#pragma GCC target("avx2") #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #include #include #include using namespace std; using namespace atcoder; #define rep(i, n) for(int i=0;i BerlekampMassey(const vector &s) { const int N = (int)s.size(); vector b, c; b.reserve(N + 1); c.reserve(N + 1); b.push_back(mint(1)); c.push_back(mint(1)); mint y = mint(1); for (int ed = 1; ed <= N; ed++) { int l = int(c.size()), m = int(b.size()); mint x = 0; for (int i = 0; i < l; i++) x += c[i] * s[ed - l + i]; b.emplace_back(mint(0)); m++; if (x == mint(0)) continue; mint freq = x / y; if (l < m) { auto tmp = c; c.insert(begin(c), m - l, mint(0)); for (int i = 0; i < m; i++) c[m - 1 - i] -= freq * b[m - 1 - i]; b = tmp; y = x; } else { for (int i = 0; i < m; i++) c[l - 1 - i] -= freq * b[m - 1 - i]; } } reverse(begin(c), end(c)); return c; } template T BostanMori(std::vector Q, std::vector P, long long N) { const int d = Q.size(); for (; N; N >>= 1) { auto Q_neg = Q; for (size_t i = 1; i < Q.size(); i += 2) Q_neg[i] *= -1; P = convolution(P, Q_neg); Q = convolution(Q, Q_neg); for (size_t i = N & 1; i < P.size(); i += 2) P[i >> 1] = P[i]; for (size_t i = 0; i < Q.size(); i += 2) Q[i >> 1] = Q[i]; P.resize(d - 1); Q.resize(d); } return P[0]; } using ll = long long; int main() { ll n, m, k; cin >> n >> m >> k; ll N = 10000; vector v(N); v[0] = 1; v[1] = m; vector dp(m + 1, 0); for(ll i = 1; i <= m; i ++) dp[m / i] ++; for(int i = 2; i < N; i ++) { rep(j, m) dp[j + 1] += dp[j]; vector nx(m + 1, 0); for(ll j = 1; j <= m; j ++) { ll num = m / j; nx[num] += dp[min(m, num + k)] - dp[max(0LL, num - k - 1)]; } swap(nx, dp); rep(j, m + 1) v[i] += dp[j]; } vector a = BerlekampMassey(v); vector b = convolution(v, a); b.resize(a.size() - 1); cout << BostanMori(a, b, n).val() << "\n"; return 0; }