#line 1 "main.cpp" //#pragma GCC target("avx") //#pragma GCC optimize("O3") //#pragma GCC optimize("unroll-loops") #include #ifdef LOCAL #include #define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__) #else #define debug(...) (static_cast(0)) #endif using namespace std; using ll = long long; using ld = long double; using pll = pair; using pii = pair; using vi = vector; using vvi = vector; using vvvi = vector; using vl = vector; using vvl = vector; using vvvl = vector; using vpii = vector; using vpll = vector; using vs = vector; template using pq = priority_queue, greater>; #define overload4(_1, _2, _3, _4, name, ...) name #define overload3(a,b,c,name,...) name #define rep1(n) for (ll UNUSED_NUMBER = 0; UNUSED_NUMBER < (n); ++UNUSED_NUMBER) #define rep2(i, n) for (ll i = 0; i < (n); ++i) #define rep3(i, a, b) for (ll i = (a); i < (b); ++i) #define rep4(i, a, b, c) for (ll i = (a); i < (b); i += (c)) #define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__) #define rrep1(n) for(ll i = (n) - 1;i >= 0;i--) #define rrep2(i,n) for(ll i = (n) - 1;i >= 0;i--) #define rrep3(i,a,b) for(ll i = (b) - 1;i >= (a);i--) #define rrep4(i,a,b,c) for(ll i = (a) + ((b)-(a)-1) / (c) * (c);i >= (a);i -= c) #define rrep(...) overload4(__VA_ARGS__, rrep4, rrep3, rrep2, rrep1)(__VA_ARGS__) #define all1(i) begin(i) , end(i) #define all2(i,a) begin(i) , begin(i) + a #define all3(i,a,b) begin(i) + a , begin(i) + b #define all(...) overload3(__VA_ARGS__, all3, all2, all1)(__VA_ARGS__) #define sum(...) accumulate(all(__VA_ARGS__),0LL) template bool chmin(T &a, const T &b){ if(a > b){ a = b; return 1; } else return 0; } template bool chmax(T &a, const T &b){ if(a < b){ a = b; return 1; } else return 0; } template auto min(const T& a){ return *min_element(all(a)); } template auto max(const T& a){ return *max_element(all(a)); } template void in(Ts&... t); #define INT(...) int __VA_ARGS__; in(__VA_ARGS__) #define LL(...) ll __VA_ARGS__; in(__VA_ARGS__) #define STR(...) string __VA_ARGS__; in(__VA_ARGS__) #define CHR(...) char __VA_ARGS__; in(__VA_ARGS__) #define DBL(...) double __VA_ARGS__; in(__VA_ARGS__) #define LD(...) ld __VA_ARGS__; in(__VA_ARGS__) #define VEC(type, name, size) vector name(size); in(name) #define VV(type, name, h, w) vector> name(h, vector(w)); in(name) ll intpow(ll a, ll b){ ll ans = 1; while(b){if(b & 1) ans *= a; a *= a; b /= 2;} return ans;} ll modpow(ll a, ll b, ll p){ ll ans = 1; a %= p;if(a < 0) a += p;while(b){ if(b & 1) (ans *= a) %= p; (a *= a) %= p; b /= 2; } return ans; } ll GCD(ll a,ll b) { if(a == 0 || b == 0) return 0; if(a % b == 0) return b; else return GCD(b,a%b);} ll LCM(ll a,ll b) { if(a == 0) return b; if(b == 0) return a;return a / GCD(a,b) * b;} namespace IO{ #define VOID(a) decltype(void(a)) struct setting{ setting(){cin.tie(nullptr); ios::sync_with_stdio(false);fixed(cout); cout.precision(12);}} setting; template struct P : P{}; template<> struct P<0>{}; template void i(T& t){ i(t, P<3>{}); } void i(vector::reference t, P<3>){ int a; i(a); t = a; } template auto i(T& t, P<2>) -> VOID(cin >> t){ cin >> t; } template auto i(T& t, P<1>) -> VOID(begin(t)){ for(auto&& x : t) i(x); } template void ituple(T& t, index_sequence){ in(get(t)...);} template auto i(T& t, P<0>) -> VOID(tuple_size{}){ ituple(t, make_index_sequence::value>{});} #undef VOID } #define unpack(a) (void)initializer_list{(a, 0)...} template void in(Ts&... t){ unpack(IO :: i(t)); } #undef unpack static const double PI = 3.1415926535897932; template struct REC { F f; REC(F &&f_) : f(forward(f_)) {} template auto operator()(Args &&...args) const { return f(*this, forward(args)...); }}; //constexpr int mod = 1000000007; constexpr int mod = 998244353; #line 2 "library/modint/Modint.hpp" template struct Modint{ int x; Modint():x(0) {} Modint(long long y): x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {} Modint &operator += (const Modint &p) { if((x += p.x) >= mod) x -= mod; return *this;} Modint &operator -= (const Modint &p) { if ((x += mod - p.x) >= mod) x -= mod; return *this;} Modint &operator *= (const Modint &p) { x = (int)(1LL * x * p.x % mod); return *this;} Modint &operator /= (const Modint &p) { *this *= p.inverse(); return *this;} Modint operator -() const{return Modint(-x);} Modint operator +(const Modint &p) const {return Modint(*this) += p;} Modint operator -(const Modint &p) const {return Modint(*this) -= p;} Modint operator *(const Modint &p) const {return Modint(*this) *= p;} Modint operator /(const Modint &p) const {return Modint(*this) /= p;} Modint &operator ++() {if(x == mod - 1) x = 0; else x++; return *this;} Modint &operator --() {if(x == 0) x = mod - 1; else x--; return *this;} bool operator == (const Modint &p) const {return x == p.x;} bool operator != (const Modint &p) const {return x != p.x;} Modint inverse() const { int a = x, b = mod, u = 1, v = 0, t; while (b > 0) { t = a / b; swap(a -= t * b, b); swap(u -= t * v, v); } return Modint(u);} Modint pow(long long n) const { Modint ret(1), mul(x); while (n > 0) { if (n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret;} friend ostream &operator<<(ostream &os, const Modint &p) { return os << p.x; } friend istream &operator>>(istream &is, Modint &a) { long long t; is >> t; a = Modint(t); return (is); } static constexpr int get_mod() {return mod;} }; #line 87 "main.cpp" using mint = Modint; using vm = vector; using vvm = vector; using vvvm = vector; vector fact, fact_inv; void make_fact(int n){ fact.resize(n+1), fact_inv.resize(n+1); fact[0] = mint(1); rep(i,1,n+1) fact[i] = fact[i-1] * mint(i); fact_inv[n] = fact[n].inverse(); rrep(i,0,n) fact_inv[i] = fact_inv[i+1] * mint(i+1); } mint ncr(int n, int r){ if(n < 0 || r < 0 || n < r) return mint(0); return fact[n] * fact_inv[r] * fact_inv[n-r];} mint npr(int n, int r){ if(n < 0 || r < 0 || n < r) return mint(0); return fact[n] * fact_inv[n-r]; } #line 2 "library/ntt/ntt.hpp" template struct NTT{ static constexpr uint32_t get_pr() { uint32_t _mod = mint::get_mod(); using u64 = uint64_t; u64 ds[32] = {}; int idx = 0; u64 m = _mod - 1; for(u64 i = 2;i * i <= m; ++i) { if(m % i == 0) { ds[idx++] = i; while(m % i == 0) m /= i; } } if (m != 1) ds[idx++] = m; uint32_t _pr = 2; while(1) { int flg = 1; for(int i = 0;i < idx; ++i) { u64 a = _pr, b = (_mod - 1) / ds[i],r = 1; while(b) { if(b & 1) r = r * a % _mod; a = a * a % _mod; b >>= 1; } if(r == 1) { flg = 0; break; } } if (flg == 1) break; ++_pr; } return _pr; }; static constexpr uint32_t mod = mint::get_mod(); static constexpr uint32_t pr = get_pr(); static constexpr int level = __builtin_ctzll(mod - 1); mint dw[level], dy[level]; void setwy(int k) { mint w[level],y[level]; w[k - 1] = mint(pr).pow((mod - 1) / (1 << k)); y[k - 1] = w[k - 1].inverse(); for(int i = k - 2;i > 0; --i) w[i] = w[i+1] * w[i+1],y[i] = y[i+1] * y[i+1]; dw[1] = w[1], dy[1] = y[1], dw[2] = w[2], dy[2] = y[2]; for(int i = 3;i < k;++i) { dw[i] = dw[i-1] * y[i-2] * w[i]; dy[i] = dy[i-1] * w[i-2] * y[i]; } } NTT() {setwy(level);} void fft4(vector &a,int k) { if((int)a.size() <= 1) return; if(k == 1) { mint a1 = a[1]; a[1] = a[0] - a[1]; a[0] = a[0] + a1; return; } if (k & 1) { int v = 1 << (k - 1); for(int j = 0;j < v; ++j) { mint ajv = a[j + v]; a[j + v] = a[j] - ajv; a[j] += ajv; } } int u = 1 << (2 + (k & 1)); int v = 1 << (k - 2 - (k & 1)); mint one = mint(1); mint imag = dw[1]; while(v) { { int j0 = 0,j1 = v; int j2 = j1 + v; int j3 = j2 + v; for(;j0 < v; ++j0,++j1,++j2,++j3) { mint t0 = a[j0], t1 = a[j1],t2 = a[j2],t3 = a[j3]; mint t0p2 = t0 + t2,t1p3 = t1 + t3; mint t0m2 = t0 - t2,t1m3 = (t1 - t3) * imag; a[j0] = t0p2 + t1p3, a[j1] = t0p2 - t1p3; a[j2] = t0m2 + t1m3, a[j3] = t0m2 - t1m3; } } mint ww = one,xx = one * dw[2],wx = one; for(int jh = 4;jh < u;) { ww = xx * xx,wx = ww * xx; int j0 = jh * v; int je = j0 + v; int j2 = je + v; for(;j0 < je;++j0,++j2) { mint t0 = a[j0], t1 = a[j0 + v] * xx, t2 = a[j2] * ww,t3 = a[j2 + v] * wx; mint t0p2 = t0 + t2,t1p3 = t1 + t3; mint t0m2 = t0 - t2,t1m3 = (t1 - t3) * imag; a[j0] = t0p2 + t1p3, a[j0 + v] = t0p2 - t1p3; a[j2] = t0m2 + t1m3, a[j2 + v] = t0m2 - t1m3; } xx *= dw[__builtin_ctzll((jh += 4))]; } u <<= 2; v >>= 2; } } void ifft4(vector &a,int k) { if((int)a.size() <= 1) return; if(k == 1) { mint a1 = a[1]; a[1] = a[0] - a[1]; a[0] = a[0] + a1; return; } int u = 1 << (k - 2); int v = 1; mint one = mint(1); mint imag = dy[1]; while(u) { { int j0 = 0,j1 = v; int j2 = j1 + v; int j3 = j2 + v; for(;j0 < v;++j0,++j1,++j2,++j3) { mint t0 = a[j0],t1 = a[j1],t2 = a[j2],t3 = a[j3]; mint t0p1 = t0 + t1, t2p3 = t2 + t3; mint t0m1 = t0 - t1, t2m3 = (t2 - t3) * imag; a[j0] = t0p1 + t2p3, a[j2] = t0p1 - t2p3; a[j1] = t0m1 + t2m3, a[j3] = t0m1 - t2m3; } } mint ww = one,xx = one * dy[2],yy = one; u <<= 2; for(int jh = 4;jh < u;) { ww = xx * xx,yy = xx * imag; int j0 = jh * v; int je = j0 + v; int j2 = je + v; for(;j0 < je;++j0,++j2) { mint t0 = a[j0], t1 = a[j0 + v], t2 = a[j2], t3 = a[j2 + v]; mint t0p1 = t0 + t1, t2p3 = t2 + t3; mint t0m1 = (t0 - t1) * xx, t2m3 = (t2 - t3) * yy; a[j0] = t0p1 + t2p3, a[j2] = (t0p1 - t2p3) * ww; a[j0 + v] = t0m1 + t2m3, a[j2 + v] = (t0m1 - t2m3) * ww; } xx *= dy[__builtin_ctzll(jh += 4)]; } u >>= 4; v <<= 2; } if(k & 1) { u = 1 << (k - 1); for(int j = 0;j < u;++j) { mint ajv = a[j] - a[j+u]; a[j] += a[j+u]; a[j+u] = ajv; } } } void ntt(vector &a) { if((int)a.size() <= 1) return; fft4(a,__builtin_ctz(a.size())); } void intt(vector &a) { if((int)a.size() <= 1) return; ifft4(a,__builtin_ctz(a.size())); mint iv = mint(a.size()).inverse(); for(auto &x:a) x *= iv; } vector multiply(const vector &a,const vector &b) { int l = a.size() + b.size() - 1; if(min(a.size(),b.size()) <= 40) { vector s(l); for(int i = 0;i < (int)a.size();++i) for(int j = 0;j < (int)b.size();++j) s[i+j] += a[i] * b[j]; return s; } int k = 2, M = 4; while(M < l) M <<= 1, ++k; //setwy(k); vector s(M), t(M); for(int i = 0;i < (int)a.size();++i) s[i] = a[i]; for(int i = 0;i < (int)b.size();++i) t[i] = b[i]; fft4(s,k); fft4(t,k); for(int i = 0;i < M;++i) s[i] *= t[i]; ifft4(s,k); s.resize(l); mint invm = mint(M).inverse(); for(int i = 0;i < l;++i) s[i] *= invm; return s; } void ntt_doubling(vector &a) { int M = (int)a.size(); auto b = a; intt(b); mint r = 1, zeta = mint(pr).pow((mint::get_mod() - 1) / (M << 1)); for(int i = 0;i < M;++i) b[i] *= r,r *= zeta; ntt(b); copy(begin(b),end(b),back_inserter(a)); } }; #line 100 "main.cpp" int main() { NTT ntt; INT(h,w); make_fact(h + w + 100); vm dp1(h+1); rep(i,1,h+1) { if(h >= i && 2 * i >= h) { int a = 2 * i - h; int b = h - i; dp1[i] = ncr(a+b,b) * fact_inv[i]; } } vm dp2(w+1); rep(i,1,w+1) { if(w >= i && 2 * i >= w) { int a = 2 * i - w; int b = w - i; dp2[i] = ncr(a+b,b) * fact_inv[i]; } } auto ret = ntt.multiply(dp1,dp2); mint ans; rep(i,ret.size()) ans += ret[i] * fact[i]; cout << ans << '\n'; }