Find the number, modulo 998244353, of sequences of length N consisting of 0, 1 and 2 such that none of their contiguous subsequences totals to X.

Constraints

* 1 \leq N \leq 3000
* 1 \leq X \leq 2N
* N and X are integers.

Input

Input is given from Standard Input in the following format:


N X


Output

Print the number, modulo 998244353, of sequences that satisfy the condition.

Examples

Input

3 3


Output

14


Input

8 6


Output

1179


Input

10 1


Output

1024


Input

9 13


Output

18402


Input

314 159


Output

459765451
// includes
#include <bits/stdc++.h>
using namespace std;

// macros
#define pb emplace_back
#define mk make_pair
#define FOR(i, a, b) for(int i=(a);i<(b);++i)
#define rep(i, n) FOR(i, 0, n)
#define rrep(i, n) for(int i=((int)(n)-1);i>=0;i--)
#define irep(itr, st) for(auto itr = (st).begin(); itr != (st).end(); ++itr)
#define irrep(itr, st) for(auto itr = (st).rbegin(); itr != (st).rend(); ++itr)
#define whole(x) (x).begin(),(x).end()
#define sz(x) ((int)(x).size())
#define bit(n) (1LL<<(n))
// functions
template <typename T> void unique(T& c){c.erase(std::unique(c.begin(), c.end()), c.end());}
template <class T>bool chmax(T &a, const T &b){if(a < b){a = b; return 1;} return 0;}
template <class T>bool chmin(T &a, const T &b){if(a > b){a = b; return 1;} return 0;}
template <typename T> istream &operator>>(istream &is, vector<T> &vec){for(auto &v: vec)is >> v; return is;}
template <typename T> ostream &operator<<(ostream &os, const vector<T>& vec){for(int i = 0; i < vec.size(); i++){ os << vec[i]; if(i + 1 != vec.size())os << " ";} return os;}
template <typename T> ostream &operator<<(ostream &os, const set<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;}
template <typename T> ostream &operator<<(ostream &os, const unordered_set<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;}
template <typename T> ostream &operator<<(ostream &os, const multiset<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;}
template <typename T> ostream &operator<<(ostream &os, const unordered_multiset<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;}
template <typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &p){os << "(" << p.first << ", " << p.second << ")"; return os;}
template <typename T1, typename T2> ostream &operator<<(ostream &os, const map<T1, T2> &mp){for(auto itr = mp.begin(); itr != mp.end(); ++itr){ os << "(" << itr->first << ", " << itr->second << ")"; auto titr = itr; if(++titr != mp.end())os << " "; } return os;}
template <typename T1, typename T2> ostream &operator<<(ostream &os, const unordered_map<T1, T2> &mp){for(auto itr = mp.begin(); itr != mp.end(); ++itr){ os << "(" << itr->first << ", " << itr->second << ")"; auto titr = itr; if(++titr != mp.end())os << " "; } return os;}
//  types
using ll = long long int;
using P = pair<int, int>;
// constants
const int inf = 1e9;
const ll linf = 1LL << 50;
const double EPS = 1e-10;
const int mod = 998244353;
const int dx[4] = {-1, 0, 1, 0};
const int dy[4] = {0, -1, 0, 1};
// io
struct fast_io{
  fast_io(){ios_base::sync_with_stdio(false); cin.tie(nullptr); cout << fixed << setprecision(20);}
} fast_io_;

template<typename T>
T extgcd(T a, T b, T &x, T &y){ 
  T d = a;
  if(b != 0){
    d = extgcd(b, a % b, y, x);
    y -= (a / b) * x;
  }else{
    x = 1, y = 0;
  }
  return d;
}

template <typename T>
T modinv(T a, T m){
  long long x = 0, y = 0;
  extgcd<long long>(a, m, x, y);
  x %= m;
  if(x < 0)x += m;
  return x;
}

template <typename T>
T power(T a, T n, T mod) {
  T res = 1;
  T tmp = n;
  T curr = a;
  while(tmp){
    if(tmp % 2 == 1){
      res = (T)(res * curr % mod);
    }
    curr = (T)(curr * curr % mod);
    tmp >>= 1;
  }

  return res;
}

struct Mint{
  const static ll default_mod = (ll)(mod);
  ll MOD = default_mod;
  ll x = 0;
  ll get_mod(){
    return MOD;
  }
  Mint(){}
  Mint(ll x_, ll MOD=default_mod): MOD(MOD){
    x = x_;
    x %= MOD;
    if(x < 0)x += MOD;
  }
  Mint(const Mint &m){
    x = m.x;
    MOD = m.MOD;
  }
  Mint &operator+=(const Mint &y){
    x = (x + y.x) % MOD;
    if(x < 0)x += MOD;
    return *this;
  }
  Mint &operator-=(const Mint &y){
    x = (x - y.x) % MOD;
    if(x < 0)x += MOD;
    return *this;
  }
  Mint &operator*=(const Mint &y){
    x = (x * y.x) % MOD;
    if(x < 0)x += MOD;
    return *this;
  }
  Mint inverse() const{
    return Mint(modinv<ll>(x, MOD), MOD);
  }
  Mint &operator/=(const Mint &y){
    x = (x * y.inverse().x) % MOD;
    if(x < 0)x += MOD;
    return *this;
  }
  Mint operator-() const{
    return Mint(-x, MOD);
  }
  Mint operator+(const Mint &y) const{
    return Mint(*this) += y;
  }
  Mint operator-(const Mint &y) const{
    return Mint(*this) -= y;
  }
  Mint operator*(const Mint &y) const{
    return Mint(*this) *= y;
  }
  Mint operator/(const Mint &y) const{
    return Mint(*this) /= y;
  }
  bool operator==(const Mint &y) const{
    return x == y.x;
  }
  bool operator!=(const Mint &y) const{
    return x != y.x;
  }
  Mint pow(long long k) const{
    long long ret = power<long long>(x, k, MOD);
    return Mint(ret, MOD);
  }
  friend ostream& operator<<(ostream &os, const Mint &m){
    return os << m.x;
  }
  friend istream& operator>>(istream &is, Mint &m){
    ll t;
    is >> t;
    m = Mint(t);
    return is;
  }
  explicit operator long long() const{
    return x;
  }
};

struct Factorial{
  int n = 0;
  static const long long mod_default = 998244353;
  long long MOD = mod_default;
  vector<long long> fac;
  vector<long long> inv_;
  explicit Factorial(){}
  explicit Factorial(int n, long long mod_=mod_default): n(n), MOD(mod_){
    assert(MOD > 0 && n < MOD);
    fac.resize(n + 1);
    inv_.resize(n + 1);
    calc_factorial();
    calc_inv();
  }
  void calc_factorial(){
    fac[0] = 1;
    for(int i = 1; i <= n; i++){
      fac[i] = i * fac[i-1] % MOD;
    }
  }
  void calc_inv(){
    inv_[n] = power<long long>(fac[n], MOD - 2, MOD);
    for(int i = n - 1; i >= 0; i--){
      inv_[i] = (i + 1) * inv_[i+1] % MOD;
    }
  }
  long long& operator[](size_t i){
    if((int)i > n){
      cerr << "list index out of range" << endl;
      abort();
    }
    return fac[i];
  }
  long long inv(size_t i){
    if((int)i > n){
      cerr << "list index out of range" << endl;
      abort();
    }
    return inv_[i];
  }
  long long comb(int n, int k){
    if(n < 0 || k < 0 || n < k)return 0;
    long long res = fac[n];
    res = res * inv_[n-k] % MOD;
    res = res * inv_[k] % MOD;
    return res;
  }
  long long perm(int n, int k){
    if(n < 0 || k < 0 || n < k)return 0;
    long long res = fac[n];
    res = res * inv_[n-k] % MOD;
    return res;
  }
  long long h(int n, int k){
    if(n == 0 && k == 0)return 1;
    return comb(n + k - 1, k);
  }
};



int main(int argc, char const* argv[])
{
  ll n, x; cin >> n >> x;
  Factorial fac(10000);
  if(x == 1){
    cout << power<ll>(2LL, n, mod) << endl;
    return 0;
  }else if(x == 2){
    cout << (n + 1) << endl;
    return 0;
  }
  if(x % 2 == 0){
    Mint res = 0;
    for(ll i = 0; i <= x - 1; i++){
      for(ll z = 0; 2 * z <= i; z++){
        ll y = i - 2 * z;
        if(y + z <= n){
          res += Mint(fac.comb(n, y)) * Mint(fac.comb(n - y, z));
        }
      }
    }
    for(ll i = 1; i < x - 1; i += 2){
      for(ll z = 0; z <= x - 1 - i - 1; z++){
        ll y = x - 2 - i - 2 * z;
        if(((i+1)/2) * 2 + y + z <= n){
          res += Mint(fac.comb(n, ((i+1)/2) * 2 + y + z)) * Mint(fac.comb(y + z, y));
        }
      }
    }
    cout << res << endl;
  }else{
    Mint res = 0;
    for(ll i = 0; i <= x - 1; i++){
      for(ll z = 0; 2 * z <= i; z++){
        ll y = i - 2 * z;
        if(y + z <= n){
          res += Mint(fac.comb(n, y)) * Mint(fac.comb(n - y, z));
        }
      }
    }
    for(ll i = 1; i < x - 1; i += 2){
      for(ll z = 0; z <= x - 1 - i - 1; z++){
        ll y = x - 2 - i - 2 * z;
        if(((i+1)/2) * 2 + y + z <= n){
          res += Mint(fac.comb(n, ((i+1)/2) * 2 + y + z)) * Mint(fac.comb(y + z, y));
        }
      }
    }
    for(ll M = 2 * x; M <= 2 * n; M += 2){
      (res += Mint(fac.comb(n, M / 2)));
    }
    cout << res << endl;
  }
  return 0;
}
