#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();
};

} // namespace nachia
#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 4 "nachia\\misc\\bit-operations.hpp"

namespace nachia{

int Popcount(unsigned long long c) noexcept {
#ifdef __GNUC__
    return __builtin_popcountll(c);
#else
    c = (c & (~0ull/3)) + ((c >> 1) & (~0ull/3));
    c = (c & (~0ull/5)) + ((c >> 2) & (~0ull/5));
    c = (c & (~0ull/17)) + ((c >> 4) & (~0ull/17));
    c = (c * (~0ull/257)) >> 56;
    return c;
#endif
}

// please ensure x != 0
int MsbIndex(unsigned long long x) noexcept {
#ifdef __GNUC__
    return 63 - __builtin_clzll(x);
#else
    int res = 0;
    for(int d=32; d>0; d>>=1) if(x >> d){ res |= d; x >>= d; }
    return res;
#endif
}

// please ensure x != 0
int LsbIndex(unsigned long long x) noexcept {
#ifdef __GNUC__
    return __builtin_ctzll(x);
#else
    return MsbIndex(x & -x);
#endif
}

}

#line 2 "nachia\\fps\\ntt-interface.hpp"

namespace nachia {

template<class mint>
struct NttInterface{

template<class Iter>
void Butterfly(Iter, int) const {}

template<class Iter>
void IButterfly(Iter, int) const {}

template<class Iter>
void BitReversal(Iter a, int N) const {
    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);
    }
}

};

} // namespace nachia
#line 5 "nachia\\fps\\ntt-acl.hpp"
#include <iterator>
#line 8 "nachia\\fps\\ntt-acl.hpp"
#include <array>

namespace nachia{
    
constexpr int bsf_constexpr(unsigned int n) {
    int x = 0;
    while (!(n & (1 << x))) x++;
    return x;
}

template <class mint>
struct NttFromAcl : NttInterface<mint> {

using u32 = unsigned int;
using u64 = unsigned long long;
    
static int ceil_pow2(int n) {
    int x = 0;
    while ((1U << x) < (u32)(n)) x++;
    return x;
}

struct fft_info {
    static constexpr u32 g = nachia::PrimitiveRoot<mint::mod()>::val;
    static constexpr int rank2 = bsf_constexpr(mint::mod()-1);
    std::array<mint, rank2+1> root;
    std::array<mint, rank2+1> iroot;

    std::array<mint, std::max(0, rank2-1)> rate2;
    std::array<mint, std::max(0, rank2-1)> irate2;

    std::array<mint, std::max(0, rank2-2)> rate3;
    std::array<mint, std::max(0, rank2-2)> irate3;

    fft_info(){
        root[rank2] = mint(g).pow((mint::mod() - 1) >> rank2);
        iroot[rank2] = root[rank2].inv();
        for(int i=rank2-1; i>=0; i--){
            root[i] = root[i+1] * root[i+1];
            iroot[i] = iroot[i+1] * iroot[i+1];
        }
        mint prod = 1, iprod = 1;
        for(int i=0; i<=rank2-2; i++){
            rate2[i] = root[i+2] * prod;
            irate2[i] = iroot[i+2] * iprod;
            prod *= iroot[i+2];
            iprod *= root[i+2];
        }
        prod = 1; iprod = 1;
        for(int i=0; i<=rank2-3; i++){
            rate3[i] = root[i+3] * prod;
            irate3[i] = iroot[i+3] * iprod;
            prod *= iroot[i+3];
            iprod *= root[i+3];
        }
    }
};

template<class RandomAccessIterator>
void Butterfly(RandomAccessIterator a, int n) const {
    int h = ceil_pow2(n);

    static const fft_info info;

    int len = 0;
    while(len < h){
        if(h-len == 1){
            int p = 1 << (h-len-1);
            mint rot = 1;
            for(int s=0; s<(1<<len); s++){
                int offset = s << (h-len);
                for(int i=0; i<p; i++){
                    auto l = a[i+offset];
                    auto r = a[i+offset+p] * rot;
                    a[i+offset] = l+r;
                    a[i+offset+p] = l-r;
                }
                if(s+1 != (1<<len)) rot *= info.rate2[LsbIndex(~(u32)(s))];
            }
            len++;
        } else {
            int p = 1 << (h-len-2);
            mint rot = 1, imag = info.root[2];
            for(int s=0; s<(1<<len); s++){
                mint rot2 = rot * rot;
                mint rot3 = rot2 * rot;
                int offset = s << (h-len);
                for(int i=0; i<p; i++){
                    auto mod2 = 1ULL * mint::mod() * mint::mod();
                    auto a0 = 1ULL * a[i+offset].val();
                    auto a1 = 1ULL * a[i+offset+p].val() * rot.val();
                    auto a2 = 1ULL * a[i+offset+2*p].val() * rot2.val();
                    auto a3 = 1ULL * a[i+offset+3*p].val() * rot3.val();
                    auto a1na3imag = 1ULL * mint(a1 + mod2 - a3).val() * imag.val();
                    auto na2 = mod2 - a2;
                    a[i+offset] = a0 + a2 + a1 + a3;
                    a[i+offset+1*p] = a0 + a2 + (2 * mod2 - (a1 + a3));
                    a[i+offset+2*p] = a0 + na2 + a1na3imag;
                    a[i+offset+3*p] = a0 + na2 + (mod2 - a1na3imag);
                }
                if(s+1 != (1<<len)) rot *= info.rate3[LsbIndex(~(u32)(s))];
            }
            len += 2;
        }
    }
}

template<class RandomAccessIterator>
void IButterfly(RandomAccessIterator a, int n) const {
    int h = ceil_pow2(n);

    static const fft_info info;
    constexpr int MOD = mint::mod();

    int len = h;
    while(len){
        if(len == 1){
            int p = 1 << (h-len);
            mint irot = 1;
            for(int s=0; s<(1<<(len-1)); s++){
                int offset = s << (h-len+1);
                for(int i=0; i<p; i++){
                    auto l = a[i+offset];
                    auto r = a[i+offset+p];
                    a[i+offset] = l+r;
                    a[i+offset+p] = (u64)(MOD + l.val() - r.val()) * irot.val();
                }
                if(s+1 != (1<<(len-1))) irot *= info.irate2[LsbIndex(~(u32)(s))];
            }
            len--;
        } else {
            int p = 1 << (h-len);
            mint irot = 1, iimag = info.iroot[2];
            for(int s=0; s<(1<<(len-2)); s++){
                mint irot2 = irot * irot;
                mint irot3 = irot2 * irot;
                int offset = s << (h-len+2);
                for(int i=0; i<p; i++){
                    auto a0 = 1ULL * a[i+offset+0*p].val();
                    auto a1 = 1ULL * a[i+offset+1*p].val();
                    auto a2 = 1ULL * a[i+offset+2*p].val();
                    auto a3 = 1ULL * a[i+offset+3*p].val();

                    auto a2na3iimag = 1ULL * mint((MOD + a2 - a3) * iimag.val()).val();

                    a[i+offset] = a0 + a1 + a2 + a3;
                    a[i+offset+1*p] = (a0 + (MOD - a1) + a2na3iimag) * irot.val();
                    a[i+offset+2*p] = (a0 + a1 + (MOD - a2) + (MOD - a3)) * irot2.val();
                    a[i+offset+3*p] = (a0 + (MOD - a1) + (MOD - a2na3iimag)) * irot3.val();
                }
                if(s+1 != (1<<(len-2))) irot *= info.irate3[LsbIndex(~(u32)(s))];
            }
            len -= 2;
        }
    }
}

};

} // namespace nachia
#line 11 "nachia\\fps\\formal-power-series-struct.hpp"

namespace nachia {

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

    int size() const noexcept { return a.size(); }
    Elem& operator[](int x) noexcept { return a[x]; }
    const Elem& operator[](int x) const noexcept { return a[x]; }
    Elem get_coeff(int x) const noexcept { return (x < size()) ? a[x] : ZeroElem(); }
    static Comb<Elem>& GetComb() { return comb; }
    static int BestNttSize(int x) noexcept { assert(x); return 1 << MsbIndex(x*2-1); }

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

    FormalPowerSeriesNTT(){ a = {  }; }
    FormalPowerSeriesNTT(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());
        nttInst.Butterfly(a.begin(), N);
        return *this;
    }
    MyType& intt() {
        nttInst.IButterfly(a.begin(), a.size());
        Elem invN = Elem(size()).inv();
        for(int i=0; i<size(); i++) a[i] *= invN;
        return *this;
    }
    MyType nttDouble(MyType vanilla) const {
        int n = size();
        assert(n == (n&-n)); // n is a power of 2
        Elem q = Elem::raw(zeta).pow((Elem::mod() - 1) / (n*2));
        Elem qq = Elem::raw(1);
        for(int i=0; i<n; i++){ vanilla[i] *= qq; qq *= q; }
        vanilla.ntt();
        MyType res = clip(0, n, 0, n*2);
        for(int i=0; i<n; i++) res[n+i] = vanilla[i];
        return res;
    }
    MyType nttDouble() const {
        MyType van = clip();
        van.intt();
        return nttDouble(std::move(van));
    }

    // Fps res(resSz);
    // for(int j=0; j<resSz-destL && j+srcL < srcR; j++) res[j+destL] = a.getCoeff(j+srcL)
    // if srcR is unspecified -> srcR = max(srcL, size());
    // if resSz is unspecified -> resSz = destL + srcR - srcL
    MyType clip(int srcL = 0, int srcR = -1, int destL = 0, int resSz = -1) const {
        if(srcR < 0) srcR = std::max(srcL, size());
        if(resSz < 0) resSz = destL + srcR - srcL;
        if(srcR > size()) srcR = size();
        MyType res(resSz);
        for(int j=0; j+destL < resSz && j+srcL < srcR; j++) res[j+destL] = a[j+srcL];
        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;
    }

    MyType& mulEach(const MyType& other, size_t maxi = ~(size_t)0){
        maxi = std::min(maxi, (size_t)std::min(size(), other.size()));
        for(size_t i=0; i<maxi; i++) a[i] *= other[i];
        return *this;
    }

    MyType& times(Elem x){
        int n = size();
        for(int i=0; i<n; i++) a[i] *= x;
        return *this;
    }

    MyType& clrRange(int l, int r){
        for(int i=l; i<r; i++) a[i] = 0;
        return *this;
    }

    static MyType convolution(const MyType& a, const MyType& b, int sz = -1){
        if(a.size() <= 30 || b.size() <= 30){
            if(a.size() > 30) return convolution(b,a);
            if(sz < 0) sz = std::max(0, a.size() + b.size() - 1);
            std::vector<Elem> res(sz);
            for(int i=0; i<a.size(); i++) for(int j=0; j<b.size() && i+j<sz; j++) res[i+j] += a[i] * b[j];
            return res;
        }
        int z = a.size() + b.size() - 1;
        int Z = BestNttSize(z);
        if(sz == -1) sz = z;
        auto ax = std::move(a.clip(0, Z).ntt().mulEach(b.clip(0, Z).ntt()).intt());
        if(sz != z) ax = ax.clip(0, sz);
        return ax;
    }
    MyType convolve(const MyType& r, int sz = -1) const { return convolution(*this, r, sz); }
    
    //   1
    // ----- = 1 + f + f^2 + f^3 + ...
    //  1-f
    MyType powerSum(int sz) const {
        if (sz == 0) { return {}; }
        int q = std::min((int)sz, 32);
        MyType x = MyType(q);
        x[0] = OneElem();
        for(int i=1; i<q; i++) for(int j=1; j<=std::min(i,(int)a.size()-1); j++) x[i] += x[i-j] * a[j];
        while(x.size() < sz){
            int hN = x.size(), N = hN*2;
            MyType a = std::move(x.clip(0, hN, 0, N).ntt());
            MyType b = std::move(clip(0, N).ntt().mulEach(a).intt().clrRange(0,hN).ntt().mulEach(a).intt());
            for(int i=0; i<hN; i++) b[i] = x[i];
            std::swap(b, x);
        }
        if(x.size() != sz) x = x.clip(0, sz);
        return x;
    }

    MyType inv(int sz) const {
        Elem iA0 = a[0].inv();
        MyType xA = std::move(clip(0, std::min(sz, size())).times(-iA0));
        xA[0] = 0;
        return std::move(xA.powerSum(sz).times(iA0));
    }
    
    MyType& difference(){
        if(size() == 0) return *this;
        for(int i=0; i+1<size(); i++) a[i] = a[i+1] * Elem::raw(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(int i=size()-1; i>=1; i--) a[i] = a[i-1] * comb.invOf(i);
        a[0] = ZeroElem();
        return *this;
    }
    
    MyType log(int sz){
        assert(sz != 0);
        assert(a[0].val() == 1);
        return convolution(inv(sz), clip().difference(), sz-1).integral();
    }

    MyType exp(int sz){
        MyType res = MyType(std::vector<Elem>{ OneElem() });
        while(res.size() < sz){
            auto z = res.size();
            res = res.clip(0, z, 0, z*2);
            auto tmp = res.log(z*2);
            tmp[0] = -OneElem();
            for(int i=0; i<z*2 && i<size(); i++) tmp[i] = tmp[i] - a[i];
            auto resntt = res;
            resntt.ntt().mulEach(tmp.ntt()).intt();
            for(int i=z; i<z*2; i++) res[i] = -resntt[i];
        }
        if(sz != res.size()) res = res.clip(0, sz);
        return res;
    }

    MyType& reverse(){ std::reverse(a.begin(), a.end()); return *this; }
    
    MyType pow(unsigned long long k){
        int n = size();
        if(k == 0){ MyType res(n); res[0] = 1; return res; }
        int ctz = 0;
        while(ctz<n && a[ctz].val() == 0) ctz++;
        if((unsigned long long)ctz >= (n-1) / k + 1) return MyType(n);
        MyType res = clip(ctz, ctz+n-ctz*k);
        Elem a0 = res[0];
        ctz *= k; n -= ctz;
        return res.times(a0.inv()).log(n).times(Elem(k)).exp(n).times(a0.pow(k)).clip(0, n, ctz);
    }

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

    std::string toString(std::string beg = "[ ", std::string delim = " ", std::string en = " ]") const {
        std::string res = beg;
        bool f = false;
        for(auto x : a){ if(f){ res += delim; } f = true; res += std::to_string(x.val()); }
        res += en;
        return res;
    }

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

    MyType axPlusB(Elem a, Elem b) const {
        auto buf = MyType(size() + 1);
        for(int i=0; i<size(); i++) buf[i] += this->a[i] * b;
        for(int 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(int i=0; i<this->size(); i++) res[i] += this->operator[](i);
        for(int 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(int i=0; i<this->size(); i++) res[i] += this->operator[](i);
        for(int i=0; i<r.size(); i++) res[i] -= r[i];
        return res;
    }

    MyType operator*(const MyType& r) const {
        auto res = convolution(*this, r);
        return std::move(res.removeLeadingZeros());
    }
    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, class NttInst> Comb<Elem> FormalPowerSeriesNTT<Elem, NttInst>::comb;
template<class Elem, class NttInst> const NttInst FormalPowerSeriesNTT<Elem, NttInst>::nttInst;

} // namespace nachia

#line 5 "nachia\\linear\\matrix-on-ring.hpp"

namespace nachia{

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

public:
    
    MatrixOnRing(int new_h=0, int new_w=0){ h = new_h; w = new_w; elems.resize(h * w); }
    MatrixOnRing(MatrixOnRing 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 MatrixOnRing Identity(int idx, Elem One){ auto res = MatrixOnRing(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]);
    }
    MatrixOnRing operator*(const MatrixOnRing& r) const {
        assert(width() == r.height());
        auto res = MatrixOnRing(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;
    }
    MatrixOnRing 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 4 "nachia\\fps\\p-recursive-matrix-product.hpp"

namespace nachia{
    

template<class Elem>
MatrixOnRing<Elem> PRecursiveMatrixProduct(
    MatrixOnRing<FormalPowerSeriesNTT<Elem>> p,
    unsigned long long idx
){
struct ShiftOfSamplingPointsOfPolynomialUpdate{
    using Fps = FormalPowerSeriesNTT<Elem>;
    int n;
    int N2;
    Fps iF, F, iFI, iFIntt1, iFntt;
    std::vector<Fps> iFIntt2s;
    ShiftOfSamplingPointsOfPolynomialUpdate(int n, std::vector<Elem> sh){
        this->n = n;
        N2 = 1; while(N2 < n*2) N2 *= 2;
        iF = Fps(n);
        F = Fps(n);
        F[0] = 1;
        for(int i=1; i<n; i++) F[i] = F[i-1] * Elem::raw(i);
        iF[n-1] = F[n-1].inv();
        for(int i=n-1; i>=1; i--) iF[i-1] = iF[i] * Elem::raw(i);
        iFI = Fps(n);
        for(int i=0; i<n; i++) iFI[i] = (i%2) ? -iF[i] : iF[i];
        iFIntt1 = iFI.clip(0, n, 0, N2); iFIntt1.ntt();
        iFntt = iF.clip(0, n, 0, N2); iFntt.ntt();
        for(size_t shi=0; shi<sh.size(); shi++){
            Elem q = 1;
            Fps T(N2); T[0] = Elem(1);
            for(int i=1; i<n; i++) T[i] = iF[i] * (q *= (sh[shi] - Elem::raw(i-1)));
            iFIntt2s.push_back(std::move(T.ntt()));
        }
    }
    std::vector<std::vector<Elem>> calc(const std::vector<Elem>& points){
        Fps P(N2);
        for(int i=0; i<n; i++) P[i] = points[i] * iF[i];
        P.ntt().mulEach(iFIntt1).intt().clrRange(n, N2).mulEach(F, n).reverse().ntt();
        std::vector<std::vector<Elem>> res2(iFIntt2s.size());
        for(size_t shi=0; shi<iFIntt2s.size(); shi++){
            res2[shi] = P.clip().mulEach(iFIntt2s[shi]).intt()
                .reverse().clrRange(n, N2).mulEach(iF, n).ntt()
                .mulEach(iFntt).intt().mulEach(F, n).clip(0, n).get_vector_moved();
        }
        return res2;
    }
};
    using u64 = unsigned long long;
    int h = p.height();
    std::vector<std::vector<Elem>> res;
    res.resize(h*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 < (u64)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*h+j].resize(b);
        for(u64 k=0; k<b; k++) res[i*h+j][k] = p[i][j].eval(Elem(maxA) * Elem(k));
    }
    auto EvalP = [p, h](Elem val) -> MatrixOnRing<Elem> {
        MatrixOnRing<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) -> MatrixOnRing<Elem> {
        MatrixOnRing<Elem> g(h, h);
        for(int y=0; y<h; y++) for(int x=0; x<h; x++) g[y][x] = res[y*h+x][idx];
        return g;
    };
    while(b < maxB){
        std::vector<Elem> sh(3);
        sh[0] = Elem(b);
        sh[1] = Elem(a) / Elem(maxA);
        sh[2] = sh[0] + sh[1];
        std::vector<std::vector<std::vector<Elem>>> shbuf(h*h);
        auto shman = ShiftOfSamplingPointsOfPolynomialUpdate(b, sh);
        for(int i=0; i<h*h; i++) shbuf[i] = shman.calc(res[i]);
        std::vector<std::vector<Elem>> resbuf;
        resbuf.assign(h*h, std::vector<Elem>(b*2));
        for(int i=0; i<h; i++) for(int j=0; j<h; j++) for(int k=0; k<h; k++){
            auto Lbeg1 = shbuf[i*h+j][1].begin();
            auto Rbeg1 = res[j*h+k].begin();
            auto destbeg1 = resbuf[i*h+k].begin();
            for(u64 id=0; id<b; id++) destbeg1[id] += Lbeg1[id] * Rbeg1[id];
            auto Lbeg2 = shbuf[i*h+j][2].begin();
            auto Rbeg2 = shbuf[j*h+k][0].begin();
            auto destbeg2 = resbuf[i*h+k].begin() + b;
            for(u64 id=0; id<b; id++) destbeg2[id] += Lbeg2[id] * Rbeg2[id];
        }
        std::swap(res, resbuf);
        a *= 2;
        b *= 2;
    }
    u64 pos = 0;
    MatrixOnRing<Elem> ans = MatrixOnRing<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 2 "nachia\\fps\\ntt-setup-manager.hpp"

namespace nachia{

template<class Elem>
class FpsNttSetupManager {
    using ElemTy = Elem;
    using Fps = typename nachia::FormalPowerSeriesNTT<Elem>;
    using MyType = FpsNttSetupManager;
    Fps raw;
    mutable Fps ntt;
    static const int THRESH = 30;
    FpsNttSetupManager(Fps _raw) : raw(std::move(_raw)) , ntt() {}
public:
    FpsNttSetupManager() : FpsNttSetupManager(Fps()) {}
    FpsNttSetupManager(Fps _raw, Fps _ntt) : raw(std::move(_raw)) , ntt(std::move(_ntt)) {}
    const Fps& getRaw() const { return raw; }
    int size() const { return raw.size(); }
    int Least(){ return Fps::BestNttSize(raw.size()); }
    static MyType FromRaw(Fps _raw){ return FpsNttSetupManager(std::move(_raw)); }
    static MyType FromNtt(Fps _ntt){
        Fps x = _ntt.clip();
        return MyType(std::move(x.intt().removeLeadingZeros()), std::move(_ntt));
    }
    void doubling() const {
        if(ntt.size() == 0) ntt = std::move(raw.clip(0, Fps::BestNttSize(raw.size())).ntt());
        ntt = ntt.nttDouble(raw.clip(0, ntt.size()));
    }
    Fps& ensureNtt(int sz) const {
        if(sz / 8 >= ntt.size()) ntt = std::move(raw.clip(0, sz).ntt());
        while(ntt.size() < sz){ doubling(); }
        return ntt;
    }
    Fps nttClip(int sz) const { return ensureNtt(sz).clip(0,sz); }
    std::pair<Fps, Fps> destruct(){ return std::make_pair(std::move(raw), std::move(ntt)); }
    MyType operator+(const MyType& r) const {
        Fps nntt;
        int z1 = std::min(ntt.size(), r.ntt.size());
        if(z1 >= std::max(size(), r.size())){
            nntt.capSize(std::min(ntt.size(), r.ntt.size()));
            for(int i=0; i<nntt.size(); i++) nntt[i] = ntt[i] + r.ntt[i];
        }
        return FpsNttSetupManager(raw + r.raw, std::move(nntt));
    }
    MyType operator*(const MyType& r) const {
        if(std::min(size(), r.size()) <= THRESH) return FromRaw(raw * r.raw);
        int sz = Fps::BestNttSize(size() + r.size() - 1);
        return FromNtt(std::move(nttClip(sz).mulEach(r.ensureNtt(sz))));
    }
};

} // 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() noexcept {
		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() noexcept { while(isspace(seekChar())) p++; }
	uint32_t nextU32() noexcept {
		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() noexcept {
		skipSpace();
		if(seekChar() == '-'){ p++; return (int32_t)(-nextU32()); }
		return (int32_t)nextU32();
	}
	uint64_t nextU64() noexcept {
		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() noexcept {
		skipSpace();
		if(seekChar() == '-'){ p++; return (int64_t)(-nextU64()); }
		return (int64_t)nextU64();
	}
	char nextChar() noexcept { 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) noexcept { dest = nextU32(); return *this; }
	MyType& operator>>(int& dest) noexcept { dest = nextI32(); return *this; }
	MyType& operator>>(unsigned long& dest) noexcept { dest = nextU64(); return *this; }
	MyType& operator>>(long& dest) noexcept { dest = nextI64(); return *this; }
	MyType& operator>>(unsigned long long& dest) noexcept { dest = nextU64(); return *this; }
	MyType& operator>>(long long& dest) noexcept { dest = nextI64(); return *this; }
	MyType& operator>>(std::string& dest){ dest = nextToken(); return *this; }
	MyType& operator>>(char& dest) noexcept { 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"
#include <atcoder/modint>
#line 7 "Main.cpp"

int main(){
    using Modint = atcoder::static_modint<998244353>;
    using Polynomial = nachia::FormalPowerSeriesNTT<Modint>;
    using PolynomialMat = nachia::MatrixOnRing<Polynomial>;
    using NttSetup = nachia::FpsNttSetupManager<Modint>;
    using NttSetupMat = nachia::MatrixOnRing<NttSetup>;
    using nachia::cin, nachia::cout;

    auto MatMod = [&](NttSetupMat mat, NttSetup mod) -> NttSetupMat {
        int n = mat.height();
        NttSetupMat res(n, n);
        int maxlen = 0;
        for(int i=0; i<n; i++) for(int j=0; j<n; j++) maxlen = std::max(maxlen, (int)mat[i][j].size());
        int deg = mod.size();
        if(maxlen < deg) return mat;
        auto K = mod.getRaw().clip().reverse().inv(maxlen - deg + 1);
        for(int i=0; i<n; i++) for(int j=0; j<n; j++){
            auto buf = mat[i][j];
            if(buf.size() < mod.size()){ res[i][j] = std::move(buf); continue; }
            int divlen = buf.size() + 1 - deg;
            auto div = std::move(buf.getRaw().clip(deg-1).reverse().convolve(K.clip(0, divlen), divlen).reverse());
            res[i][j] = NttSetup::FromRaw((mat[i][j].getRaw() - (NttSetup::FromRaw(div) * mod).getRaw()).clip(0, deg-1));
        }
        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>{};
            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;

        auto ConstructNttSetup = [](std::vector<Modint> x){ return NttSetup::FromRaw(x); };

        std::vector<NttSetupMat> FX;
        std::vector<NttSetup> KX;
        FX.assign(segN*2, NttSetupMat::Identity(2, ConstructNttSetup({1})));
        KX.assign(segN*2, ConstructNttSetup({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] = ConstructNttSetup({ -Modint(k)*2, Modint(2) }); // 2N - 2k
                FX[segN+q][0][1] = ConstructNttSetup({ Modint(k)*(1-k) / 2, Modint(k) }); // Nk + k(1-k)/2
                FX[segN+q][1][0] = ConstructNttSetup({ 1 });
                FX[segN+q][1][1] = ConstructNttSetup({});
            }
            else{
                unsigned long long N = NK[queries[q].second].first;
                KX[segN+q] = ConstructNttSetup({ -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<NttSetupMat> FXmodKX(segN*2);
        FXmodKX[1] = MatMod(NttSetupMat::Identity(2, ConstructNttSetup({1})), std::move(KX[1]));

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

        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].getRaw().eval(0);
            }
        }

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