#ifdef NACHIA #define _GLIBCXX_DEBUG #else #define NDEBUG #endif #include #include #include #include using i64 = long long; using u64 = unsigned long long; #define rep(i,n) for(i64 i=0; i void chmin(A& l, const A& r){ if(r < l) l = r; } template void chmax(A& l, const A& r){ if(l < r) l = r; } using namespace std; #include #include #include namespace nachia{ // ax + by = gcd(a,b) // return ( x, - ) std::pair 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 struct GarnerMod{ using Int = unsigned int; using IntLong = unsigned long long; std::vector mods; std::vector dynmods; std::vector> table_coeff; std::vector table_coeffinv; void precalc(std::vector new_mods){ mods = std::move(new_mods); dynmods.resize(mods.size()); for(size_t i=0; i(nmods, 1)); for(int j=0; j& x) const { int nmods = mods.size(); std::vector table_const(nmods); FinishType res = 0; FinishType res_coeff = 1; for(int j=0; j calc(std::vector> x) const { int n = x[0].size(), m = x.size(); std::vector res(n); std::vector buf(m); for(int i=0; i std::vector PartConvolution(std::vector A, std::vector B) { std::vector> AA(A.size()); for(std::size_t i=0; i> BB(B.size()); for(std::size_t i=0; i res(AB.size()); for(std::size_t i=0; i std::vector Convolution(std::vector A, std::vector B){ auto Q1 = PartConvolution(A, B); auto Q2 = PartConvolution(A, B); auto Q3 = PartConvolution(A, B); GarnerMod garner; garner.precalc({ 998244353, 897581057, 880803841 }); return garner.calc({ Q1, Q2, Q3 }); } } // namespace nachia namespace nachia{ template Modint KthTermOfRationalGF( std::vector denom, std::vector 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 Modint KthTermOfLinearRecurrence( std::vector denom, std::vector 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 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 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 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; }