結果

問題 No.3044 よくあるカエルさん
ユーザー 👑 Nachia
提出日時 2025-03-02 18:24:19
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 5 ms / 2,000 ms
コード長 8,918 bytes
コンパイル時間 3,998 ms
コンパイル使用メモリ 147,260 KB
実行使用メモリ 8,608 KB
最終ジャッジ日時 2025-03-02 18:24:25
合計ジャッジ時間 5,211 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge4
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 * 1
other AC * 20
権限があれば一括ダウンロードができます

ソースコード

diff # 

#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.size() == numer.size());
    assert(denom[0].val() != 0);
    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>;


void testcase(){
    i64 N, T; cin >> N >> T;
    i64 K, L; cin >> K >> L;
    vector<Modint> A(T+1);
    A[0] = 1;
    A[1] = -Modint(K-1) / 6;
    A[2] = -Modint(L-K) / 6;
    A[T] = -Modint(6-L+1) / 6;
    vector<Modint> D(T+1); D[0] = 1;
    auto res = nachia::KthTermOfRationalGF(A, D, N-1);
    cout << res.val() << "\n";
}

int main(){
    ios::sync_with_stdio(false); cin.tie(nullptr);
    testcase();
    return 0;
}
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