#include #include #define rep(i, a, b) for (ll i = (ll)(a); i < (ll)(b); i++) using namespace atcoder; using namespace std; typedef long long ll; using mint = modint998244353; template struct Matrix { vector> A; Matrix() {} Matrix(size_t n, size_t m) : A(n, std::vector(m, zero())) {} Matrix(size_t n) : A(n, std::vector(n, zero())) {}; T zero() { return (T(0)); } size_t height() const { return (A.size()); } size_t width() const { return (A[0].size()); } inline const vector &operator[](int k) const { return (A.at(k)); } inline vector &operator[](int k) { return (A.at(k)); } static Matrix I(size_t n) { Matrix mat(n); for (int i = 0; i < n; i++) mat[i][i] = 1; return (mat); } Matrix &operator+=(const Matrix &B) { size_t n = height(), m = width(); assert(n == B.height() && m == B.width()); for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) (*this)[i][j] += B[i][j]; return (*this); } Matrix &operator-=(const Matrix &B) { size_t n = height(), m = width(); assert(n == B.height() && m == B.width()); for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) (*this)[i][j] -= B[i][j]; return (*this); } Matrix &operator*=(const Matrix &B) { size_t n = height(), m = B.width(), p = width(); assert(p == B.height()); vector> C(n, vector(m, zero())); for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) for (int k = 0; k < p; k++) C[i][j] = (C[i][j] + (*this)[i][k] * B[k][j]); A.swap(C); return (*this); } Matrix &operator^=(long long k) { Matrix B = Matrix::I(height()); while (k > 0) { if (k & 1) B *= *this; *this *= *this; k >>= 1LL; } A.swap(B.A); return (*this); } Matrix operator+(const Matrix &B) const { return (Matrix(*this) += B); } Matrix operator-(const Matrix &B) const { return (Matrix(*this) -= B); } Matrix operator*(const Matrix &B) const { return (Matrix(*this) *= B); } Matrix operator^(const long long k) const { return (Matrix(*this) ^= k); } bool operator==(const Matrix &B) const { size_t n = height(), m = width(); if (n != B.height() || m != B.width()) return false; for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) if ((*this)[i][j] != B[i][j]) return false; return true; } friend ostream &operator<<(ostream &os, Matrix &p) { size_t n = p.height(), m = p.width(); for (int i = 0; i < n; i++) { for (int j = 0; j < m; j++) { os << p[i][j] << (j + 1 == m ? "\n" : " "); } } return (os); } T determinant() { // O(n^3) Matrix B(*this); assert(width() == height()); T ret = 1; for (int i = 0; i < width(); i++) { int idx = -1; for (int j = i; j < width(); j++) { if (B[j][i] != 0) idx = j; } if (idx == -1) return (0); if (i != idx) { ret *= -1; swap(B[i], B[idx]); } ret *= B[i][i]; T vv = B[i][i]; for (int j = 0; j < width(); j++) { B[i][j] /= vv; } for (int j = i + 1; j < width(); j++) { T a = B[j][i]; for (int k = 0; k < width(); k++) { B[j][k] -= B[i][k] * a; } } } return (ret); } }; int main() { const int mod = 998244353; int n, m, k; cin >> n >> m >> k; vector ct(m + 1); rep(i, 1, m + 1) { ct[m / i]++; } int len = 0; vector id, idct; rep(i, 0, m + 1) { if (ct[i]) { id.push_back(i); idct.push_back(ct[i]); len++; } } Matrix v(len, len); rep(i, 0, len) rep(j, 0, len) { if (abs(id[i] - id[j]) > k) continue; v[i][j] = idct[i]; } v ^= n - 1; mint ans = 0; rep(i, 0, len) rep(j, 0, len) { ans += v[i][j] * idct[j]; } cout << ans.val() << endl; }