == '\0') break;
			buf.push_back(ch);
			p++;
		}
		return buf;
	}
	MyType& operator>>(unsigned int& dest){ dest = nextU32(); return *this; }
	MyType& operator>>(int& dest){ dest = nextI32(); return *this; }
	MyType& operator>>(unsigned long& dest){ dest = nextU64(); return *this; }
	MyType& operator>>(long& dest){ dest = nextI64(); return *this; }
	MyType& operator>>(unsigned long long& dest){ dest = nextU64(); return *this; }
	MyType& operator>>(long long& dest){ dest = nextI64(); return *this; }
	MyType& operator>>(std::string& dest){ dest = nextToken(); return *this; }
	MyType& operator>>(char& dest){ dest = nextChar(); return *this; }
} cin;

struct FastOutputTable{
	char LZ[1000][4] = {};
	char NLZ[1000][4] = {};
	constexpr FastOutputTable(){
		using u32 = uint_fast32_t;
		for(u32 d=0; d<1000; d++){
			LZ[d][0] = ('0' + d / 100 % 10);
			LZ[d][1] = ('0' + d /  10 % 10);
			LZ[d][2] = ('0' + d /   1 % 10);
			LZ[d][3] = '\0';
		}
		for(u32 d=0; d<1000; d++){
			u32 i = 0;
			if(d >= 100) NLZ[d][i++] = ('0' + d / 100 % 10);
			if(d >=  10) NLZ[d][i++] = ('0' + d /  10 % 10);
			if(d >=   1) NLZ[d][i++] = ('0' + d /   1 % 10);
			NLZ[d][i++] = '\0';
		}
	}
};

struct COutStream{
private:
	using u32 = uint32_t;
	using u64 = uint64_t;
	using MyType = COutStream;
	static const u32 OUTPUT_BUF_SIZE = 1 << 17;
	static char Q[OUTPUT_BUF_SIZE];
	static constexpr FastOutputTable TB = FastOutputTable();
	u32 p = 0;
	static constexpr u32 P10(u32 d){ return d ? P10(d-1)*10 : 1; }
	static constexpr u64 P10L(u32 d){ return d ? P10L(d-1)*10 : 1; }
	template<class T, class U> static void Fil(T& m, U& l, U x) noexcept { m = l/x; l -= m*x; }
	void next_dig9(u32 x){
		u32 y;
		Fil(y, x, P10(6));
		nextCstr(TB.LZ[y]);
		Fil(y, x, P10(3));
		nextCstr(TB.LZ[y]); nextCstr(TB.LZ[x]);
	}
public:
	void nextChar(char c){
		Q[p++] = c;
		if(p == OUTPUT_BUF_SIZE){ fwrite(Q, p, 1, stdout); p = 0; }
	}
	void nextEoln(){ nextChar('\n'); }
	void nextCstr(const char* s){ while(*s) nextChar(*(s++)); }
	void nextU32(uint32_t x){
		u32 y = 0;
		if(x >= P10(9)){
			Fil(y, x, P10(9));
			nextCstr(TB.NLZ[y]); next_dig9(x);
		}
		else if(x >= P10(6)){
			Fil(y, x, P10(6));
			nextCstr(TB.NLZ[y]);
			Fil(y, x, P10(3));
			nextCstr(TB.LZ[y]); nextCstr(TB.LZ[x]);
		}
		else if(x >= P10(3)){
			Fil(y, x, P10(3));
			nextCstr(TB.NLZ[y]); nextCstr(TB.LZ[x]);
		}
		else if(x >= 1) nextCstr(TB.NLZ[x]);
		else nextChar('0');
	}
	void nextI32(int32_t x){
		if(x >= 0) nextU32(x);
		else{ nextChar('-'); nextU32((u32)-x); }
	}
	void nextU64(uint64_t x){
		u32 y = 0;
		if(x >= P10L(18)){
			Fil(y, x, P10L(18));
			nextU32(y);
			Fil(y, x, P10L(9));
			next_dig9(y); next_dig9(x);
		}
		else if(x >= P10L(9)){
			Fil(y, x, P10L(9));
			nextU32(y); next_dig9(x);
		}
		else nextU32(x);
	}
	void nextI64(int64_t x){
		if(x >= 0) nextU64(x);
		else{ nextChar('-'); nextU64((u64)-x); }
	}
	void writeToFile(bool flush = false){
		fwrite(Q, p, 1, stdout);
		if(flush) fflush(stdout);
		p = 0;
	}
	COutStream(){ Q[0] = 0; }
	~COutStream(){ writeToFile(); }
	MyType& operator<<(unsigned int tg){ nextU32(tg); return *this; }
	MyType& operator<<(unsigned long tg){ nextU64(tg); return *this; }
	MyType& operator<<(unsigned long long tg){ nextU64(tg); return *this; }
	MyType& operator<<(int tg){ nextI32(tg); return *this; }
	MyType& operator<<(long tg){ nextI64(tg); return *this; }
	MyType& operator<<(long long tg){ nextI64(tg); return *this; }
	MyType& operator<<(const std::string& tg){ nextCstr(tg.c_str()); return *this; }
	MyType& operator<<(const char* tg){ nextCstr(tg); return *this; }
	MyType& operator<<(char tg){ nextChar(tg); return *this; }
} cout;

char CInStream::Q[INPUT_BUF_SIZE];
char COutStream::Q[OUTPUT_BUF_SIZE];

} // namespace nachia
#line 5 "Main.cpp"

int main(){
    using Modint = nachia::StaticModint<998244353>;
    using Polynomial = nachia::FormalPowerSeriesNTT<Modint>;
    using PolynomialMat = nachia::SimpleMatrix<Polynomial>;
    using nachia::cin, nachia::cout;

    auto MatMod = [&](const PolynomialMat& mat, const Polynomial& mod) -> PolynomialMat {
        int n = mat.height();
        PolynomialMat res(n, n);
        for(int i=0; i<n; i++) for(int j=0; j<n; j++) res[i][j] = nachia::PolynomialDivision(mat[i][j], mod).second;
        return res;
    };

    int T; cin >> T;
    if(T <= 5){
        for(int t=0; t<T; t++){
            unsigned long long N, K; cin >> N >> K;
            if(K >= 998244353){ cout << "0\n"; continue; }
            PolynomialMat M_nX = PolynomialMat(2,2);
            M_nX[0][0] = std::vector<Modint>{ Modint(N) * 2 , -Modint(2) }; // 2N - 2k
            M_nX[0][1] = std::vector<Modint>{ 0, (Modint(N)*2+1) / 2, -Modint(1) / 2 }; // (2N+1)k/2 - k^2/2
            M_nX[1][0] = std::vector<Modint>{ 1 };
            M_nX[1][1] = std::vector<Modint>{ 0 };
            auto ansMat = nachia::PRecursiveMatrixProduct(M_nX, K);
            Modint ans = ansMat[0][0];
            cout << ans.val() << '\n';
        }
    }
    else{
        int MAX_K = 100000;
        int MATRIX_QUERY = 1001001001;

        std::vector<std::pair<unsigned long long, int>> NK(T);
        for(auto& nk : NK) cin >> nk.first >> nk.second;
        std::vector<std::pair<int, int>> queries;
        for(int k=0; k<MAX_K; k++) queries.emplace_back(k, MATRIX_QUERY);
        for(int t=0; t<T; t++) queries.emplace_back(NK[t].second, t);
        std::sort(queries.begin(), queries.end());

        int segN = 1;
        while(segN < (int)queries.size()) segN *= 2;

        std::vector<PolynomialMat> FX;
        std::vector<Polynomial> KX;
        FX.assign(segN*2, PolynomialMat::Identity(2, Polynomial(std::vector<Modint>{1})));
        KX.assign(segN*2, Polynomial(std::vector<Modint>{1}));
        for(int q=0; q<(int)queries.size(); q++){
            if(queries[q].second == MATRIX_QUERY){
                int k = queries[q].first;
                FX[segN+q][0][0] = std::vector<Modint>{ -Modint(k)*2, Modint(2) }; // 2N - 2k
                FX[segN+q][0][1] = std::vector<Modint>{ Modint(k)*(1-k) / 2, Modint(k) }; // Nk + k(1-k)/2
                FX[segN+q][1][0] = std::vector<Modint>{ 1 };
                FX[segN+q][1][1] = std::vector<Modint>{ 0 };
            }
            else{
                unsigned long long N = NK[queries[q].second].first;
                KX[segN+q] = Polynomial(std::vector<Modint>{ -Modint(N), 1 }); // x - N
            }
        }

        for(int i=segN-1; i>=1; i--) FX[i] = FX[i*2+1] * FX[i*2];
        for(int i=segN-1; i>=1; i--) KX[i] = KX[i*2+1] * KX[i*2];
        
        std::vector<PolynomialMat> FXmodKX(segN*2);
        FXmodKX[1] = MatMod(PolynomialMat::Identity(2, Polynomial(std::vector<Modint>{1})), KX[1]);

        for(int i=1; i<=segN-1; i++){
            FXmodKX[i*2] = MatMod(FXmodKX[i], KX[i*2]);
            FXmodKX[i*2+1] = MatMod(FX[i*2] * FXmodKX[i], KX[i*2+1]);
        }

        std::vector<Modint> ans(T);
        for(int q=0; q<(int)queries.size(); q++){
            if(queries[q].second != MATRIX_QUERY){
                ans[queries[q].second] = FXmodKX[segN+q][0][0].eval(0);
            }
        }

        for(int i=0; i<T; i++) cout << ans[i].val() << '\n';
    }
    return 0;
}