#include using namespace std; template struct ModInt{ long long val; constexpr ModInt(const long long _val = 0) noexcept : val(_val) { normalize(); } void normalize(){ val = (val % Modulus + Modulus) % Modulus; } inline ModInt &operator+=(const ModInt &rhs) noexcept { if(val += rhs.val, val >= Modulus) val -= Modulus; return *this; } inline ModInt &operator-=(const ModInt &rhs) noexcept { if(val -= rhs.val, val < 0) val += Modulus; return *this; } inline ModInt &operator*=(const ModInt &rhs) noexcept { val = val * rhs.val % Modulus; return *this; } inline ModInt &operator/=(const ModInt &rhs) noexcept { val = val * inv(rhs.val).val % Modulus; return *this; } inline ModInt &operator++() noexcept { if(++val >= Modulus) val -= Modulus; return *this; } inline ModInt operator++(int) noexcept { ModInt t = val; if(++val >= Modulus) val -= Modulus; return t; } inline ModInt &operator--() noexcept { if(--val < 0) val += Modulus; return *this; } inline ModInt operator--(int) noexcept { ModInt t = val; if(--val < 0) val += Modulus; return t; } inline ModInt operator-() const noexcept { return (Modulus - val) % Modulus; } inline ModInt inv(void) const { return inv(val); } ModInt pow(long long n){ assert(0 <= n); ModInt x = *this, r = 1; while(n){ if(n & 1) r *= x; x *= x; n >>= 1; } return r; } ModInt inv(const long long n) const { long long a = n, b = Modulus, u = 1, v = 0; while(b){ long long t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v); } u %= Modulus; if(u < 0) u += Modulus; return u; } friend inline ModInt operator+(const ModInt &lhs, const ModInt &rhs) noexcept { return ModInt(lhs) += rhs; } friend inline ModInt operator-(const ModInt &lhs, const ModInt &rhs) noexcept { return ModInt(lhs) -= rhs; } friend inline ModInt operator*(const ModInt &lhs, const ModInt &rhs) noexcept { return ModInt(lhs) *= rhs; } friend inline ModInt operator/(const ModInt &lhs, const ModInt &rhs) noexcept { return ModInt(lhs) /= rhs; } friend inline bool operator==(const ModInt &lhs, const ModInt &rhs) noexcept { return lhs.val == rhs.val; } friend inline bool operator!=(const ModInt &lhs, const ModInt &rhs) noexcept { return lhs.val != rhs.val; } friend inline istream &operator>>(istream &is, ModInt &x) noexcept { is >> x.val; x.normalize(); return is; } friend inline ostream &operator<<(ostream &os, const ModInt &x) noexcept { return os << x.val; } }; template struct Matrix{ int n, m; vector val; Matrix(int _n, int _m) : n(_n), m(_m), val(_n *_m){} Matrix(const vector> &mat){ n = mat.size(); m = mat[0].size(); val.resize(n * m); for(int i = 0; i < n; ++i){ for(int j = 0; j < m; ++j){ val[i * m + j] = mat[i][j]; } } } static Matrix e(int _n){ Matrix res(_n, _n); for(int i = 0; i < _n; ++i){ res[i][i] = T{1}; } return res; } auto operator[](int i){ return val.begin() + i * m; } auto operator[](int i) const { return val.begin() + i * m; } inline Matrix &operator+=(const Matrix &rhs){ for(int i = 0; i < n * m; ++i){ val[i] += rhs[i]; } return *this; } inline Matrix &operator-=(const Matrix &rhs){ for(int i = 0; i < n * m; ++i){ val[i] -= rhs[i]; } return *this; } inline Matrix operator*(const Matrix &rhs){ assert(m == rhs.n); const int l = rhs.m; Matrix res(n, l); for(int i = 0; i < n; ++i){ for(int j = 0; j < m; ++j){ for(int k = 0; k < l; ++k){ res[i][k] += val[i * m + j] * rhs[j][k]; } } } return res; } inline Matrix &operator*=(const Matrix &rhs){ return *this = *this * rhs; } friend inline Matrix operator+(const Matrix &lhs, const Matrix &rhs) noexcept { return Matrix(lhs) += rhs; } friend inline Matrix operator-(const Matrix &lhs, const Matrix &rhs) noexcept { return Matrix(lhs) -= rhs; } friend inline bool operator==(const Matrix &lhs, const Matrix &rhs) noexcept { return lhs.val == rhs.val; } friend inline bool operator!=(const Matrix &lhs, const Matrix &rhs) noexcept { return lhs.val != rhs.val; } friend inline ostream &operator<<(ostream &os, const Matrix &mat) noexcept { const int _n = mat.n; const int _m = mat.m; for(int i = 0; i < _n; ++i){ for(int j = 0; j < _m; ++j){ os << mat[i][j] << " \n"[j == _m - 1]; } } return os; } Matrix inv() const { Matrix a = *this, b = e(n); for(int i = 0; i < n; ++i){ if(a[i][i] == 0){ for(int j = i + 1; j < n; ++j){ if(a[j][i] != 0){ for(int k = i; k < n; ++k) swap(a[i][k], a[j][k]); for(int k = 0; k < n; ++k) swap(b[i][k], b[j][k]); break; } } } if(a[i][i] == 0) throw "Inverse does not exist."; const T x = T{1} / a[i][i]; for(int k = i; k < n; ++k) a[i][k] *= x; for(int k = 0; k < n; ++k) b[i][k] *= x; for(int j = 0; j < n; ++j){ if(i != j){ const T x = a[j][i]; for(int k = i; k < n; ++k) a[j][k] -= a[i][k] * x; for(int k = 0; k < n; ++k) b[j][k] -= b[i][k] * x; } } } return b; } Matrix pow(long long r) const { if(r == 0) return e(n); if(r < 0) return inv().pow(-r); Matrix res = e(n), a = *this; while(r > 0){ if(r & 1) res *= a; a *= a; r >>= 1; } return res; } Matrix pow2(string &r) const { if(r == "0") return e(n); Matrix res = e(n), a = *this; int siz = r.size(); for(int i = siz - 1; i >= 0; i--){ if(r[i] == '1') res *= a; a *= a; } return res; } T det() const { Matrix a = *this; T res = 1; for(int i = 0; i < n; ++i){ if(a[i][i] == 0){ for(int j = i + 1; j < n; ++j){ if(a[j][i] != 0){ for(int k = i; k < n; ++k){ swap(a[i][k], a[j][k]); } res = -res; break; } } } if(a[i][i] == 0) return 0; res *= a[i][i]; const T x = T{1} / a[i][i]; for(int k = i; k < n; ++k){ a[i][k] *= x; } for(int j = i + 1; j < n; ++j){ const T x = a[j][i]; for(int k = i; k < n; ++k){ a[j][k] -= a[i][k] * x; } } } return res; } Matrix transpose() const { Matrix res(m, n), a = *this; for(int i = 0; i < n; ++i){ for(int j = 0; j < m; ++j){ res[j][i] = a[i][j]; } } return res; } Matrix gauss() const { Matrix a = *this; int r = 0; for(int i = 0; i < m; ++i){ int pivot = -1; for(int j = r; j < n; ++j){ if(a[j][i] != 0){ pivot = j; break; } } if(pivot == -1) continue; for(int j = 0; j < m; ++j){ swap(a[pivot][j], a[r][j]); } const T s = a[r][i]; for(int j = i; j < m; ++j){ a[r][j] /= s; } for(int j = 0; j < n; ++j){ if(j == r) continue; const T s = a[j][i]; if(s == 0) continue; for(int k = i; k < m; ++k){ a[j][k] -= a[r][k] * s; } } ++r; } return a; } int rank(bool is_gaussed = false) const { Matrix a = *this; if(!is_gaussed){ return (n >= m ? a : a.transpose()).gauss().rank(true); } int r = 0; for(int i = 0; i < n; ++i){ while(r < m && a[i][r] == 0) ++r; if(r == m){ return i; } ++r; } return n; } // Rotate 90 degrees clockwise Matrix rotate() const { Matrix res(m, n), a = *this; for(int i = 0; i < m; ++i){ for(int j = 0; j < n; ++j){ res[i][j] = a[n - j - 1][i]; } } return res; } }; template struct compress{ vector sorted; vector compressed; compress(const vector &vec){ int n = vec.size(); compressed.resize(n); for(T x : vec){ sorted.emplace_back(x); } sort(sorted.begin(), sorted.end()); sorted.erase(unique(sorted.begin(), sorted.end()), sorted.end()); for(int i = 0; i < n; ++i){ compressed[i] = lower_bound(sorted.begin(), sorted.end(), vec[i]) - sorted.begin(); } } int get(const T &x) const{ return lower_bound(sorted.begin(), sorted.end(), x) - sorted.begin(); } T inv(const int x) const{ return sorted[x]; } size_t size() const{ return sorted.size(); } vector getCompressed() const{ return compressed; } }; using mint = ModInt<998244353>; int main(){ ios::sync_with_stdio(false); cin.tie(nullptr); long long n; int m, k; cin >> n >> m >> k; vector q; for(int i = 1; i <= m; i++){ q.push_back(m / i); } compress comp(q); int siz = comp.size(); Matrix dp(siz, siz), mat(1, siz); for(int i = 0; i < siz; i++){ for(int j = 1; j <= m; j++){ if(abs(m / j - comp.inv(i)) <= k){ dp[i][comp.get(m / j)]++; } } } for(int i = 1; i <= m; i++){ mat[0][comp.get(m / i)] += 1; } dp = dp.pow(n - 1); mat *= dp; mint ans = 0; for(int i = 0; i < siz; i++){ ans += mat[0][i]; } cout << ans << "\n"; }