#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

using namespace std;

using Int = long long;

template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }
#define COLOR(s) ("\x1b[" s "m")

////////////////////////////////////////////////////////////////////////////////
template <unsigned M_> struct ModInt {
  static constexpr unsigned M = M_;
  unsigned x;
  constexpr ModInt() : x(0U) {}
  constexpr ModInt(unsigned x_) : x(x_ % M) {}
  constexpr ModInt(unsigned long long x_) : x(x_ % M) {}
  constexpr ModInt(int x_) : x(((x_ %= static_cast<int>(M)) < 0) ? (x_ + static_cast<int>(M)) : x_) {}
  constexpr ModInt(long long x_) : x(((x_ %= static_cast<long long>(M)) < 0) ? (x_ + static_cast<long long>(M)) : x_) {}
  ModInt &operator+=(const ModInt &a) { x = ((x += a.x) >= M) ? (x - M) : x; return *this; }
  ModInt &operator-=(const ModInt &a) { x = ((x -= a.x) >= M) ? (x + M) : x; return *this; }
  ModInt &operator*=(const ModInt &a) { x = (static_cast<unsigned long long>(x) * a.x) % M; return *this; }
  ModInt &operator/=(const ModInt &a) { return (*this *= a.inv()); }
  ModInt pow(long long e) const {
    if (e < 0) return inv().pow(-e);
    ModInt a = *this, b = 1U; for (; e; e >>= 1) { if (e & 1) b *= a; a *= a; } return b;
  }
  ModInt inv() const {
    unsigned a = M, b = x; int y = 0, z = 1;
    for (; b; ) { const unsigned q = a / b; const unsigned c = a - q * b; a = b; b = c; const int w = y - static_cast<int>(q) * z; y = z; z = w; }
    assert(a == 1U); return ModInt(y);
  }
  ModInt operator+() const { return *this; }
  ModInt operator-() const { ModInt a; a.x = x ? (M - x) : 0U; return a; }
  ModInt operator+(const ModInt &a) const { return (ModInt(*this) += a); }
  ModInt operator-(const ModInt &a) const { return (ModInt(*this) -= a); }
  ModInt operator*(const ModInt &a) const { return (ModInt(*this) *= a); }
  ModInt operator/(const ModInt &a) const { return (ModInt(*this) /= a); }
  template <class T> friend ModInt operator+(T a, const ModInt &b) { return (ModInt(a) += b); }
  template <class T> friend ModInt operator-(T a, const ModInt &b) { return (ModInt(a) -= b); }
  template <class T> friend ModInt operator*(T a, const ModInt &b) { return (ModInt(a) *= b); }
  template <class T> friend ModInt operator/(T a, const ModInt &b) { return (ModInt(a) /= b); }
  explicit operator bool() const { return x; }
  bool operator==(const ModInt &a) const { return (x == a.x); }
  bool operator!=(const ModInt &a) const { return (x != a.x); }
  friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a.x; }
};
////////////////////////////////////////////////////////////////////////////////

constexpr unsigned MO = 998244353;
using Mint = ModInt<MO>;

constexpr int LIM_INV = 200'010;
Mint inv[LIM_INV], fac[LIM_INV], invFac[LIM_INV];

void prepare() {
  inv[1] = 1;
  for (int i = 2; i < LIM_INV; ++i) {
    inv[i] = -((Mint::M / i) * inv[Mint::M % i]);
  }
  fac[0] = invFac[0] = 1;
  for (int i = 1; i < LIM_INV; ++i) {
    fac[i] = fac[i - 1] * i;
    invFac[i] = invFac[i - 1] * inv[i];
  }
}
Mint binom(Int n, Int k) {
  if (n < 0) {
    if (k >= 0) {
      return ((k & 1) ? -1 : +1) * binom(-n + k - 1, k);
    } else if (n - k >= 0) {
      return (((n - k) & 1) ? -1 : +1) * binom(-k - 1, n - k);
    } else {
      return 0;
    }
  } else {
    if (0 <= k && k <= n) {
      assert(n < LIM_INV);
      return fac[n] * invFac[k] * invFac[n - k];
    } else {
      return 0;
    }
  }
}


Mint brute(int N, int D) {
cerr<<"[brute] N = "<<N<<", D = "<<D<<endl;
  // created on day n
  vector<Mint> as(N + 1);
  for (int n = 0; n <= N; ++n) {
    as[n] = (n <= 2) ? 1 : (as[n - 1] + as[n - 2]);
  }
  Mint ans = 0;
  Mint bads[2] = {};
  // n remaining days
  for (int n = 0; n <= N; ++n) {
    vector<Mint> fs(D + 1, 0);
    for (int d = 0; d <= D; ++d) {
      /*
        [x^<=n] (x/(1-x^2))^d
        = [x^n] x^d(1+x) / (1-x^2)^(d+1)
      */
      if (n - d >= 0) {
        fs[d] = binom(d + ((n - d) >> 1), d);
      }
    }
// vector<Mint>gs(D+1,0);for(int d0=0;d0<=D;++d0)for(int d1=0;d0+d1<=D;++d1)gs[d0+d1]+=fs[d0]*fs[d1];
// cerr<<n<<": "<<fs<<" "<<gs<<endl;
    Mint all = 0, bad = 0;
    for (int d = 0; d <= D; ++d) all += fs[d] * fs[D - d];
    for (int d = 0; d <= D - 2; ++d) bad += fs[d] * fs[D - 2 - d];
    ans += as[N - n] * (all - bads[(n + 1) & 1]);
    bads[n & 1] += bad;
  }
  ans /= 2;
  return ans;
}

Mint slow(int N, int D) {
  // created on day n
  vector<Mint> as(N + 1);
  for (int n = 0; n <= N; ++n) {
    as[n] = (n <= 2) ? 1 : (as[n - 1] + as[n - 2]);
  }
  auto bs = as;
  for (int n = 2; n <= N; ++n) {
    bs[n] += bs[n - 2];
  }
// cerr<<"as = "<<as<<endl;
// cerr<<"bs = "<<bs<<endl;
  
  // some shift of 1/(1+x)(1-x)^(d+1) for each parity
  auto calc = [&](int d) -> vector<Mint> {
    vector<Mint> ret(N + 1, 0);
    if (d >= 0) {
      vector<Mint> cs(N + 1);
      for (int n = 0; n <= N; ++n) cs[n] = binom(d + n, d);
      for (int n = 1; n <= N; ++n) cs[n] -= cs[n - 1];
// cerr<<"d = "<<d<<", cs = "<<cs<<endl;
      if (d & 1) {
        for (int n = (d + 1) / 2; n <= N; ++n) ret[n] += 2 * cs[n - (d + 1) / 2];
      } else {
        for (int n = d / 2; n <= N; ++n) ret[n] += cs[n - d / 2];
        for (int n = d / 2 + 1; n <= N; ++n) ret[n] += cs[n - (d / 2 + 1)];
      }
    }
    return ret;
  };
  const auto fs = calc(D);
  const auto gs = calc(D - 2);
// cerr<<"fs = "<<fs<<endl;
// cerr<<"gs = "<<gs<<endl;
  
  Mint ans = 0;
  for (int n = 0; n <= N; ++n) ans += as[N - n] * fs[n];
  for (int n = 0; n < N; ++n) ans -= bs[N - n - 1] * gs[n];
  ans /= 2;
  return ans;
}

int main() {
  prepare();
  
  int N, D;
  for (; ~scanf("%d%d", &N, &D); ) {
    Mint ans = 0;
    if (N <= 5000 && D <= 5000) {
      ans = slow(N, D);
    } else {
      assert(false);
    }
    printf("%u\n", ans.x);
  }
  return 0;
}