結果

問題 No.3080 Colonies on Line
ユーザー 👑 Nachia
提出日時 2025-03-28 22:56:08
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 5,628 ms / 6,500 ms
コード長 25,806 bytes
コンパイル時間 4,039 ms
コンパイル使用メモリ 156,812 KB
実行使用メモリ 17,856 KB
最終ジャッジ日時 2025-03-28 22:57:27
合計ジャッジ時間 73,252 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge3
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 35
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ソースコード

diff #
プレゼンテーションモードにする

#ifdef NACHIA
#define _GLIBCXX_DEBUG
#else
#define NDEBUG
#endif
#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
using i64 = long long;
using u64 = unsigned long long;
#define rep(i,n) for(i64 i=0; i<i64(n); i++)
const i64 INF = 1001001001001001001;
template<typename A> void chmin(A& l, const A& r){ if(r < l) l = r; }
template<typename A> void chmax(A& l, const A& r){ if(l < r) l = r; }
using namespace std;
#include <atcoder/convolution>
#include <cassert>
#include <utility>
namespace nachia{
// ax + by = gcd(a,b)
// return ( x, - )
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, a);
}
} // namespace nachia
namespace nachia{
class DynamicModSupplier{
    using u64 = unsigned long long;
    using Int = unsigned int;
private:
    u64 imod;
    Int mod;
    // atcoder library
    u64 reduce2(u64 z) const noexcept {
        // atcoder library
#ifdef _MSC_VER
        u64 x; _umul128(z, im, &x);
#else
        using u128 = unsigned __int128;
        u64 x = (u64)(((u128)(z)*imod) >> 64);
#endif
        return z - x * mod;
    }
public:
    DynamicModSupplier(unsigned int MOD = 998244353) : mod(MOD) {
        assert(2 <= MOD);
        assert(MOD < (1u << 31));
        imod = (u64)(-1) / mod + 1;
    }
    Int reduce(u64 z) const noexcept {
        Int v = reduce2(z);
        if(mod <= v) v += mod;
        return v;
    }
    Int add(Int a, Int b) const { a += b; if(a >= mod){ a -= mod; } return a; }
    Int sub(Int a, Int b) const { a -= b; if(a >= mod){ a += mod; } return a; }
    Int mul(Int a, Int b) const { return reduce((u64)a * b); }
    Int muladd(Int a, Int b, Int c) const { return reduce((u64)a * b + c); }
    Int inv(Int a) const {
        Int v = ExtGcd(a, mod).first;
        return (v < mod) ? v : (v + mod);
    }
    Int pow(Int a, u64 i) const {
        Int r = a, ans = 1;
        while(i){
            if(i & 1) ans = mul(ans, r);
            i /= 2;
            r = mul(r, r);
        }
        return ans;
    }
    Int getMod() const { return mod; }
};
} // namespace nachia
namespace nachia{
template<class FinishType>
struct GarnerMod{
    using Int = unsigned int;
    using IntLong = unsigned long long;
    std::vector<Int> mods;
    std::vector<DynamicModSupplier> dynmods;
    std::vector<std::vector<Int>> table_coeff;
    std::vector<Int> table_coeffinv;
    void precalc(std::vector<Int> new_mods){
        mods = std::move(new_mods);
        dynmods.resize(mods.size());
        for(size_t i=0; i<mods.size(); i++) dynmods[i] = DynamicModSupplier(mods[i]);
        int nmods = mods.size();
        table_coeff.assign(nmods+1, std::vector<Int>(nmods, 1));
        for(int j=0; j<nmods; j++){
            for(int k=0; k<nmods; k++) table_coeff[j+1][k] = table_coeff[j][k];
            for(int k=j+1; k<nmods; k++) table_coeff[j+1][k] = dynmods[k].mul(table_coeff[j+1][k], mods[j] % mods[k]);
        }
        table_coeffinv.resize(nmods);
        for(int i=0; i<nmods; i++) table_coeffinv[i] = dynmods[i].inv(table_coeff[i][i]);
    }
    FinishType calc(const std::vector<Int>& x) const {
        int nmods = mods.size();
        std::vector<Int> table_const(nmods);
        FinishType res = 0;
        FinishType res_coeff = 1;
        for(int j=0; j<nmods; j++){
            Int t = dynmods[j].mul(dynmods[j].sub(x[j], table_const[j]), table_coeffinv[j]);
            for(int k=j+1; k<nmods; k++){
                table_const[k] = dynmods[k].muladd(t, table_coeff[j][k], table_const[k]);
            }
            res += res_coeff * FinishType(t);
            res_coeff *= mods[j];
        }
        return res;
    }
    std::vector<FinishType> calc(std::vector<std::vector<Int>> x) const {
        int n = x[0].size(), m = x.size();
        std::vector<FinishType> res(n);
        std::vector<Int> buf(m);
        for(int i=0; i<n; i++){
            for(int j=0; j<m; j++) buf[j] = x[j][i];
            res[i] = calc(buf);
        }
        return res;
    }
};
} // namespace nachia
namespace nachia{
template<class Modint, unsigned int nttmod> std::vector<unsigned int>
    PartConvolution(std::vector<Modint> A, std::vector<Modint> B)
{
    std::vector<atcoder::static_modint<nttmod>> AA(A.size());
    for(std::size_t i=0; i<A.size(); i++) AA[i] = A[i].val();
    std::vector<atcoder::static_modint<nttmod>> BB(B.size());
    for(std::size_t i=0; i<B.size(); i++) BB[i] = B[i].val();
    auto AB = atcoder::convolution(AA, BB);
    std::vector<unsigned int> res(AB.size());
    for(std::size_t i=0; i<AB.size(); i++) res[i] = AB[i].val();
    return res;
}
template<class Modint>
std::vector<Modint> Convolution(std::vector<Modint> A, std::vector<Modint> B){
    auto Q1 = PartConvolution<Modint, 998244353>(A, B);
    auto Q2 = PartConvolution<Modint, 897581057>(A, B);
    auto Q3 = PartConvolution<Modint, 880803841>(A, B);
    GarnerMod<Modint> garner;
    garner.precalc({ 998244353, 897581057, 880803841 });
    return garner.calc({ Q1, Q2, Q3 });
}
} // namespace nachia
namespace nachia{
template<class Modint>
Modint KthTermOfRationalGF(
    std::vector<Modint> denom,
    std::vector<Modint> numer,
    unsigned long long K
){
    assert(denom.size() != 0);
    assert(denom[0].val() != 0);
    if(denom.size() < numer.size()) denom.resize(numer.size());
    if(denom.size() > numer.size()) numer.resize(denom.size());
    int n = (int)denom.size();
    while(K != 0){
        auto Qn = denom;
        Qn.push_back(Modint(0));
        for(int i=1; i<n; i+=2) Qn[i] = -Qn[i];
        int f = K % 2;
        denom = Convolution(denom, Qn);
        for(int i=0; i<n; i++) denom[i] = denom[i*2];
        denom.resize(n);
        numer = Convolution(numer, Qn);
        for(int i=0; i<n; i++) numer[i] = numer[i*2+f];
        numer.resize(n);
        K /= 2;
    }
    return numer[0] / denom[0];
}
// divisor of fractional representation
//   and first terms
template<class Modint>
Modint KthTermOfLinearRecurrence(
    std::vector<Modint> denom,
    std::vector<Modint> firstTerms,
    unsigned long long K
){
    assert(denom.size() <= firstTerms.size());
    firstTerms.resize(denom.size());
    auto numer = Convolution(firstTerms, denom);
    numer.resize(denom.size());
    return KthTermOfRationalGF(std::move(denom), std::move(numer), K);
}
} // namespace nachia
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 { return x; }
    my_type& operator+=(const my_type& r) { auto t = x + r.x; if(t >= MOD) t -= MOD; x = t; return *this; }
    my_type operator+(const my_type& r) const { my_type res = *this; return res += r; }
    my_type& operator-=(const my_type& r) { auto t = x + MOD - r.x; if(t >= MOD) t -= MOD; x = t; return *this; }
    my_type operator-(const my_type& r) const { 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){ x = (u64)x * r.x % MOD; return *this; }
    my_type operator*(const my_type& r) const { my_type res = *this; return res *= r; }
    bool operator==(const my_type& r) const { return x == r.x; }
    my_type pow(unsigned long long i) const {
        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 { return x; }
    int hval() const { return int(x > MOD/2 ? x - MOD : x); }
    static constexpr unsigned int mod() { return MOD; }
    static my_type raw(unsigned int val) { 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()); }
};
} // namespace nachia
using Modint = nachia::StaticModint<998244353>;
namespace nachia{
template<unsigned int MOD>
struct PrimitiveRoot{
    using u64 = unsigned long long;
    static constexpr u64 powm(u64 a, u64 i) {
        u64 res = 1, aa = a;
        for( ; i; i /= 2){
            if(i & 1) res = res * aa % MOD;
            aa = aa * aa % MOD;
        }
        return res;
    }
    static constexpr bool ExamineVal(unsigned int g){
        u64 t = MOD - 1;
        for(u64 d=2; d*d<=t; d+=1+(d&1)) 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(u64 x=2; x<MOD; x++) if(ExamineVal(x)) return x;
        return 0;
    }
    static const unsigned int val = GetVal();
};
} // namespace nachia
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
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
    using u64 = unsigned long long;
    int q = (x >> 32) ? 32 : 0;
    auto m = x >> q;
    constexpr u64 hi = 0x88888888;
    constexpr u64 mi = 0x11111111;
    m = (((m | ~(hi - (m & ~hi))) & hi) * mi) >> 35;
    m = (((m | ~(hi - (m & ~hi))) & hi) * mi) >> 31;
    q += (m & 0xf) << 2;
    q += 0x3333333322221100 >> (((x >> q) & 0xf) << 2) & 0xf;
    return q;
#endif
}
// please ensure x != 0
int LsbIndex(unsigned long long x) noexcept {
#ifdef __GNUC__
    return __builtin_ctzll(x);
#else
    return MsbIndex(x & -x);
#endif
}
}
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
#include <iterator>
#include <array>
namespace nachia{
template <class mint>
struct Ntt : 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;
}
    
static constexpr int bsf_constexpr(unsigned int n) {
    int x = 0;
    while (!(n & (1 << x))) x++;
    return x;
}
struct fft_info {
    static constexpr u32 g = nachia::PrimitiveRoot<mint::mod()>::val;
    static constexpr int rank2 = bsf_constexpr(mint::mod()-1);
    using RootTable = std::array<mint, rank2+1>;
    RootTable root, iroot, rate3, 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<=rank2-3; 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 ButterflyLayered(RandomAccessIterator a, int n, int stride, int repeat) const {
    static const fft_info info;
    int h = n * stride;
    
    while(repeat--){
    int len = 1;
    int p = h;
    if(ceil_pow2(n)%2 == 1){
        p >>= 1;
        for(int i=0; i<p; i++){
            mint l = a[i], r = a[i+p];
            a[i] = l+r; a[i+p] = l-r;
        }
        len <<= 1;
    }
    for( ; p > stride; ){
        p >>= 2;
        mint rot = 1, imag = info.root[2];
        u64 mod2 = u64(mint::mod()) * mint::mod();
        int offset = p;
        for(int s=0; s<len; s++){
            if(s) rot *= info.rate3[LsbIndex(~(u32)(s-1))];
            mint rot2 = rot * rot;
            mint rot3 = rot2 * rot;
            for(int i=offset-p; i<offset; i++){
                u64 a0 = u64(a[i].val());
                u64 a1 = u64(a[i+p].val()) * rot.val();
                u64 a2 = u64(a[i+2*p].val()) * rot2.val();
                u64 a3 = u64(a[i+3*p].val()) * rot3.val();
                u64 a1na3imag = u64(mint(a1 + mod2 - a3).val()) * imag.val();
                u64 na2 = mod2 - a2;
                a[i] = a0 + a2 + a1 + a3;
                a[i+1*p] = a0 + a2 + (2 * mod2 - (a1 + a3));
                a[i+2*p] = a0 + na2 + a1na3imag;
                a[i+3*p] = a0 + na2 + (mod2 - a1na3imag);
            }
            offset += p << 2;
        }
        len <<= 2;
    }
    
    a += h;
    }
}
template<class RandomAccessIterator>
void Butterfly(RandomAccessIterator a, int n) const {
    ButterflyLayered(a, n, 1, 1);
}
template<class RandomAccessIterator>
void IButterflyLayered(RandomAccessIterator a, int n, int stride, int repeat) const {
    static const fft_info info;
    constexpr int MOD = mint::mod();
    
    while(repeat--){
    
    int len = n;
    int p = stride;
    for( ; 2 < len; ){
        len >>= 2;
        mint irot = 1, iimag = info.iroot[2];
        int offset = p;
        for(int s=0; s<len; s++){
            if(s) irot *= info.irate3[LsbIndex(~(u32)(s-1))];
            mint irot2 = irot * irot;
            mint irot3 = irot2 * irot;
            for(int i=offset-p; i<offset; i++){
                u64 a0 = a[i].val();
                u64 a1 = a[i+p].val();
                u64 a2 = a[i+2*p].val();
                u64 a3 = a[i+3*p].val();
                u64 a2na3iimag = mint((a2 + MOD - a3) * iimag.val()).val();
                a[i] = a0 + a1 + a2 + a3;
                a[i+p] = (a0 + (MOD - a1) + a2na3iimag) * irot.val();
                a[i+2*p] = (a0 + a1 + (MOD - a2) + (MOD - a3)) * irot2.val();
                a[i+3*p] = (a0 + (MOD - a1) + (MOD - a2na3iimag)) * irot3.val();
            }
            offset += p << 2;
        }
        p <<= 2;
    }
    if(len == 2){
        for(int i=0; i<p; i++){
            mint l = a[i], r = a[i+p];
            a[i] = l+r; a[i+p] = l-r;
        }
        p <<= 1;
    }
    
    a += p;
    }
}
template<class RandomAccessIterator>
void IButterfly(RandomAccessIterator a, int n) const {
    IButterflyLayered(a, n, 1, 1);
}
};
} // namespace nachia
namespace nachia {
template<class Elem, class NttInst = Ntt<Elem>>
struct FpsNtt {
public:
    using Fps = FpsNtt;
    using ElemTy = Elem;
    static constexpr unsigned int MOD = Elem::mod();
    static constexpr int CONV_THRES = 30;
    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;
    int RSZ(int& sz) const { return sz = (sz < 0 ? size() : sz); }
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 getCoeff(int x) const noexcept { return (0 <= x && 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); }
    Fps move(){ return std::move(*this); }
    Fps& set(int i, Elem c){ a[i] = c; return *this; }
    Fps& 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;
    }
    FpsNtt(){}
    FpsNtt(int sz) : a(sz, ZeroElem()) {}
    FpsNtt(int sz, Elem e) : a(sz, e) {}
    FpsNtt(std::vector<Elem>&& src) : a(std::move(src)) {}
    FpsNtt(const std::vector<Elem>& src) : a(src) {}
    
    Fps& ntt() {
        capSize(BestNttSize(size()));
        nttInst.Butterfly(a.begin(), size());
        return *this;
    }
    Fps& intt() {
        nttInst.IButterfly(a.begin(), a.size());
        return times(Elem::raw(size()).inv());
    }
    Fps nttDouble(Fps vanilla) const {
        int n = size();
        assert(n != 0 && n == (n&-n)); // n is a power of 2
        Elem q = Elem::raw(zeta).pow((Elem::mod() - 1) / (n*2));
        Elem qq = OneElem();
        for(int i=0; i<n; i++){ vanilla[i] *= qq; qq *= q; }
        vanilla.ntt();
        Fps res = clip(0, n*2);
        for(int i=0; i<n; i++) res[n+i] = vanilla[i];
        return res;
    }
    Fps nttDouble() const { return nttDouble(clip().intt().move()); }
    // 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
    Fps clip(int srcL, int srcR = -1, int destL = 0, int resSz = -1) const {
        srcR = RSZ(srcR);
        if(resSz < 0) resSz = destL + srcR - srcL;
        int rj = std::min(std::min(srcR, size()) - srcL, resSz - destL);
        Fps res(resSz);
        for(int j=std::max(0, -srcL); j<rj; j++) res[j+destL] = a[j+srcL];
        return res;
    }
    Fps clip() const { return *this; }
    Fps& capSize(int l, int r) {
        if(r <= (int)size()) a.resize(r);
        if(size() <= l) a.resize(l, ZeroElem());
        return *this;
    }
    Fps& capSize(int z){ a.resize(RSZ(z), ZeroElem()); return *this; }
    Fps& times(Elem x){ for(int i=0; i<size(); i++){ a[i] *= x; } return *this; }
    Fps& timesFactorial(int z = -1){ comb.extend(RSZ(z)); for(int i=0; i<z; i++){ a[i] *= comb.factorial(i); } return *this; }
    Fps& timesInvFactorial(int z = -1){ comb.extend(RSZ(z)); for(int i=0; i<z; i++){ a[i] *= comb.invFactorial(i); } return *this; }
    Fps& clrRange(int l, int r){ for(int i=l; i<r; i++){ a[i] = ZeroElem(); } return *this; }
    Fps& negate(){ for(auto& e : a){ e = -e; } return *this; }
    Fps& mulEach(const Fps& other, int maxi = -1){
        maxi = std::min(RSZ(maxi), std::min(size(), other.size()));
        for(int i=0; i<maxi; i++) a[i] *= other[i];
        return *this;
    }
    Fps& reverse(int sz = -1){ RSZ(sz); std::reverse(a.begin(), a.begin() + sz); return *this; }
    Fps& revRange(int l, int r = -1){ RSZ(r); std::reverse(a.begin() + l, a.begin() + r); return *this; }
    static Fps convolution(const Fps& a, const Fps& b, int sz = -1){
        if(std::min(a.size(), b.size()) <= CONV_THRES){
            if(a.size() > b.size()) return convolution(b, a, sz);
            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 = BestNttSize(a.size() + b.size() - 1);
        return a.clip(0, Z).ntt().mulEach(b.clip(0, Z).ntt()).intt().capSize(sz).move();
    }
    Fps convolve(const Fps& r, int sz = -1) const { return convolution(*this, r, sz); }
    
    //   1
    // ----- = 1 + f + f^2 + f^3 + ...
    //  1-f
    Fps powerSum(int sz) const {
        RSZ(sz);
        if(sz == 0) return {};
        int q = std::min(sz, 32);
        Fps x = Fps(q).set(0, OneElem()).move();
        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;
            Fps a = x.clip(0, N).ntt().move();
            Fps b = clip(0, N).ntt().mulEach(a).intt().clrRange(0,hN).ntt().mulEach(a).intt().move();
            for(int i=0; i<hN; i++) b[i] = x[i];
            std::swap(b, x);
        }
        return x.capSize(sz).move();
    }
    Fps inv(int sz = -1) const {
        RSZ(sz);
        Elem iA0 = a[0].inv();
        return clip(0, std::min(sz, size())).times(-iA0).set(0, ZeroElem()).powerSum(sz).times(iA0).move();
    }
    
    Fps& difference(){
        if(size() == 0) return *this;
        for(int i=0; i+1<size(); i++) a[i] = a[i+1] * Elem::raw(i+1);
        return capSize(size()-1);
    }
    Fps& integral(){
        if(size() == 0) return capSize(1);
        capSize(size()+1);
        comb.extend(size());
        for(int i=size()-1; i>=1; i--) a[i] = a[i-1] * comb.invOf(i);
        return set(0, ZeroElem());
    }
    
    Fps log(int sz = -1){
        RSZ(sz);
        assert(sz != 0);
        assert(a[0].val() == 1);
        return convolution(inv(sz), clip().difference(), sz-1).integral();
    }
    Fps exp(int sz = -1){
        RSZ(sz);
        Fps res = Fps(1).set(0, OneElem());
        while(res.size() < sz){
            auto z = res.size();
            auto tmp = res.capSize(z*2).log().set(0, -OneElem()).move();
            for(int i=0; i<z*2 && i<size(); i++) tmp[i] -= a[i];
            auto resntt = res.clip().ntt().mulEach(tmp.ntt()).intt().move();
            for(int i=z; i<z*2; i++) res[i] = -resntt[i];
        }
        return res.capSize(0, sz).move();
    }
    
    Fps pow(unsigned long long k, int sz = -1){
        int n = RSZ(sz);
        if(k == 0) return Fps(n).set(0, OneElem()).move();
        int ctz = 0;
        while(ctz<n && a[ctz].val() == 0) ctz++;
        if((unsigned long long)ctz >= (n-1) / k + 1) return Fps(n);
        Elem a0 = a[ctz];
        return clip(ctz, ctz+n-ctz*k).times(a0.inv()).log().times(Elem(k)).exp().times(a0.pow(k)).clip(0, -1, ctz*k);
    }
    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> getVectorMoved(){ return std::move(a); }
    Fps& operator+=(const Fps& r){
        capSize(std::max(size(), r.size()));
        for(int i=0; i<r.size(); i++) a[i] += r[i];
        return *this;
    }
    Fps& operator-=(const Fps& r){
        capSize(std::max(size(), r.size()));
        for(int i=0; i<r.size(); i++) a[i] -= r[i];
        return *this;
    }
    Fps operator+(const Fps& r) const { return (clip(0, std::max(size(), r.size())) += r).move(); }
    Fps operator-(const Fps& r) const { return (clip(0, std::max(size(), r.size())) -= r).move(); }
    Fps operator-() const { return (clip().negate()).move(); }
    Fps operator*(const Fps& r) const { return convolve(r).removeLeadingZeros().move(); }
    Fps& operator*=(const Fps& r){ return (*this) = operator*(r); }
    Fps& operator*=(Elem m){ return times(m); }
    Fps operator*(Elem m) const { return (clip() *= m).move(); }
    Elem eval(Elem x) const {
        Elem res = 0;
        for(int i=size()-1; i>=0; i--) res = res * x + a[i];
        return res;
    }
};
template<class Elem, class NttInst> Comb<Elem> FpsNtt<Elem, NttInst>::comb;
template<class Elem, class NttInst> const NttInst FpsNtt<Elem, NttInst>::nttInst;
} // namespace nachia
using Fps = nachia::FpsNtt<Modint>;
void testcase(){
    i64 N, K; cin >> N >> K;
    Fps fden(K+1), fnum(K+2);
    fden[0] = 1;
    rep(i,K) fden[1+i] -= 1;
    rep(i,K) fnum[2+i] += 1;
    Fps t = Fps(2).set(0,1).set(1,-1);
    Fps gden = t * fden - fnum.clip(-K);
    Fps gnum = t * fnum;
    gden = gden * t * t;
    auto ans = nachia::KthTermOfRationalGF(gden.getVectorMoved(), gnum.getVectorMoved(), N);
    ans += 1;
    cout << ans.val() << "\n";
}
int main(){
    ios::sync_with_stdio(false); cin.tie(nullptr);
    testcase();
    return 0;
}
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