Problem: zscoder has a deck of n+m custom-made cards, which consists of n cards labelled from 1 to n and m jokers. Since zscoder is lonely, he wants to play a game with himself using those cards. 

Initially, the deck is shuffled uniformly randomly and placed on the table. zscoder has a set S which is initially empty. 

Every second, zscoder draws the top card from the deck. 

  * If the card has a number x written on it, zscoder removes the card and adds x to the set S. 
  * If the card drawn is a joker, zscoder places all the cards back into the deck and reshuffles (uniformly randomly) the n+m cards to form a new deck (hence the new deck now contains all cards from 1 to n and the m jokers). Then, if S currently contains all the elements from 1 to n, the game ends. Shuffling the deck doesn't take time at all. 



What is the expected number of seconds before the game ends? We can show that the answer can be written in the form P/Q where P, Q are relatively prime integers and Q ≠ 0 mod 998244353. Output the value of (P ⋅ Q^{-1}) modulo 998244353.

Input

The only line of the input contains two integers n and m (1 ≤ n, m ≤ 2 ⋅ 10^{6}).

Output

Output a single integer, the value of (P ⋅ Q^{-1}) modulo 998244353.

Examples

Input


2 1


Output


5


Input


3 2


Output


332748127


Input


14 9


Output


969862773

Note

For the first sample, it can be proven that the expected time before the game ends is 5 seconds.

For the second sample, it can be proven that the expected time before the game ends is 28/3 seconds.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ull = unsigned long long;
using li = __int128;
using uli = unsigned __int128;
using ld = long double;
using pii = pair<int, int>;
using vi = vector<int>;
void doReplace() {}
template <typename T, typename U, typename... Vs>
void doReplace(T& t, const U& u, Vs&&... vs) {
  t = u;
  doReplace(vs...);
}
template <typename T, typename... Us>
T minim(T& was, const T& cand, Us&&... us) {
  if (was > cand) {
    was = cand;
    doReplace(us...);
  }
  return was;
}
template <typename T, typename... Us>
T maxim(T& was, const T& cand, Us&&... us) {
  if (was < cand) {
    was = cand;
    doReplace(us...);
  }
  return was;
}
template <typename D>
D dPower(D base, ll exponent) {
  if (exponent < 0) {
    return dPower(1 / base, -exponent);
  }
  if (exponent == 0) {
    return 1;
  }
  if ((exponent & 1) == 1) {
    return dPower(base, exponent - 1) * base;
  } else {
    D res = dPower(base, exponent >> 1);
    return res * res;
  }
}
class NumberIterator : iterator<forward_iterator_tag, int> {
 public:
  int v;
  NumberIterator(int v) : v(v) {}
  operator int&() { return v; }
  int operator*() { return v; }
};
class range : pii {
 public:
  range(int begin, int end) : pii(begin, max(begin, end)) {}
  range(int n) : pii(0, max(0, n)) {}
  NumberIterator begin() { return first; }
  NumberIterator end() { return second; }
};
template <typename T>
class arr {
  T* b;
  int n;
  void allocate(int sz) {
    n = sz;
    if (sz > 0) {
      b = (T*)(::operator new(sz * sizeof(T)));
    } else {
      b = nullptr;
    }
  }

 public:
  arr(int n = 0) { allocate(n); }
  arr(int n, const T& init) {
    allocate(n);
    for (int i : range(n)) {
      ::new ((void*)(b + i)) T(init);
    }
  }
  arr(T* b, int n) : arr(b, b + n) {}
  arr(T* b, T* e) : b(b), n(e - b) {}
  arr(initializer_list<T> l) : arr(l.size()) {
    if (n > 0) {
      memcpy(b, l.begin(), n * sizeof(T));
    }
  }
  int size() const { return n; }
  T* begin() { return b; }
  const T* begin() const { return b; }
  T* end() { return b + n; }
  const T* end() const { return b + n; }
  arr<T> clone() const {
    arr<T> res(n);
    copy(b, b + n, res.begin());
    return res;
  }
  T& operator[](int at) { return b[at]; }
  const T& operator[](int at) const { return b[at]; }
  bool operator==(const arr& other) const {
    if (n != other.n) {
      return false;
    }
    for (int i : range(n)) {
      if (b[i] != other.b[i]) {
        return false;
      }
    }
    return true;
  }
  vector<T> view() { return vector<T>(b, b + min(n, 50)); }
};
void decreaseByOne() {}
template <typename T, class... Vs>
void decreaseByOne(arr<T>& array, Vs&... vs) {
  int n = array.size();
  for (int i : range(n)) {
    array[i]--;
  }
  decreaseByOne(vs...);
}
template <typename T, typename U>
void decreaseByOne(arr<pair<T, U>>& v) {
  for (auto& p : v) {
    p.first--;
    p.second--;
  }
}
template <typename T>
class arr2d {
  T* b;
  int d1;
  int d2;
  int sz;
  void allocate(int n) {
    if (n > 0) {
      b = (T*)(::operator new(n * sizeof(T)));
    } else {
      b = nullptr;
    }
  }

 public:
  arr2d(int d1 = 0, int d2 = 0) : d1(d1), d2(d2), sz(d1 * d2) { allocate(sz); }
  arr2d(int d1, int d2, const T& init) : d1(d1), d2(d2), sz(d1 * d2) {
    allocate(sz);
    for (int i : range(sz)) {
      ::new ((void*)(b + i)) T(init);
    }
  }
  arr2d(T* b, int d1, int d2) : b(b), d1(d1), d2(d2), sz(d1 * d2) {}
  int size() const { return sz; }
  int dim1() const { return d1; }
  int dim2() const { return d2; }
  T* begin() { return b; }
  T* end() { return b + sz; }
  T& operator()(int i1, int i2) { return b[i1 * d2 + i2]; }
  const T& operator()(int i1, int i2) const { return b[i1 * d2 + i2]; }
  T& operator[](const pii& p) { return operator()(p.first, p.second); }
  const T& operator[](const pii& p) const {
    return operator()(p.first, p.second);
  }
  arr<T> operator[](int at) { return arr<T>(b + at * d2, d2); }
  vector<vector<T>> view() {
    vector<vector<T>> res(min(d1, 50));
    for (int i : range(res.size())) {
      res[i] = (*this)[i].view();
    }
    return res;
  }
  arr2d<T> clone() {
    arr2d<T> res(d1, d2);
    copy(b, b + sz, res.b);
    return res;
  }
};
inline bool isWhitespace(int c) { return isspace(c) || c == EOF; }
class Input {
 private:
  bool exhausted = false;
  int bufSize = 4096;
  char* buf = new char[bufSize];
  int bufRead = 0;
  int bufAt = 0;

 public:
  inline int get() {
    if (exhausted) {
      return EOF;
    }
    if (bufRead == bufAt) {
      bufRead = fread(buf, sizeof(char), bufSize, stdin);
      bufAt = 0;
    }
    if (bufRead == bufAt) {
      exhausted = true;
      return EOF;
    }
    return buf[bufAt++];
  }
  inline int peek() {
    if (exhausted) {
      return EOF;
    }
    if (bufRead == bufAt) {
      bufRead = fread(buf, sizeof(char), bufSize, stdin);
      bufAt = 0;
    }
    if (bufRead == bufAt) {
      exhausted = true;
      return EOF;
    }
    return buf[bufAt];
  }

 private:
  template <typename T>
  inline T readInteger() {
    int c = skipWhitespace();
    int sgn = 1;
    if (c == '-') {
      sgn = -1;
      c = get();
    }
    T res = 0;
    do {
      if (!isdigit(c)) {
        return sgn * res;
      }
      res *= 10;
      res += c - '0';
      c = get();
    } while (!isWhitespace(c));
    return res * sgn;
  }
  void initArrays(int) {}
  template <typename T, class... Vs>
  void initArrays(int n, arr<T>& array, Vs&... vs) {
    array = arr<T>(n, T());
    initArrays(n, vs...);
  }
  template <typename T, class... Vs>
  void initArrays(int n, vector<T>&, Vs&... vs) {
    initArrays(n, vs...);
  }
  void readImpl(int) {}
  template <typename T, class... Vs>
  void readImpl(int i, arr<T>& arr, Vs&... vs) {
    arr[i] = readType<T>();
    readImpl(i, vs...);
  }
  template <typename T, class... Vs>
  void readImpl(int i, vector<T>& arr, Vs&... vs) {
    arr.push_back(readType<T>());
    readImpl(i, vs...);
  }

 public:
  inline int skipWhitespace() {
    int c;
    while (isWhitespace(c = get()) && c != EOF)
      ;
    return c;
  }
  inline int peekNext() {
    while (isWhitespace(peek()) && peek() != EOF) {
      get();
    }
    return peek();
  }
  inline int readInt() { return readInteger<int>(); }
  inline ll readLong() { return readInteger<ll>(); }
  inline unsigned readUnsigned() { return readInteger<unsigned>(); }
  string readString() {
    int c = skipWhitespace();
    if (c == EOF) {
      return "";
    }
    string res;
    do {
      res.push_back(c);
    } while (!isWhitespace(c = get()));
    return res;
  }
  arr<int> readIntArray(int size) { return readArray<int>(size); }
  arr<ll> readLongArray(int size) { return readArray<ll>(size); }
  arr<double> readDoubleArray(int size) { return readArray<double>(size); }
  arr<string> readStringArray(int size) { return readArray<string>(size); }
  arr<char> readCharArray(int size) { return readArray<char>(size); }
  template <typename T>
  T readType() {
    throw "Operation not supported";
  }
  template <typename U, typename V>
  pair<U, V> readType() {
    U first = readType<U>();
    V second = readType<V>();
    return make_pair(first, second);
  }
  template <typename T>
  arr<T> readArray(int n) {
    arr<T> res(n, T());
    for (int i : range(n)) {
      res[i] = readType<T>();
    }
    return res;
  }
  template <class... Vs>
  void readArrays(int n, Vs&... vs) {
    initArrays(n, vs...);
    for (int i : range(n)) {
      readImpl(i, vs...);
    }
  }
  template <typename U, typename V>
  arr<pair<U, V>> readArray(int n) {
    arr<pair<U, V>> res(n);
    for (int i : range(n)) {
      res[i] = readType<U, V>();
    }
    return res;
  }
  template <typename T>
  arr2d<T> readTable(int rows, int cols) {
    arr2d<T> result(rows, cols);
    for (int i : range(rows)) {
      for (int j : range(cols)) {
        result(i, j) = readType<T>();
      }
    }
    return result;
  }
  arr2d<int> readIntTable(int rows, int cols) {
    return readTable<int>(rows, cols);
  }
  arr2d<char> readCharTable(int rows, int cols) {
    return readTable<char>(rows, cols);
  }
  string readLine() {
    int c = get();
    if (c == EOF) {
      return "";
    }
    string res;
    do {
      res.push_back(c);
      c = get();
    } while (c != '\n' && c != '\r' && c != EOF);
    return res;
  }
  inline double readDouble() {
    int c = skipWhitespace();
    int sgn = 1;
    if (c == '-') {
      sgn = -1;
      c = get();
    }
    double res = 0;
    do {
      if (tolower(c) == 'e') {
        return sgn * res * dPower(double(10), readInt());
      }
      if (!isdigit(c)) {
        return sgn * res;
      }
      res *= 10;
      res += c - '0';
      c = get();
    } while (!isWhitespace(c) && c != '.');
    if (c == '.') {
      double add = 0;
      int length = 0;
      c = get();
      do {
        if (tolower(c) == 'e') {
          return sgn * (res + add * dPower(double(10), -length)) *
                 dPower(double(10), readInt());
        }
        if (!isdigit(c)) {
          res += add * dPower(10, -length);
          return res * sgn;
        }
        add *= 10;
        add += c - '0';
        length++;
        c = get();
      } while (!isWhitespace(c));
      res += add * dPower(double(10), -length);
    }
    return res * sgn;
  }
  inline char readChar() {
    int c = skipWhitespace();
    if (c == EOF) {
      return 0;
    }
    return c;
  }
  inline bool isExhausted() { return exhausted; }
  inline void setBufSize(int newBufSize) {
    if (newBufSize > bufSize) {
      char* newBuf = new char[newBufSize];
      memcpy(newBuf, buf, bufSize);
      buf = newBuf;
    }
    bufSize = newBufSize;
  }
};
template <>
inline double Input::readType() {
  return readDouble();
}
template <>
inline int Input::readType() {
  return readInt();
}
template <>
inline ll Input::readType() {
  return readLong();
}
template <>
inline unsigned Input::readType() {
  return readUnsigned();
}
template <>
inline char Input::readType() {
  return readChar();
}
template <>
inline string Input::readType() {
  return readString();
}
Input in;
class Output {
 private:
  ostream* out;
  template <typename T>
  inline void printSingle(const T& value) {
    *out << value;
  }
  template <typename T>
  void printSingle(const vector<T>& array) {
    size_t n = array.size();
    for (int i : range(n)) {
      *out << array[i];
      if (i + 1 != n) {
        *out << ' ';
      }
    }
  }
  template <typename T>
  void printSingle(const arr<T>& array) {
    int n = array.size();
    for (int i : range(n)) {
      *out << array[i];
      if (i + 1 != n) {
        *out << ' ';
      }
    }
  }
  template <typename T>
  void printSingle(const arr2d<T>& array) {
    size_t n = array.dim1();
    size_t m = array.dim2();
    for (int i : range(n)) {
      for (int j : range(m)) {
        *out << array(i, j);
        if (j + 1 != m) {
          *out << ' ';
        }
      }
      if (i + 1 != n) {
        *out << '\n';
      }
    }
  }
  template <typename T, typename U>
  inline void printSingle(const pair<T, U>& value) {
    *out << value.first << ' ' << value.second;
  }

 public:
  bool autoflush;
  Output(ostream& out, bool autoflush) : out(&out), autoflush(autoflush) {
    setPrecision(20);
  }
  void setOut(ostream& nOut) {
    out = &nOut;
    setPrecision(20);
  }
  inline void print() {}
  template <typename T, typename... Targs>
  inline void print(const T& first, const Targs... args) {
    printSingle(first);
    if (sizeof...(args) != 0) {
      *out << ' ';
      print(args...);
    }
    if (autoflush) {
      flush();
    }
  }
  template <typename... Targs>
  inline void printLine(const Targs... args) {
    print(args...);
    *out << '\n';
    if (autoflush) {
      flush();
    }
  }
  inline void flush() { out->flush(); }
  inline void setPrecision(int digs) { *out << fixed << setprecision(digs); }
};
Output out(cout, false);
Output err(cerr, true);
template <typename T>
T gcd(T a, T b) {
  a = abs(a);
  b = abs(b);
  while (b != 0) {
    a = a % b;
    swap(a, b);
  }
  return a;
}
template <typename T>
T lcm(T a, T b) {
  return a / gcd(a, b) * b;
}
template <typename T>
T power(const T& a, ll b) {
  if (b == 0) {
    return 1;
  }
  if ((b & 1) == 0) {
    T res = power(a, b >> 1);
    return res * res;
  } else {
    return power(a, b - 1) * a;
  }
}
template <typename T>
T factorial(int n) {
  T result = 1;
  for (int i = 2; i <= n; i++) {
    result *= i;
  }
  return result;
}
template <typename T>
arr<T> factorials(int length) {
  arr<T> result(length);
  if (length > 0) {
    result[0] = 1;
  }
  for (int i = 1; i < length; i++) {
    result[i] = result[i - 1] * i;
  }
  return result;
}
template <typename T>
arr<T> powers(T base, int length) {
  arr<T> result(length);
  if (length > 0) {
    result[0] = 1;
  }
  for (int i = 1; i < length; i++) {
    result[i] = result[i - 1] * base;
  }
  return result;
}
class Rational {
  void normalize() {
    if (den < 0) {
      den = -den;
      num = -num;
    }
    ll g = gcd(num, den);
    num /= g;
    den /= g;
  }

 public:
  ll num;
  ll den;
  Rational(ll num = 0, ll den = 1) : num(num), den(den) { normalize(); }
  Rational(const Rational& other) : num(other.num), den(other.den) {}
  Rational& operator+=(const Rational& other) {
    ll g = gcd(den, other.den);
    num = num * (other.den / g) + (den / g) * other.num;
    den *= other.den / g;
    normalize();
    return *this;
  }
  Rational& operator-=(const Rational& other) {
    ll g = gcd(den, other.den);
    num = num * (other.den / g) - (den / g) * other.num;
    den *= other.den / g;
    normalize();
    return *this;
  }
  Rational& operator*=(const Rational& other) {
    ll g = gcd(den, other.num);
    num *= other.num / g;
    den /= g;
    den *= other.den;
    normalize();
    return *this;
  }
  Rational& operator/=(const Rational& other) {
    ll g = gcd(den, other.den);
    num *= other.den / g;
    den /= g;
    den *= other.num;
    normalize();
    return *this;
  }
  Rational operator-() const { return Rational(-num, den); }
  Rational abs() const {
    if (num >= 0) {
      return *this;
    }
    return -(*this);
  }
};
Rational operator+(const Rational& a, const Rational& b) {
  Rational res = a;
  res += b;
  return res;
}
Rational operator-(const Rational& a, const Rational& b) {
  Rational res = a;
  res -= b;
  return res;
}
Rational operator*(const Rational& a, const Rational& b) {
  Rational res = a;
  res *= b;
  return res;
}
Rational operator/(const Rational& a, const Rational& b) {
  Rational res = a;
  res /= b;
  return res;
}
Rational operator-(const Rational& a) { return Rational(-a.num, a.den); }
bool operator<(const Rational& a, const Rational& b) {
  return a.num * b.den < a.den * b.num;
}
bool operator>(const Rational& a, const Rational& b) { return b < a; }
bool operator>=(const Rational& a, const Rational& b) { return !(a < b); }
bool operator<=(const Rational& a, const Rational& b) { return !(b < a); }
bool operator==(const Rational& a, const Rational& b) {
  return a.num == b.num && a.den == b.den;
}
bool operator!=(const Rational& a, const Rational& b) { return !(b == a); }
ostream& operator<<(ostream& out, const Rational& val) {
  return out << val.num << '/' << val.den;
}
class ReverseNumberIterator : public NumberIterator {
 public:
  ReverseNumberIterator(int v) : NumberIterator(v) {}
  ReverseNumberIterator& operator++() {
    --v;
    return *this;
  }
};
class RevRange : pii {
 public:
  RevRange(int begin, int end) : pii(begin - 1, min(begin, end) - 1) {}
  RevRange(int n) : pii(n - 1, min(n, 0) - 1) {}
  ReverseNumberIterator begin() { return first; }
  ReverseNumberIterator end() { return second; }
};
const int MOD7 = 1000000007;
const int MOD9 = 1000000009;
const int MODF = 998244353;
int mod = MOD7;
ll gcd(ll a, ll b, ll& x, ll& y) {
  if (a == 0) {
    x = 0;
    y = 1;
    return b;
  }
  int d = gcd(b % a, a, y, x);
  x -= (b / a) * y;
  return d;
}
class modint {
 public:
  int n;
  modint() : n(0) {}
  modint(ll n, bool special = false) {
    if (special) {
      this->n = -1;
      return;
    }
    if (n >= 0 && n < mod) {
      this->n = n;
      return;
    }
    n %= mod;
    if (n < 0) {
      n += mod;
    }
    this->n = n;
  }
  modint& operator+=(const modint& other) {
    n += other.n;
    if (n >= mod) {
      n -= mod;
    }
    return *this;
  }
  modint& operator-=(const modint& other) {
    n -= other.n;
    if (n < 0) {
      n += mod;
    }
    return *this;
  }
  modint& operator*=(const modint& other) {
    n = ll(n) * other.n % mod;
    return *this;
  }
  modint& operator/=(const modint& other) { return *this *= other.inverse(); }
  modint operator-() {
    if (n == 0) {
      return 0;
    }
    return modint(mod - n);
  }
  modint inverse() const {
    ll x, y;
    ll g = gcd(ll(n), ll(mod), x, y);
    return x;
  }
  int log(modint alpha);
};
modint nullModint(-1, true);
modint operator+(const modint& a, const modint& b) { return modint(a) += b; }
modint operator-(const modint& a, const modint& b) { return modint(a) -= b; }
modint operator*(const modint& a, const modint& b) { return modint(a) *= b; }
modint operator/(const modint& a, const modint& b) { return modint(a) /= b; }
ostream& operator<<(ostream& out, const modint& val) { return out << val.n; }
bool operator==(const modint& a, const modint& b) { return a.n == b.n; }
bool operator!=(const modint& a, const modint& b) { return a.n != b.n; }
namespace std {
template <>
struct hash<modint> {
  size_t operator()(const modint& n) const { return n.n; }
};
}  // namespace std
int modint::log(modint alpha) {
  unordered_map<modint, int> base;
  int exp = 0;
  modint pow = 1;
  modint inv = *this;
  modint alInv = alpha.inverse();
  while (exp * exp < mod) {
    if (inv == 1) {
      return exp;
    }
    base[inv] = exp++;
    pow *= alpha;
    inv *= alInv;
  }
  modint step = pow;
  for (int i = 1;; i++) {
    if (base.count(pow)) {
      return exp * i + base[pow];
    }
    pow *= step;
  }
}
arr<modint> inverses(int length) {
  arr<modint> result(length);
  if (length > 1) {
    result[1] = 1;
  }
  for (int i = 2; i < length; i++) {
    result[i] = -(mod / i) * result[mod % i];
  }
  return result;
}
arr<modint> inverseFactorials(int length) {
  auto result = inverses(length);
  if (length > 0) {
    result[0] = 1;
  }
  for (int i = 1; i < length; i++) {
    result[i] *= result[i - 1];
  }
  return result;
}
class Combinations {
 private:
  arr<modint> fact;
  arr<modint> invFactorial;

 public:
  Combinations(int length) {
    fact = factorials<modint>(length);
    invFactorial = inverseFactorials(length);
  }

 public:
  modint c(int n, int k) const {
    if (k < 0 || k > n) {
      return 0;
    }
    return fact[n] * invFactorial[k] * invFactorial[n - k];
  }
  modint operator()(int n, int k) const { return c(n, k); }
  modint factorial(int n) const { return fact[n]; }
  modint inverseFactorial(int n) const { return invFactorial[n]; }
};
arr<modint> bernoulli(int length, Combinations* c = nullptr) {
  arr<modint> b(length);
  if (c == nullptr) {
    c = new Combinations(length + 1);
  }
  if (length > 0) {
    b[0] = 1;
  }
  for (int i : range(1, length)) {
    b[i] = 0;
    for (int j : range(1, i + 1)) {
      b[i] += (*c)(i + 1, j + 1) * b[i - j];
    }
    b[i] = -b[i];
    b[i] /= i + 1;
  }
  return b;
}
class HZSTasuetKarti {
 public:
  void solve() {
    int n = in.readInt();
    int m = in.readInt();
    mod = MODF;
    modint res = 0;
    modint delta = modint(m + n + 1) / (m + 1);
    Combinations c(n + m + 2);
    modint sum = 0;
    modint d = 1;
    for (int i : range(1, n + 1)) {
      modint cc = c(i + m - 1, i);
      res = (sum + delta * (d + cc)) / d;
      d += cc;
      sum += res * cc;
    }
    out.printLine(res);
  }
};
int main() {
  std::ios::sync_with_stdio(false);
  std::cin.tie(0);
  HZSTasuetKarti solver;
  solver.solve();
  fflush(stdout);
  return 0;
}