#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using Int = long long; template ostream &operator<<(ostream &os, const pair &a) { return os << "(" << a.first << ", " << a.second << ")"; }; template ostream &operator<<(ostream &os, const vector &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; } template void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; } template bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; } template bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; } #define COLOR(s) ("\x1b[" s "m") //////////////////////////////////////////////////////////////////////////////// template struct ModInt { static constexpr unsigned M = M_; unsigned x; constexpr ModInt() : x(0U) {} constexpr ModInt(unsigned x_) : x(x_ % M) {} constexpr ModInt(unsigned long long x_) : x(x_ % M) {} constexpr ModInt(int x_) : x(((x_ %= static_cast(M)) < 0) ? (x_ + static_cast(M)) : x_) {} constexpr ModInt(long long x_) : x(((x_ %= static_cast(M)) < 0) ? (x_ + static_cast(M)) : x_) {} ModInt &operator+=(const ModInt &a) { x = ((x += a.x) >= M) ? (x - M) : x; return *this; } ModInt &operator-=(const ModInt &a) { x = ((x -= a.x) >= M) ? (x + M) : x; return *this; } ModInt &operator*=(const ModInt &a) { x = (static_cast(x) * a.x) % M; return *this; } ModInt &operator/=(const ModInt &a) { return (*this *= a.inv()); } ModInt pow(long long e) const { if (e < 0) return inv().pow(-e); ModInt a = *this, b = 1U; for (; e; e >>= 1) { if (e & 1) b *= a; a *= a; } return b; } ModInt inv() const { unsigned a = M, b = x; int y = 0, z = 1; for (; b; ) { const unsigned q = a / b; const unsigned c = a - q * b; a = b; b = c; const int w = y - static_cast(q) * z; y = z; z = w; } assert(a == 1U); return ModInt(y); } ModInt operator+() const { return *this; } ModInt operator-() const { ModInt a; a.x = x ? (M - x) : 0U; return a; } ModInt operator+(const ModInt &a) const { return (ModInt(*this) += a); } ModInt operator-(const ModInt &a) const { return (ModInt(*this) -= a); } ModInt operator*(const ModInt &a) const { return (ModInt(*this) *= a); } ModInt operator/(const ModInt &a) const { return (ModInt(*this) /= a); } template friend ModInt operator+(T a, const ModInt &b) { return (ModInt(a) += b); } template friend ModInt operator-(T a, const ModInt &b) { return (ModInt(a) -= b); } template friend ModInt operator*(T a, const ModInt &b) { return (ModInt(a) *= b); } template friend ModInt operator/(T a, const ModInt &b) { return (ModInt(a) /= b); } explicit operator bool() const { return x; } bool operator==(const ModInt &a) const { return (x == a.x); } bool operator!=(const ModInt &a) const { return (x != a.x); } friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a.x; } }; //////////////////////////////////////////////////////////////////////////////// constexpr unsigned MO = 998244353; using Mint = ModInt; // singular ==> return false; // solution: a[j][n] bool linearSystem(vector> &a) { const int n = a.size(); for (int h = 0; h < n; ++h) { for (int i = h; i < n; ++i) if (a[i][h]) { swap(a[h], a[i]); break; } if (!a[h][h]) return false; const Mint s = a[h][h].inv(); for (int j = h + 1; j <= n; ++j) a[h][j] *= s; for (int i = h + 1; i < n; ++i) { for (int j = h + 1; j <= n; ++j) a[i][j] -= a[i][h] * a[h][j]; } } for (int i = n; --i >= 0; ) { for (int j = i + 1; j < n; ++j) a[i][n] -= a[i][j] * a[j][n]; } return true; } int N, K; Mint f[220'010][22]; void add(int v, int u, Mint c) { for (int k = 0; k <= K; ++k) f[v][k] += f[u][k] * c; } int main() { for (int numCases; ~scanf("%d", &numCases); ) { for (int caseId = 1; caseId <= numCases; ++caseId) { scanf("%d%d", &N, &K); for (int u = 0; u < K + N + K; ++u) fill(f[u], f[u] + (K + 1), 0); for (int k = 0; k < K; ++k) f[K + k][k] = 1; for (int u = K; u < K + N; ++u) { // u -> [u-K, u+K] add(u + K, u, 2*K + 1); f[u + K][K] -= (2*K + 1); for (int d = -K; d < K; ++d) add(u + K, u + d, -1); } //for(int u=0;u> a(K, vector(K + 1)); for (int i = 0; i < K; ++i) { const int u = K + N + i; for (int k = 0; k < K; ++k) a[i][k] = f[u][k]; a[i][K] = -f[u][K]; } const bool status = linearSystem(a); assert(status); // ? vector ans(K + N + K, 0); for (int u = 0; u < K + N + K; ++u) { for (int k = 0; k < K; ++k) ans[u] += f[u][k] * a[k][K]; ans[u] += f[u][K]; } for (int u = K; u < K + N; ++u) { if (u > K) printf(" "); printf("%u", ans[u].x); } puts(""); } #ifndef LOCAL break; #endif } return 0; }