#define LOCAL #include using namespace std; #pragma region Macros typedef long long ll; typedef __int128_t i128; typedef unsigned int uint; typedef unsigned long long ull; #define ALL(x) (x).begin(), (x).end() template istream& operator>>(istream& is, vector& v) { for (T& x : v) is >> x; return is; } template ostream& operator<<(ostream& os, const vector& v) { for (size_t i = 0; i < v.size(); i++) { os << v[i] << (i + 1 == v.size() ? "" : " "); } return os; } template ostream& operator<<(ostream& os, const pair& p) { os << '(' << p.first << ',' << p.second << ')'; return os; } template ostream& operator<<(ostream& os, const map& m) { os << '{'; for (auto itr = m.begin(); itr != m.end();) { os << '(' << itr->first << ',' << itr->second << ')'; if (++itr != m.end()) os << ','; } os << '}'; return os; } template ostream& operator<<(ostream& os, const unordered_map& m) { os << '{'; for (auto itr = m.begin(); itr != m.end();) { os << '(' << itr->first << ',' << itr->second << ')'; if (++itr != m.end()) os << ','; } os << '}'; return os; } template ostream& operator<<(ostream& os, const set& s) { os << '{'; for (auto itr = s.begin(); itr != s.end();) { os << *itr; if (++itr != s.end()) os << ','; } os << '}'; return os; } template ostream& operator<<(ostream& os, const multiset& s) { os << '{'; for (auto itr = s.begin(); itr != s.end();) { os << *itr; if (++itr != s.end()) os << ','; } os << '}'; return os; } template ostream& operator<<(ostream& os, const unordered_set& s) { os << '{'; for (auto itr = s.begin(); itr != s.end();) { os << *itr; if (++itr != s.end()) os << ','; } os << '}'; return os; } template ostream& operator<<(ostream& os, const deque& v) { for (size_t i = 0; i < v.size(); i++) { os << v[i] << (i + 1 == v.size() ? "" : " "); } return os; } template ostream& operator<<(ostream& os, const array& v) { for (size_t i = 0; i < N; i++) { os << v[i] << (i + 1 == N ? "" : " "); } return os; } template void print_tuple(ostream&, const T&) {} template void print_tuple(ostream& os, const T& t) { if (i) os << ','; os << get(t); print_tuple(os, t); } template ostream& operator<<(ostream& os, const tuple& t) { os << '{'; print_tuple<0, tuple, Args...>(os, t); return os << '}'; } void debug_out() { cerr << '\n'; } template void debug_out(Head&& head, Tail&&... tail) { cerr << head; if (sizeof...(Tail) > 0) cerr << ", "; debug_out(move(tail)...); } #ifdef LOCAL #define debug(...) \ cerr << " "; \ cerr << #__VA_ARGS__ << " :[" << __LINE__ << ":" << __FUNCTION__ << "]" << '\n'; \ cerr << " "; \ debug_out(__VA_ARGS__) #else #define debug(...) void(0) #endif template T gcd(T x, T y) { return y != 0 ? gcd(y, x % y) : x; } template T lcm(T x, T y) { return x / gcd(x, y) * y; } int topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); } int topbit(long long t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); } int botbit(signed a) { return a == 0 ? 32 : __builtin_ctz(a); } int botbit(long long a) { return a == 0 ? 64 : __builtin_ctzll(a); } int popcount(signed t) { return __builtin_popcount(t); } int popcount(long long t) { return __builtin_popcountll(t); } bool ispow2(int i) { return i && (i & -i) == i; } long long MSK(int n) { return (1LL << n) - 1; } template T ceil(T x, T y) { assert(y >= 1); return (x > 0 ? (x + y - 1) / y : x / y); } template T floor(T x, T y) { assert(y >= 1); return (x > 0 ? x / y : (x - y + 1) / y); } template inline bool chmin(T1& a, T2 b) { if (a > b) { a = b; return true; } return false; } template inline bool chmax(T1& a, T2 b) { if (a < b) { a = b; return true; } return false; } template void mkuni(vector& v) { sort(v.begin(), v.end()); v.erase(unique(v.begin(), v.end()), v.end()); } template int lwb(const vector& v, const T& x) { return lower_bound(v.begin(), v.end(), x) - v.begin(); } #pragma endregion #include #include "atcoder/modint" namespace atcoder { template std::istream& operator>>(std::istream& is, static_modint& x) { int64_t v; x = static_modint{(is >> v, v)}; return is; } template std::ostream& operator<<(std::ostream& os, const static_modint& x) { return os << x.val(); } template std::ostream& operator<<(std::ostream& os, const dynamic_modint& x) { return os << x.val(); } } // namespace atcoder const int INF = 1e9; const long long IINF = 1e18; const int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1}; const char dir[4] = {'D', 'R', 'U', 'L'}; const long long MOD = 1000000007; // const long long MOD = 998244353; using mint = atcoder::modint998244353; const int MAX = 2010; int main() { cin.tie(0); ios::sync_with_stdio(false); int C, X; cin >> C >> X; if (X == 0) { cout << mint(C + 1).inv() << '\n'; return 0; } vector> dp(2, vector(X + 1, 0)), ndp(2, vector(X + 1, 0)); dp[0][0] = 1; for (int k = 1; k < MAX; k++) { mint prob = mint(C + k).inv(); for (int i = 0; i < 2; i++) { for (int j = 0; j <= X; j++) { mint& val = dp[i][j]; if (val == 0) continue; ndp[i][j] += val * prob * (j + max(0, C + k - 1 - X)); if (X <= C + k - 1) ndp[1][j] += val * prob; if (j + 1 < X or (i == 1 and j + 1 <= X)) ndp[i][j + 1] += val * prob * (min(X, C + k) - j); val = 0; } } swap(dp, ndp); } mint ans = 0; for (int i = 0; i < 2; i++) { for (int j = 0; j <= X; j++) { mint& val = dp[i][j]; if (val == 0) continue; if (i == 1) ans += val; else ans += val * (X - j) / (X + 1 - j); } } cout << ans << '\n'; return 0; }