#include #include #include using namespace std; using namespace atcoder; using mint = modint998244353; // in : DFT(v) (len(v) = z) // out : DFT(v) (len(v) = 2 * z) template void FPS_twice(std::vector &v){ int z = v.size(); T e = (T(atcoder::internal::primitive_root_constexpr(T::mod()))).pow(T::mod() / (2 * z)); auto cp = v; atcoder::internal::butterfly_inv(cp); T tmp = (T)(1) / (T)(z); for (int i = 0; i < z; i++){ cp[i] *= tmp; tmp *= e; } atcoder::internal::butterfly(cp); for (int i = 0; i < z; i++) v.push_back(cp[i]); }; // s.t |v| = 2 ^ s (no assert) template void FPS_pick_even_odd(std::vector &v, int odd){ int z = v.size() / 2; T half = (T)(1) / (T)(2); if (odd == 0){ for (int i = 0; i < z; i++){ v[i] = (v[i * 2] + v[i * 2 + 1]) * half; } v.resize(z); } else { T e = (T(atcoder::internal::primitive_root_constexpr(T::mod()))).pow(T::mod() / (2 * z)); T ie = T(1) / e; std::vector es = {half}; while ((int)es.size() != z){ std::vector n_es((int)es.size() * 2); for (int i = 0; i < (int)es.size(); i++){ n_es[i * 2] = (es[i]); n_es[i * 2 + 1] = (es[i] * ie); } ie *= ie; std::swap(n_es, es); } for (int i = 0; i < z; i ++){ v[i] = (v[i * 2] - v[i * 2 + 1]) * es[i]; } v.resize(z); } } int main(){ long long N, B, C; cin >> N >> B >> C; // Binom vector fact(N + 1, 1), fact_inv(N + 1, 1); for (int i = 0; i < N; i++){ fact[i + 1] = fact[i] * (i + 1); } fact_inv[N] = fact[N].inv(); for (int i = N; i > 0; i--){ fact_inv[i - 1] = fact_inv[i] * i; } int z = 8; while (z <= N) z *= 2; vector f(2, vector(z)); for (int i = 0; i <= N; i++){ f[i & 1][i / 2] = fact[N] * fact_inv[i] * fact_inv[N - i]; } internal::butterfly(f[0]); internal::butterfly(f[1]); vector g(z, 1); int k = 0; for (int d = 0; d < 60; d++){ FPS_pick_even_odd(g, 1 & (k + B + C)); FPS_twice(g); for (int i = 0; i < z; i++){ g[i] *= f[C & 1][i]; } k = (k + 1 - (B & 1) + (C & 1)) / 2; B /= 2, C /= 2; } mint ans = 0; for (int i = 0; i < z; i++) ans += g[i]; if (k) ans = 0; else ans /= z; cout << ans.val() << "\n"; }