#include using namespace std; #include #include using namespace atcoder; using mint = modint998244353; #define rep(i, n) for (int i = 0; i < (n); i++) // Formal Power Series using vm = vector; struct fps : vm { #define d (*this) #define s int(vm::size()) template fps(Args...args): vm(args...) {} fps(initializer_list a): vm(a.begin(),a.end()) {} void rsz(int n) { if (s < n) resize(n);} fps& low_(int n) { resize(n); return d;} fps low(int n) const { return fps(d).low_(n);} mint& operator[](int i) { rsz(i+1); return vm::operator[](i);} mint operator[](int i) const { return i= 0; --i) r = r*x+d[i]; return r; } fps operator-() const { fps r(d); rep(i,s) r[i] = -r[i]; return r;} fps& operator+=(const fps& a) { rsz(a.size()); rep(i,a.size()) d[i] += a[i]; return d;} fps& operator-=(const fps& a) { rsz(a.size()); rep(i,a.size()) d[i] -= a[i]; return d;} fps& operator*=(const fps& a) { return d = convolution(d, a);} fps& operator*=(mint a) { rep(i,s) d[i] *= a; return d;} fps& operator/=(mint a) { rep(i,s) d[i] /= a; return d;} fps operator+(const fps& a) const { return fps(d) += a;} fps operator-(const fps& a) const { return fps(d) -= a;} fps operator*(const fps& a) const { return fps(d) *= a;} fps operator*(mint a) const { return fps(d) *= a;} fps operator/(mint a) const { return fps(d) /= a;} fps operator~() const { fps r({d[0].inv()}); for (int i = 1; i < s; i <<= 1) r = r*mint(2) - (r*r*low(i<<1)).low(i<<1); return r.low_(s); } fps& operator/=(const fps& a) { int w = s; d *= ~a; return d.low_(w);} fps operator/(const fps& a) const { return fps(d) /= a;} fps integ() const { fps r; rep(i,s) r[i+1] = d[i]/(i+1); return r; } #undef s #undef d }; ostream& operator<<(ostream&o,const fps&a) { rep(i,a.size()) o<<(i?" ":"")<> N >> K; vm A(N + 1), B(N + 1); A[0] = 1; B[0] = 1; for (int c = 1, p = 1, s = 4; p <= N; p += s, s += 3, c++) { if (c % 2 == 0) { if (p <= N) A[p] = 1; if (p + c <= N) A[p + c] = 1; } else { if (p <= N) A[p] = -1; if (p + c <= N) A[p + c] = -1; } if (c % 2 == 0) { if (p * (K + 1) <= N) B[p * (K + 1)] = 1; if ((p + c) * (K + 1) <= N) B[(p + c) * (K + 1)] = 1; } else { if (p * (K + 1) <= N) B[p * (K + 1)] = -1; if ((p + c) * (K + 1) <= N) B[(p + c) * (K + 1)] = -1; } } fps c = fps(B) / fps(A); for (int i = 1; i <= N; i++) cout << c[i].val() << ' '; }