#include using namespace std; #ifdef LOCAL #include #else #define debug(...) 42 #endif template T inverse(T a, T m) { T u = 0, v = 1; while (a != 0) { T t = m / a; m -= t * a; swap(a, m); u -= t * v; swap(u, v); } assert(m == 1); return u; } template class Modular { public: using Type = typename decay::type; constexpr Modular() : value() {} template Modular(const U& x) { value = normalize(x); } template static Type normalize(const U& x) { Type v; if (-mod() <= x && x < mod()) v = static_cast(x); else v = static_cast(x % mod()); if (v < 0) v += mod(); return v; } const Type& operator()() const { return value; } template explicit operator U() const { return static_cast(value); } constexpr static Type mod() { return T::value; } Modular& operator+=(const Modular& other) { if ((value += other.value) >= mod()) value -= mod(); return *this; } Modular& operator-=(const Modular& other) { if ((value -= other.value) < 0) value += mod(); return *this; } template Modular& operator+=(const U& other) { return *this += Modular(other); } template Modular& operator-=(const U& other) { return *this -= Modular(other); } Modular& operator++() { return *this += 1; } Modular& operator--() { return *this -= 1; } Modular operator++(int) { Modular result(*this); *this += 1; return result; } Modular operator--(int) { Modular result(*this); *this -= 1; return result; } Modular operator-() const { return Modular(-value); } template typename enable_if::Type, int>::value, Modular>::type& operator*=(const Modular& rhs) { #ifdef _WIN32 uint64_t x = static_cast(value) * static_cast(rhs.value); uint32_t xh = static_cast(x >> 32), xl = static_cast(x), d, m; asm( "divl %4; \n\t" : "=a" (d), "=d" (m) : "d" (xh), "a" (xl), "r" (mod()) ); value = m; #else value = normalize(static_cast(value) * static_cast(rhs.value)); #endif return *this; } template typename enable_if::Type, long long>::value, Modular>::type& operator*=(const Modular& rhs) { long long q = static_cast(static_cast(value) * rhs.value / mod()); value = normalize(value * rhs.value - q * mod()); return *this; } template typename enable_if::Type>::value, Modular>::type& operator*=(const Modular& rhs) { value = normalize(value * rhs.value); return *this; } Modular& operator/=(const Modular& other) { return *this *= Modular(inverse(other.value, mod())); } friend const Type& abs(const Modular& x) { return x.value; } template friend bool operator==(const Modular& lhs, const Modular& rhs); template friend bool operator<(const Modular& lhs, const Modular& rhs); template friend V& operator>>(V& stream, Modular& number); private: Type value; }; template bool operator==(const Modular& lhs, const Modular& rhs) { return lhs.value == rhs.value; } template bool operator==(const Modular& lhs, U rhs) { return lhs == Modular(rhs); } template bool operator==(U lhs, const Modular& rhs) { return Modular(lhs) == rhs; } template bool operator!=(const Modular& lhs, const Modular& rhs) { return !(lhs == rhs); } template bool operator!=(const Modular& lhs, U rhs) { return !(lhs == rhs); } template bool operator!=(U lhs, const Modular& rhs) { return !(lhs == rhs); } template bool operator<(const Modular& lhs, const Modular& rhs) { return lhs.value < rhs.value; } template Modular operator+(const Modular& lhs, const Modular& rhs) { return Modular(lhs) += rhs; } template Modular operator+(const Modular& lhs, U rhs) { return Modular(lhs) += rhs; } template Modular operator+(U lhs, const Modular& rhs) { return Modular(lhs) += rhs; } template Modular operator-(const Modular& lhs, const Modular& rhs) { return Modular(lhs) -= rhs; } template Modular operator-(const Modular& lhs, U rhs) { return Modular(lhs) -= rhs; } template Modular operator-(U lhs, const Modular& rhs) { return Modular(lhs) -= rhs; } template Modular operator*(const Modular& lhs, const Modular& rhs) { return Modular(lhs) *= rhs; } template Modular operator*(const Modular& lhs, U rhs) { return Modular(lhs) *= rhs; } template Modular operator*(U lhs, const Modular& rhs) { return Modular(lhs) *= rhs; } template Modular operator/(const Modular& lhs, const Modular& rhs) { return Modular(lhs) /= rhs; } template Modular operator/(const Modular& lhs, U rhs) { return Modular(lhs) /= rhs; } template Modular operator/(U lhs, const Modular& rhs) { return Modular(lhs) /= rhs; } template Modular power(const Modular& a, const U& b) { assert(b >= 0); Modular x = a, res = 1; U p = b; while (p > 0) { if (p & 1) res *= x; x *= x; p >>= 1; } return res; } template bool IsZero(const Modular& number) { return number() == 0; } template string to_string(const Modular& number) { return to_string(number()); } // U == std::ostream? but done this way because of fastoutput template U& operator<<(U& stream, const Modular& number) { return stream << number(); } // U == std::istream? but done this way because of fastinput template U& operator>>(U& stream, Modular& number) { typename common_type::Type, long long>::type x; stream >> x; number.value = Modular::normalize(x); return stream; } /* using ModType = int; struct VarMod { static ModType value; }; ModType VarMod::value; ModType& md = VarMod::value; using Mint = Modular; */ constexpr int md = 998244353; using Mint = Modular::type, md>>; vector fact(1, 1); vector inv_fact(1, 1); Mint C(int n, int k) { if (k < 0 || k > n) { return 0; } while ((int) fact.size() < n + 1) { fact.push_back(fact.back() * (int) fact.size()); inv_fact.push_back(1 / fact.back()); } return fact[n] * inv_fact[k] * inv_fact[n - k]; } int main() { ios_base::sync_with_stdio(false); cin.tie(0); int n, b, w; cin >> n >> b >> w; int t = n - b - w; if (t < 0) { cout << 0 << '\n'; return 0; } Mint ans = 0; // first B = 1st, last B < N // 0x + 1y + 2z = t - 1 // x + y + z = b - 1 // t + b <= n - 1 // ... // x - z = b - t // x = b - t + z debug(t); if (true || t - 1 + b <= n - 1) { for (int z = 0; z <= n; z++) { int x = b - t + z; if (x < 0) { continue; } int y = b - 1 - x - z; if (y < 0 || y != t - 1 - 2 * z) { continue; } debug(x, y, z); // C(w + z, z) ans += (w == 0 ? 1 : C(w + z, z)) * C(b - 1, x) * C(b - 1 - x, y); } } // first B = 1st, last B = N // 0x + 1y + 2z = t // x + y + z = b - 1 // b - 1 spaces // add condition? if (true || t + b <= n) { for (int z = 0; z <= n; z++) { int x = b - 1 - t + z; if (x < 0) { continue; } int y = b - 1 - x - z; if (y < 0 || y != t - 2 * z) { continue; } debug(x, y, z); ans += (w == 0 ? 1 : C(w + z - 1, z - 1)) * C(b - 1, x) * C(b - 1 - x, y); } } // first B > 1st, last B < N // 0x + 1y + 2z = t - 2 // x + y + z = b - 1 // 1 + (t - 2) + b <= n - 1 // x - z = b - 1 - (t - 2) // x - z = b - t + 1 // add condition? if (true || t - 2 + b <= n - 2) { for (int z = 0; z <= n; z++) { int x = b - t + 1 + z; if (x < 0) { continue; } int y = b - 1 - x - z; if (y < 0 || y != t - 2 - 2 * z) { continue; } debug(x, y, z); ans += (w == 0 ? 1 : C(w + z + 1, z + 1)) * C(b - 1, x) * C(b - 1 - x, y); } } // first B > 1st, last B = N // 0x + 1y + 2z = t - 1 // x + y + z = b - 1 // 1 + t - 1 + b <= n // x - z = b - 1 - (t - 1) // x - z = b - t if (true || 1 + t - 1 + b <= n) { for (int z = 0; z <= n; z++) { int x = b - t + z; if (x < 0) { continue; } int y = b - 1 - x - z; if (y < 0 || y != t - 1 - 2 * z) { continue; } debug(x, y, z); ans += (w == 0 ? 1 : C(w + z, z)) * C(b - 1, x) * C(b - 1 - x, y); } } cout << ans << '\n'; return 0; }