Problem p03622 (C++)

Buggy submission (status: Time Limit Exceeded):
/**
 * code generated by JHelper
 * More info: https://github.com/AlexeyDmitriev/JHelper
 * @author
 */

#ifndef MAJK_LIB
#define MAJK_LIB

#include <algorithm>
#include <bitset>
#include <cassert>
#include <cmath>
#include <fstream>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <unordered_map>
#include <vector>
using namespace std;

#define x first
#define y second
constexpr int MOD = 1000000007;

typedef std::pair<int, int> pii;
typedef long long ll;
typedef unsigned long long ull;
typedef unsigned int ui;

template <typename T, typename U>
std::istream &operator>>(std::istream &i, pair<T, U> &p) {
  i >> p.x >> p.y;
  return i;
}
template <typename T> std::istream &operator>>(std::istream &i, vector<T> &t) {
  for (auto &v : t) {
    i >> v;
  }
  return i;
}
template <typename T>
std::ostream &operator<<(std::ostream &o, const vector<T> &t) {
  for (size_t i = 0; i < t.size(); ++i) {
    o << t[i] << " \n"[i == t.size() - 1];
  }
  return o;
}
template <typename T> using minheap = priority_queue<T, vector<T>, greater<T>>;
template <typename T> using maxheap = priority_queue<T, vector<T>, less<T>>;
auto fraclt = [](const pii &a, const pii &b) {
  return (ll)a.x * b.y < (ll)b.x * a.y;
};
struct cmpfrac {
  bool operator()(const pii &a, const pii &b) const {
    return (ll)a.x * b.y < (ll)b.x * a.y;
  }
};
template <typename T> bool in(T a, T b, T c) { return a <= b && b < c; }
int logceil(ll x) {
  int b = 0;
  while (x) {
    x >>= 1;
    ++b;
  }
  return b;
}

namespace std {
template <typename T, typename U> struct hash<pair<T, U>> {
  hash<T> t;
  hash<U> u;
  size_t operator()(const pair<T, U> &p) const {
    return t(p.x) ^ (u(p.y) << 7);
  }
};
} // namespace std
template <typename T, typename F> T bsh(T l, T h, const F &f) {
  T r = -1, m;
  while (l <= h) {
    m = (l + h) / 2;
    if (f(m)) {
      l = m + 1;
      r = m;
    } else {
      h = m - 1;
    }
  }
  return r;
}
template <typename T, typename F> T bsl(T l, T h, const F &f) {
  T r = -1, m;
  while (l <= h) {
    m = (l + h) / 2;
    if (f(m)) {
      h = m - 1;
      r = m;
    } else {
      l = m + 1;
    }
  }
  return r;
}
template <typename T> T gcd(T a, T b) {
  if (a < b)
    swap(a, b);
  return b ? gcd(b, a % b) : a;
}

template <typename T> class vector2 : public vector<vector<T>> {
public:
  vector2() {}
  vector2(size_t a, size_t b, T t = T())
      : vector<vector<T>>(a, vector<T>(b, t)) {}
};
template <typename T> class vector3 : public vector<vector<vector<T>>> {
public:
  vector3() {}
  vector3(size_t a, size_t b, size_t c, T t = T())
      : vector<vector<vector<T>>>(a, vector<vector<T>>(b, vector<T>(c, t))) {}
};
template <typename T> struct bounded_priority_queue {
  inline bounded_priority_queue(ui X) : A(X), B(0) {}
  inline void push(ui L, T V) {
    B = max(B, L);
    A[L].push(V);
  }
  inline const T &top() const { return A[B].front(); }
  inline void pop() {
    A[B].pop();
    while (B > 0 && A[B].empty())
      --B;
  }
  inline bool empty() const { return A[B].empty(); }
  inline void clear() {
    B = 0;
    for (auto &a : A)
      a = queue<T>();
  }

private:
  vector<queue<T>> A;
  ui B;
};

#endif
#ifndef MOD_H
#define MOD_H

template <unsigned int N> class Field {
  typedef unsigned int ui;
  typedef unsigned long long ull;
  inline ui pow(ui a, ui p) {
    ui r = 1, e = a;
    while (p) {
      if (p & 1) {
        r = ((ull)r * e) % N;
      }
      e = ((ull)e * e) % N;
      p >>= 1;
    }
    return r;
  }
  /*extended GCD(slow):ll t=0,nt=1,r=N,nr=a;while(nr){ll
   * q=r/nr;t-=q*nt;swap(t,nt);r-=q*nr;swap(r,nr);}assert(r<=1);return(t<0)?t+N:t;*/
  inline ui inv(ui a) { return pow(a, N - 2); }

public:
  inline Field(int x = 0) : v(x) {}
  inline Field<N> pow(int p) { return (*this) ^ p; }
  inline Field<N> operator^(int p) { return {(int)pow(v, (ui)p)}; }
  inline Field<N> &operator+=(const Field<N> &o) {
    if ((ll)v + o.v >= N)
      v = (ll)v + o.v - N;
    else
      v = v + o.v;
    return *this;
  }
  inline Field<N> &operator-=(const Field<N> &o) {
    if (v < o.v)
      v = N - o.v + v;
    else
      v = v - o.v;
    return *this;
  }
  inline Field<N> &operator*=(const Field<N> &o) {
    v = (ull)v * o.v % N;
    return *this;
  }
  inline Field<N> &operator/=(const Field<N> &o) { return *this *= inv(o.v); }
  inline Field<N> operator+(const Field<N> &o) const {
    Field<N> r{*this};
    return r += o;
  }
  inline Field<N> operator-(const Field<N> &o) const {
    Field<N> r{*this};
    return r -= o;
  }
  inline Field<N> operator*(const Field<N> &o) const {
    Field<N> r{*this};
    return r *= o;
  }
  inline Field<N> operator/(const Field<N> &o) const {
    Field<N> r{*this};
    return r /= o;
  }
  inline Field<N> operator-() {
    if (v)
      return {(int)(N - v)};
    else
      return {0};
  };
  inline Field<N> &operator++() {
    ++v;
    if (v == N)
      v = 0;
    return *this;
  }
  inline Field<N> operator++(int) {
    Field<N> r{*this};
    ++*this;
    return r;
  }
  inline Field<N> &operator--() {
    --v;
    if (v == -1)
      v = N - 1;
    return *this;
  }
  inline Field<N> operator--(int) {
    Field<N> r{*this};
    --*this;
    return r;
  }
  inline bool operator==(const Field<N> &o) const { return o.v == v; }
  inline bool operator!=(const Field<N> &o) const { return o.v != v; }
  inline explicit operator ui() const { return v; }
  inline static vector<Field<N>> fact(int t) {
    vector<Field<N>> F(t + 1, 1);
    for (int i = 2; i <= t; ++i) {
      F[i] = F[i - 1] * i;
    }
    return F;
  }
  inline static vector<Field<N>> invfact(int t) {
    vector<Field<N>> F(t + 1, 1);
    Field<N> X{1};
    for (int i = 2; i <= t; ++i) {
      X = X * i;
    }
    F[t] = 1 / X;
    for (int i = t - 1; i >= 2; --i) {
      F[i] = F[i + 1] * (i + 1);
    }
    return F;
  }

private:
  ui v;
};
template <unsigned int N> istream &operator>>(std::istream &is, Field<N> &f) {
  unsigned int v;
  is >> v;
  f = v;
  return is;
}
template <unsigned int N>
ostream &operator<<(std::ostream &os, const Field<N> &f) {
  return os << (unsigned int)f;
}
template <unsigned int N> Field<N> operator+(int i, const Field<N> &f) {
  return Field<N>(i) + f;
}
template <unsigned int N> Field<N> operator-(int i, const Field<N> &f) {
  return Field<N>(i) - f;
}
template <unsigned int N> Field<N> operator*(int i, const Field<N> &f) {
  return Field<N>(i) * f;
}
template <unsigned int N> Field<N> operator/(int i, const Field<N> &f) {
  return Field<N>(i) / f;
}

typedef Field<1000000007> FieldMod;

struct Ring {
  static int div(int p, int q, int N) {
    ll t = 0, nt = 1, r = N, nr = q;
    while (nr) {
      ll q = r / nr;
      t -= q * nt;
      r -= q * nr;
      swap(t, nt);
      swap(r, nr);
    }
    t = (t < 0) ? t + N : t;
    r = (r < 0) ? r + N : r;
    if (gcd(p, N) % r) {
      return 0;
    }
    return (int)(((ll)t * (ll)p / r) % N);
  }
};
#endif

#include <array>

template <ui P> struct Group {};
template <> struct Group<4194304001u> {
  constexpr static ui bits = 25, root = 199, rootInverse = 758768563u;
};
template <> struct Group<998244353u> {
  constexpr static ui bits = 23, root = 31, rootInverse = 128805723;
};
template <> struct Group<104857601u> {
  constexpr static ui bits = 22, root = 21, rootInverse = 49932191;
};
template <> struct Group<924844033u> {
  constexpr static ui bits = 21, root = 3597, rootInverse = 508059997;
};

template <ui Prime> class FFT {
public:
  typedef Field<Prime> F;

  FFT() {
    OMEGA[Group<Prime>::bits] = Group<Prime>::root;
    OMEGA_INV[Group<Prime>::bits] = Group<Prime>::rootInverse;
    for (size_t i = Group<Prime>::bits; i > 0; --i) {
      OMEGA[i - 1] = ui((ull(OMEGA[i]) * ull(OMEGA[i])) % Prime);
      OMEGA_INV[i - 1] = ui((ull(OMEGA_INV[i]) * ull(OMEGA_INV[i])) % Prime);

      // cerr << OMEGA[i-1] << ' ' << OMEGA_INV[i-1] << endl;
    }
  }

  void fft(std::vector<F> &V, bool inverse = false) {
    int P = 1;
    while ((1u << P) < V.size())
      ++P;
    V.resize(1u << P);
    fft(V, P, inverse);
  }

  void fft(std::vector<F> &V, const int P, bool inverse = false) {
    if (P == 0)
      return;
    if (P > Group<Prime>::bits)
      throw std::runtime_error("Number of bits in FFT too large");
    if (V.size() != (1 << P))
      throw std::runtime_error("Vector has wrong size");
    for (int i = 1, j = 0; i < (1 << P); ++i) {
      int bit = (1 << (P - 1));
      for (; j >= bit; bit >>= 1)
        j -= bit;
      j += bit;
      if (i < j)
        std::swap(V[i], V[j]);
    }

    for (int B = 1; B <= P; ++B) {
      F omega = inverse ? OMEGA_INV[B] : OMEGA[B];
      for (int i = 0; i < (1 << P); i += (1 << B)) {
        F x = 1;
        for (int j = 0; j < (1 << (B - 1)); j++) {
          F u = V[i + j], v = V[i + j + (1 << (B - 1))] * x;
          V[i + j] = u + v;
          V[i + j + (1 << (B - 1))] = u - v;
          x *= omega;
        }
      }
    }

    if (inverse) {
      F q = 1 / F(1 << P);
      for (F &v : V)
        v *= q;
    }
  }

private:
  std::array<ui, Group<Prime>::bits + 1> OMEGA, OMEGA_INV;
};

template <ui Prime> class SelfConvolve {
  using F = Field<Prime>;

public:
  SelfConvolve(vector<F> &Ans, vector<F> &Coef) : Ans(Ans), Coef(Coef) {
    int size = 1 << logceil(Ans.size());
    Ans.resize(size);
    Coef.resize(size);
    perform(0, size);
  }

private:
  void perform(int pos, int size) {
    if (size <= 128) {
      for (int i = 1; i < size; ++i) {
        for (int j = 0; j < i; ++j) {
          Ans[pos + i] += Ans[pos + j] * Coef[i - j - 1];
        }
      }
    } else {
      perform(pos, size / 2);
      vector<F> Cur(size, 0), Mul(size, 0);
      for (int i = 0; i < size / 2; ++i)
        Cur[i] = Ans[i + pos];
      for (int i = 0; i < size; ++i)
        Mul[i] = Coef[i];
      Z.fft(Cur);
      Z.fft(Mul);
      for (int i = 0; i < size; ++i)
        Cur[i] *= Mul[i];
      Z.fft(Cur, true);
      for (int i = 0; i < size / 2; ++i)
        Ans[pos + size / 2 + i] += Cur[i + size / 2 - 1];

      perform(pos + size / 2, size / 2);
    }
  }

  FFT<Prime> Z;
  vector<F> &Ans, &Coef;
};

typedef Field<998244353> TF;
class F {
public:
  FFT<998244353u> Z;
  vector<TF> All, Conv1, Conv2, Ans;

  void solve(istream &cin, ostream &cout) {
    int N, M;
    cin >> N >> M;
    int size = 1 << logceil(min(N, M));

    auto F = TF::fact(max(M + N, 2 * size));
    auto I = TF::invfact(max(M + N, 2 * size));

    All.clear();
    Conv2.clear();
    All.resize(2 * size);
    Conv1.resize(size);
    Conv2.resize(2 * size);
    for (int i = 0; i < size; ++i) {
      All[i] = F[2 * i] * I[i] * I[i];
      Conv1[i] = i > 0 ? All[i] - F[2 * i] * I[i + 1] * I[i - 1] : 1;
      Conv2[i] = Conv1[i] * (2 * i + 3);
      Conv1[i] *= 2;
    }

    Z.fft(All);
    Z.fft(Conv2);
    for (int i = 0; i < 2 * size; ++i)
      Conv2[i] *= All[i];
    Z.fft(Conv2, true);
    Ans = vector<TF>(size, 0);
    for (int i = 1; i < size; ++i) {
      Ans[i] = Conv2[i - 1];
    }

    SelfConvolve<998244353>{Ans, Conv1};
    if (N == M) {
      cout << Ans[N] * I[2 * N] * F[N] * F[N] << endl;
    } else {
      if (M < N)
        swap(N, M);
      TF ret = Ans[N] + F[2 * N] * I[N] * I[N] * (M - N);
      for (int i = 0; i < N; ++i) {
        TF ways = F[N - i + M - i - 1] * I[N - i] * I[M - i - 1] -
                  F[N - i + M - i - 1] * I[N - i - 1] * I[M - i];
        ret += ways * Ans[i] + ways * F[2 * i] * I[i] * I[i] * (M - i);
      }
      cout << ret * I[N + M] * F[N] * F[M] << endl;
    }
  }
};

int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
  F solver;
  std::istream &in(std::cin);
  std::ostream &out(std::cout);
  solver.solve(in, out);
  return 0;
}


Fixed submission:
/**
 * code generated by JHelper
 * More info: https://github.com/AlexeyDmitriev/JHelper
 * @author
 */

#ifndef MAJK_LIB
#define MAJK_LIB

#include <algorithm>
#include <bitset>
#include <cassert>
#include <cmath>
#include <fstream>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <unordered_map>
#include <vector>
using namespace std;

#define x first
#define y second
constexpr int MOD = 1000000007;

typedef std::pair<int, int> pii;
typedef long long ll;
typedef unsigned long long ull;
typedef unsigned int ui;

template <typename T, typename U>
std::istream &operator>>(std::istream &i, pair<T, U> &p) {
  i >> p.x >> p.y;
  return i;
}
template <typename T> std::istream &operator>>(std::istream &i, vector<T> &t) {
  for (auto &v : t) {
    i >> v;
  }
  return i;
}
template <typename T>
std::ostream &operator<<(std::ostream &o, const vector<T> &t) {
  for (size_t i = 0; i < t.size(); ++i) {
    o << t[i] << " \n"[i == t.size() - 1];
  }
  return o;
}
template <typename T> using minheap = priority_queue<T, vector<T>, greater<T>>;
template <typename T> using maxheap = priority_queue<T, vector<T>, less<T>>;
auto fraclt = [](const pii &a, const pii &b) {
  return (ll)a.x * b.y < (ll)b.x * a.y;
};
struct cmpfrac {
  bool operator()(const pii &a, const pii &b) const {
    return (ll)a.x * b.y < (ll)b.x * a.y;
  }
};
template <typename T> bool in(T a, T b, T c) { return a <= b && b < c; }
int logceil(ll x) {
  int b = 0;
  while (x) {
    x >>= 1;
    ++b;
  }
  return b;
}

namespace std {
template <typename T, typename U> struct hash<pair<T, U>> {
  hash<T> t;
  hash<U> u;
  size_t operator()(const pair<T, U> &p) const {
    return t(p.x) ^ (u(p.y) << 7);
  }
};
} // namespace std
template <typename T, typename F> T bsh(T l, T h, const F &f) {
  T r = -1, m;
  while (l <= h) {
    m = (l + h) / 2;
    if (f(m)) {
      l = m + 1;
      r = m;
    } else {
      h = m - 1;
    }
  }
  return r;
}
template <typename T, typename F> T bsl(T l, T h, const F &f) {
  T r = -1, m;
  while (l <= h) {
    m = (l + h) / 2;
    if (f(m)) {
      h = m - 1;
      r = m;
    } else {
      l = m + 1;
    }
  }
  return r;
}
template <typename T> T gcd(T a, T b) {
  if (a < b)
    swap(a, b);
  return b ? gcd(b, a % b) : a;
}

template <typename T> class vector2 : public vector<vector<T>> {
public:
  vector2() {}
  vector2(size_t a, size_t b, T t = T())
      : vector<vector<T>>(a, vector<T>(b, t)) {}
};
template <typename T> class vector3 : public vector<vector<vector<T>>> {
public:
  vector3() {}
  vector3(size_t a, size_t b, size_t c, T t = T())
      : vector<vector<vector<T>>>(a, vector<vector<T>>(b, vector<T>(c, t))) {}
};
template <typename T> struct bounded_priority_queue {
  inline bounded_priority_queue(ui X) : A(X), B(0) {}
  inline void push(ui L, T V) {
    B = max(B, L);
    A[L].push(V);
  }
  inline const T &top() const { return A[B].front(); }
  inline void pop() {
    A[B].pop();
    while (B > 0 && A[B].empty())
      --B;
  }
  inline bool empty() const { return A[B].empty(); }
  inline void clear() {
    B = 0;
    for (auto &a : A)
      a = queue<T>();
  }

private:
  vector<queue<T>> A;
  ui B;
};

#endif
#ifndef MOD_H
#define MOD_H

template <unsigned int N> class Field {
  typedef unsigned int ui;
  typedef unsigned long long ull;
  inline ui pow(ui a, ui p) {
    ui r = 1, e = a;
    while (p) {
      if (p & 1) {
        r = ((ull)r * e) % N;
      }
      e = ((ull)e * e) % N;
      p >>= 1;
    }
    return r;
  }
  /*extended GCD(slow):ll t=0,nt=1,r=N,nr=a;while(nr){ll
   * q=r/nr;t-=q*nt;swap(t,nt);r-=q*nr;swap(r,nr);}assert(r<=1);return(t<0)?t+N:t;*/
  inline ui inv(ui a) { return pow(a, N - 2); }

public:
  inline Field(int x = 0) : v(x) {}
  inline Field<N> pow(int p) { return (*this) ^ p; }
  inline Field<N> operator^(int p) { return {(int)pow(v, (ui)p)}; }
  inline Field<N> &operator+=(const Field<N> &o) {
    if ((ll)v + o.v >= N)
      v = (ll)v + o.v - N;
    else
      v = v + o.v;
    return *this;
  }
  inline Field<N> &operator-=(const Field<N> &o) {
    if (v < o.v)
      v = N - o.v + v;
    else
      v = v - o.v;
    return *this;
  }
  inline Field<N> &operator*=(const Field<N> &o) {
    v = (ull)v * o.v % N;
    return *this;
  }
  inline Field<N> &operator/=(const Field<N> &o) { return *this *= inv(o.v); }
  inline Field<N> operator+(const Field<N> &o) const {
    Field<N> r{*this};
    return r += o;
  }
  inline Field<N> operator-(const Field<N> &o) const {
    Field<N> r{*this};
    return r -= o;
  }
  inline Field<N> operator*(const Field<N> &o) const {
    Field<N> r{*this};
    return r *= o;
  }
  inline Field<N> operator/(const Field<N> &o) const {
    Field<N> r{*this};
    return r /= o;
  }
  inline Field<N> operator-() {
    if (v)
      return {(int)(N - v)};
    else
      return {0};
  };
  inline Field<N> &operator++() {
    ++v;
    if (v == N)
      v = 0;
    return *this;
  }
  inline Field<N> operator++(int) {
    Field<N> r{*this};
    ++*this;
    return r;
  }
  inline Field<N> &operator--() {
    --v;
    if (v == -1)
      v = N - 1;
    return *this;
  }
  inline Field<N> operator--(int) {
    Field<N> r{*this};
    --*this;
    return r;
  }
  inline bool operator==(const Field<N> &o) const { return o.v == v; }
  inline bool operator!=(const Field<N> &o) const { return o.v != v; }
  inline explicit operator ui() const { return v; }
  inline static vector<Field<N>> fact(int t) {
    vector<Field<N>> F(t + 1, 1);
    for (int i = 2; i <= t; ++i) {
      F[i] = F[i - 1] * i;
    }
    return F;
  }
  inline static vector<Field<N>> invfact(int t) {
    vector<Field<N>> F(t + 1, 1);
    Field<N> X{1};
    for (int i = 2; i <= t; ++i) {
      X = X * i;
    }
    F[t] = 1 / X;
    for (int i = t - 1; i >= 2; --i) {
      F[i] = F[i + 1] * (i + 1);
    }
    return F;
  }

private:
  ui v;
};
template <unsigned int N> istream &operator>>(std::istream &is, Field<N> &f) {
  unsigned int v;
  is >> v;
  f = v;
  return is;
}
template <unsigned int N>
ostream &operator<<(std::ostream &os, const Field<N> &f) {
  return os << (unsigned int)f;
}
template <unsigned int N> Field<N> operator+(int i, const Field<N> &f) {
  return Field<N>(i) + f;
}
template <unsigned int N> Field<N> operator-(int i, const Field<N> &f) {
  return Field<N>(i) - f;
}
template <unsigned int N> Field<N> operator*(int i, const Field<N> &f) {
  return Field<N>(i) * f;
}
template <unsigned int N> Field<N> operator/(int i, const Field<N> &f) {
  return Field<N>(i) / f;
}

typedef Field<1000000007> FieldMod;

struct Ring {
  static int div(int p, int q, int N) {
    ll t = 0, nt = 1, r = N, nr = q;
    while (nr) {
      ll q = r / nr;
      t -= q * nt;
      r -= q * nr;
      swap(t, nt);
      swap(r, nr);
    }
    t = (t < 0) ? t + N : t;
    r = (r < 0) ? r + N : r;
    if (gcd(p, N) % r) {
      return 0;
    }
    return (int)(((ll)t * (ll)p / r) % N);
  }
};
#endif

#include <array>

template <ui P> struct Group {};
template <> struct Group<4194304001u> {
  constexpr static ui bits = 25, root = 199, rootInverse = 758768563u;
};
template <> struct Group<998244353u> {
  constexpr static ui bits = 23, root = 31, rootInverse = 128805723;
};
template <> struct Group<104857601u> {
  constexpr static ui bits = 22, root = 21, rootInverse = 49932191;
};
template <> struct Group<924844033u> {
  constexpr static ui bits = 21, root = 3597, rootInverse = 508059997;
};

template <ui Prime> class FFT {
public:
  typedef Field<Prime> F;

  FFT() {
    OMEGA[Group<Prime>::bits] = Group<Prime>::root;
    OMEGA_INV[Group<Prime>::bits] = Group<Prime>::rootInverse;
    for (size_t i = Group<Prime>::bits; i > 0; --i) {
      OMEGA[i - 1] = ui((ull(OMEGA[i]) * ull(OMEGA[i])) % Prime);
      OMEGA_INV[i - 1] = ui((ull(OMEGA_INV[i]) * ull(OMEGA_INV[i])) % Prime);

      // cerr << OMEGA[i-1] << ' ' << OMEGA_INV[i-1] << endl;
    }
  }

  void fft(std::vector<F> &V, bool inverse = false) {
    int P = 1;
    while ((1u << P) < V.size())
      ++P;
    V.resize(1u << P);
    fft(V, P, inverse);
  }

  void fft(std::vector<F> &V, const int P, bool inverse = false) {
    if (P == 0)
      return;
    if (P > Group<Prime>::bits)
      throw std::runtime_error("Number of bits in FFT too large");
    if (V.size() != (1 << P))
      throw std::runtime_error("Vector has wrong size");
    for (int i = 1, j = 0; i < (1 << P); ++i) {
      int bit = (1 << (P - 1));
      for (; j >= bit; bit >>= 1)
        j -= bit;
      j += bit;
      if (i < j)
        std::swap(V[i], V[j]);
    }

    for (int B = 1; B <= P; ++B) {
      F omega = inverse ? OMEGA_INV[B] : OMEGA[B];
      for (int i = 0; i < (1 << P); i += (1 << B)) {
        F x = 1;
        for (int j = 0; j < (1 << (B - 1)); j++) {
          F u = V[i + j], v = V[i + j + (1 << (B - 1))] * x;
          V[i + j] = u + v;
          V[i + j + (1 << (B - 1))] = u - v;
          x *= omega;
        }
      }
    }

    if (inverse) {
      F q = 1 / F(1 << P);
      for (F &v : V)
        v *= q;
    }
  }

private:
  std::array<ui, Group<Prime>::bits + 1> OMEGA, OMEGA_INV;
};

template <ui Prime> class SelfConvolve {
  using F = Field<Prime>;

public:
  SelfConvolve(vector<F> &Ans, vector<F> &Coef) : Ans(Ans), Coef(Coef) {
    perform(0, Ans.size());
  }

private:
  void perform(int pos, int size) {
    if (size <= 128) {
      for (int i = 1; i < size; ++i) {
        for (int j = 0; j < i; ++j) {
          Ans[pos + i] += Ans[pos + j] * Coef[i - j - 1];
        }
      }
    } else {
      perform(pos, size / 2);
      vector<F> Cur(size, 0), Mul(size, 0);
      for (int i = 0; i < size / 2; ++i)
        Cur[i] = Ans[i + pos];
      for (int i = 0; i < size; ++i)
        Mul[i] = Coef[i];
      Z.fft(Cur);
      Z.fft(Mul);
      for (int i = 0; i < size; ++i)
        Cur[i] *= Mul[i];
      Z.fft(Cur, true);
      for (int i = 0; i < size / 2; ++i)
        Ans[pos + size / 2 + i] += Cur[i + size / 2 - 1];

      perform(pos + size / 2, size / 2);
    }
  }

  FFT<Prime> Z;
  vector<F> &Ans, &Coef;
};

typedef Field<998244353> TF;
class F {
public:
  FFT<998244353u> Z;
  vector<TF> All, Conv1, Conv2, Ans;

  void solve(istream &cin, ostream &cout) {
    int N, M;
    cin >> N >> M;
    int size = 1 << logceil(min(N, M));

    auto F = TF::fact(max(M + N, 2 * size));
    auto I = TF::invfact(max(M + N, 2 * size));

    All.clear();
    Conv2.clear();
    All.resize(2 * size);
    Conv1.resize(size);
    Conv2.resize(2 * size);
    for (int i = 0; i < size; ++i) {
      All[i] = F[2 * i] * I[i] * I[i];
      Conv1[i] = i > 0 ? All[i] - F[2 * i] * I[i + 1] * I[i - 1] : 1;
      Conv2[i] = Conv1[i] * (2 * i + 3);
      Conv1[i] *= 2;
    }

    Z.fft(All);
    Z.fft(Conv2);
    for (int i = 0; i < 2 * size; ++i)
      Conv2[i] *= All[i];
    Z.fft(Conv2, true);
    Ans = vector<TF>(size, 0);
    for (int i = 1; i < size; ++i) {
      Ans[i] = Conv2[i - 1];
    }

    SelfConvolve<998244353>{Ans, Conv1};
    if (N == M) {
      cout << Ans[N] * I[2 * N] * F[N] * F[N] << endl;
    } else {
      if (M < N)
        swap(N, M);
      TF ret = Ans[N] + F[2 * N] * I[N] * I[N] * (M - N);
      for (int i = 0; i < N; ++i) {
        TF ways = F[N - i + M - i - 1] * I[N - i] * I[M - i - 1] -
                  F[N - i + M - i - 1] * I[N - i - 1] * I[M - i];
        ret += ways * Ans[i] + ways * F[2 * i] * I[i] * I[i] * (M - i);
      }
      cout << ret * I[N + M] * F[N] * F[M] << endl;
    }
  }
};

int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
  F solver;
  std::istream &in(std::cin);
  std::ostream &out(std::cout);
  solver.solve(in, out);
  return 0;
}