#include namespace { #pragma GCC diagnostic ignored "-Wunused-function" #include #pragma GCC diagnostic warning "-Wunused-function" using namespace std; using namespace atcoder; #define rep(i,n) for(int i = 0; i < (int)(n); i++) #define rrep(i,n) for(int i = (int)(n) - 1; i >= 0; i--) #define all(x) begin(x), end(x) #define rall(x) rbegin(x), rend(x) template bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; } else return false; } template bool chmin(T& a, const T& b) { if (b < a) { a = b; return true; } else return false; } using ll = long long; using P = pair; using VI = vector; using VVI = vector; using VL = vector; using VVL = vector; using mint = modint998244353; // https://web.archive.org/web/20220813130855/https://opt-cp.com/orbit-counting-lemma/ // 有理式 p(x) / q(x) で表される形式的冪級数の x^n の係数を計算 template struct bostan_mori { vector p, q; bostan_mori(vector &_p, vector &_q) : p(_p), q(_q) {} void rev(vector &f) const { int d = f.size(); rep(i, d) if (i&1) f[i] = -f[i]; } void even(vector &f) const { int d = (f.size() + 1) >> 1; rep(i, d) f[i] = f[i<<1]; f.resize(d); } void odd(vector &f) const { int d = f.size() >> 1; rep(i, d) f[i] = f[i<<1|1]; f.resize(d); } T operator[] (ll n) const { vector _p(p), _q(q), _q_rev(q); rev(_q_rev); for (; n; n >>= 1) { _p = convolution(move(_p), _q_rev); if (n&1) odd(_p); else even(_p); _q = convolution(move(_q), move(_q_rev)); even(_q); _q_rev = _q; rev(_q_rev); } return _p[0] / _q[0]; } }; } int main() { ios::sync_with_stdio(false); cin.tie(0); ll n; int k; cin >> n >> k; vector f(k + 3), g(2 * k + 4); f[2] += 1; f[k+2] += -1; g[0] += 1; g[1] += -4; g[2] += 5; g[3] += -2; g[k+1] += 1; g[k+2] += -3; g[k+3] += 2; g[2*k+2] += 1; g[2*k+3] += -1; auto bm = bostan_mori(f, g); auto ans = bm[n] + 1; cout << ans.val() << '\n'; }