#include namespace { #pragma GCC diagnostic push #pragma GCC diagnostic ignored "-Wunused-function" #include #pragma GCC diagnostic pop 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://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); int n, m; cin >> n >> m; vector> f(m), g(m); for(int k = 1; k <= m; k++) { f[k-1].resize(k + 1); // x - x^k f[k-1][1] += 1; f[k-1][k] += -1; // 1-2x^k+x^(k+1) g[k-1].resize(k + 2); g[k-1][0] += 1; g[k-1][k] += -2; g[k-1][k+1] += 1; } vector> g_sf(m + 1), g_sb(m + 1); g_sf[0] = {1}, g_sb[m] = {1}; rep(k, m) g_sf[k + 1] = convolution(g_sf[k], g[k]); rrep(k, m) g_sb[k] = convolution(g_sb[k + 1], g[k]); vector& p = g_sf[m]; vector q = g_sf[m]; rep(k, m) { auto t = convolution(convolution(g_sf[k], f[k]), g_sb[k + 1]); int sz = t.size(); if ((int)q.size() < sz) q.resize(sz); rep(i, sz) q[i] -= t[i]; } bostan_mori bm(p, q); cout << bm[n].val() << '\n'; }