Problem p02662 (C++) — buggy submission, verdict: Time Limit Exceeded

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

#include <bits/stdc++.h>
using namespace std;
using ll = long long;

#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")

#define VI vector<int>
#define G(size_1) vector<vector<int>>(size_1, vector<int>())
#define SZ(x) ((int)(x).size())
#define READ                                                                   \\
  ({                                                                           \\
    int t;                                                                     \\
    cin >> t;                                                                  \\
    t;                                                                         \\
  })
#define PII pair<int, int>

#define FOR(i, _begin, _end)                                                   \\
  for (__typeof(_end) end = _end, begin = _begin,                              \\
                      i = (begin) - ((begin) > (end));                         \\
       i != (end) - ((begin) > (end)); i += 1 - 2 * ((begin) > (end)))
#define REP(i, end) for (__typeof(end) i = 0, _len = (end); i < (_len); i += 1)
#define ALL(x) (x).begin(), (x).end()
#define F first
#define S second
#define y0 y3487465
#define y1 y8687969
#define j0 j1347829
#define j1 j234892
#define MOD(x, m) ((((x) % (m)) + (m)) % (m))
#define BIT(n) (1LL << (n))
#define UNIQUE(v) v.erase(unique(v.begin(), v.end()), v.end());
#define EB emplace_back
#define PB push_back
#define fcout cout << fixed << setprecision(12)
#define fcerr cerr << fixed << setprecision(12)
#define print(x) cout << (x) << endl
#define fprint(x) cout << fixed << setprecision(12) << (x) << endl
#define BYE(a)                                                                 \\
  do {                                                                         \\
    cout << (a) << endl;                                                       \\
    return;                                                                    \\
  } while (false)

#ifdef DEBUG
#define ERR(args...)                                                           \\
  {                                                                            \\
    string _s = #args;                                                         \\
    replace(_s.begin(), _s.end(), ',', ' ');                                   \\
    stringstream _ss(_s);                                                      \\
    istream_iterator<string> _it(_ss);                                         \\
    _err(cerr, _it, args);                                                     \\
  }
#define DBG(x) cerr << #x << " is " << x << endl;
#else
#define DBG(x) {};
#define ERR(args...) {};
#endif
void _err(std::ostream &cerr, istream_iterator<string> it) { cerr << endl; }
template <typename T, typename... Args>
void _err(std::ostream &cerr, istream_iterator<string> it, T a, Args... args) {
  cerr << *it << " = " << a << "  ";
  _err(cerr, ++it, args...);
}

const double pi = 2 * acos(.0);
const int inf = 0x3f3f3f3f;
const ll mod = (ll)(1e9) + 7;

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 (b < a) {
    a = b;
    return 1;
  }
  return 0;
}

template <typename T> istream &operator>>(istream &is, vector<T> &V) {
  for (auto &&ele : V)
    is >> ele;
  return is;
}

template <typename T> ostream &operator<<(ostream &os, const vector<T> V) {
  os << "[";
  int cnt = 0;
  T curr;
  if (!V.empty()) {
    for (int i = 0; i < V.size() - 1; ++i) {
      if (V[i] == curr)
        cnt++;
      else
        cnt = 0;
      if (cnt == 4)
        os << "... ";
      if (cnt < 4)
        os << i << ":" << V[i] << " ";
      curr = V[i];
    }
    os << V.size() - 1 << ":" << V.back();
  }
  os << "]\\n";
  return os;
}

template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> P) {
  os << "(";
  os << P.first << "," << P.second;
  os << ")";
  return os;
}

template <typename T, typename U>
ostream &operator<<(ostream &os, const set<T, U> V) {
  os << "{";
  if (!V.empty()) {
    auto it = V.begin();
    for (int i = 0; i < V.size() - 1; ++i) {
      os << *it << " ";
      it++;
    }
    os << *it;
  }
  os << "}\\n";
  return os;
}

template <typename K, typename H, typename P>
ostream &operator<<(ostream &os, const unordered_set<K, H, P> V) {
  os << "{";
  if (!V.empty()) {
    auto it = V.begin();
    for (int i = 0; i < V.size() - 1; ++i) {
      os << *it << " ";
      it++;
    }
    os << *it;
  }
  os << "}\\n";
  return os;
}

template <typename K, typename C>
ostream &operator<<(ostream &os, const multiset<K, C> V) {
  os << "{";
  if (!V.empty()) {
    auto it = V.begin();
    for (int i = 0; i < V.size() - 1; ++i) {
      os << *it << " ";
      it++;
    }
    os << *it;
  }
  os << "}";
  return os;
}

template <typename K, typename T, typename C>
ostream &operator<<(ostream &os, const map<K, T, C> V) {
  os << "{";
  if (!V.empty()) {
    auto it = V.begin();
    for (int i = 0; i < V.size() - 1; ++i) {
      os << "(";
      os << it->first << "," << it->second;
      os << ") ";
      it++;
    }
    os << "(";
    os << it->first << "," << it->second;
    os << ")";
  }
  os << "}\\n";
  return os;
}

template <typename K, typename T, typename C>
ostream &operator<<(ostream &os, const unordered_map<K, T, C> V) {
  os << "{";
  if (!V.empty()) {
    auto it = V.begin();
    for (int i = 0; i < V.size() - 1; ++i) {
      os << "(";
      os << it->first << "," << it->second;
      os << ") ";
      it++;
    }
    os << "(";
    os << it->first << "," << it->second;
    os << ")";
  }
  os << "}\\n";
  return os;
}

template <typename T> ostream &operator<<(ostream &os, const deque<T> V) {
  os << "[";
  if (!V.empty()) {
    for (int i = 0; i < V.size() - 1; ++i) {
      os << V[i] << "->";
    }
    if (!V.empty())
      os << V.back();
  }
  os << "]\\n";
  return os;
};

template <typename T, typename Cont, typename Comp>
ostream &operator<<(ostream &os, const priority_queue<T, Cont, Comp> V) {
  priority_queue<T, Cont, Comp> _V = V;
  os << "[";
  if (!_V.empty()) {
    while (_V.size() > 1) {
      os << _V.top() << "->";
      _V.pop();
    }
    os << _V.top();
  }
  os << "]\\n";
  return os;
};

template <class F> struct y_combinator {
  F f; // the lambda will be stored here

  // a forwarding operator():
  template <class... Args> decltype(auto) operator()(Args &&...args) const {
    // we pass ourselves to f, then the arguments.
    // the lambda should take the first argument as `auto&& recurse` or similar.
    return f(*this, std::forward<Args>(args)...);
  }
};
// helper function that deduces the type of the lambda:
template <class F> y_combinator<std::decay_t<F>> recursive(F &&f) {
  return {std::forward<F>(f)};
}

struct hash_pair {
  template <class T1, class T2> size_t operator()(const pair<T1, T2> &p) const {
    auto hash1 = hash<T1>{}(p.first);
    auto hash2 = hash<T2>{}(p.second);
    return hash1 ^ hash2;
  }
};

template <typename T, typename U> std::vector<T> multi_vector(int n, U v) {
  return std::vector<T>(n, v);
}

template <typename U, typename... Args> auto multi_vector(int n, Args... args) {
  auto val = multi_vector<U>(std::forward<Args>(args)...);
  return std::vector<decltype(val)>(n, std::move(val));
}
template <signed M, unsigned T> struct mod_int {
  constexpr static signed MODULO = M;
  constexpr static unsigned TABLE_SIZE = T;

  signed x;

  mod_int() : x(0) {}

  mod_int(long long y)
      : x(static_cast<signed>(y >= 0 ? y % MODULO : MODULO - (-y) % MODULO)) {}

  mod_int(int y) : x(y >= 0 ? y % MODULO : MODULO - (-y) % MODULO) {}

  explicit operator int() const { return x; }

  explicit operator long long() const { return x; }

  explicit operator double() const { return x; }

  mod_int &operator+=(const mod_int &rhs) {
    if ((x += rhs.x) >= MODULO)
      x -= MODULO;
    return *this;
  }

  mod_int &operator-=(const mod_int &rhs) {
    if ((x += MODULO - rhs.x) >= MODULO)
      x -= MODULO;
    return *this;
  }

  mod_int &operator*=(const mod_int &rhs) {
    x = static_cast<signed>(1LL * x * rhs.x % MODULO);
    return *this;
  }

  mod_int &operator/=(const mod_int &rhs) {
    x = static_cast<signed>((1LL * x * rhs.inv().x) % MODULO);
    return *this;
  }

  mod_int operator-() const { return mod_int(-x); }

  mod_int operator+(const mod_int &rhs) const { return mod_int(*this) += rhs; }

  mod_int operator-(const mod_int &rhs) const { return mod_int(*this) -= rhs; }

  mod_int operator*(const mod_int &rhs) const { return mod_int(*this) *= rhs; }

  mod_int operator/(const mod_int &rhs) const { return mod_int(*this) /= rhs; }

  bool operator<(const mod_int &rhs) const { return x < rhs.x; }

  mod_int inv() const {
    assert(x != 0);
    if (x <= static_cast<signed>(TABLE_SIZE)) {
      if (_inv[1].x == 0)
        prepare();
      return _inv[x];
    } else {
      signed a = x, b = MODULO, u = 1, v = 0, t;
      while (b) {
        t = a / b;
        a -= t * b;
        std::swap(a, b);
        u -= t * v;
        std::swap(u, v);
      }
      return mod_int(u);
    }
  }

  mod_int pow(long long t) const {
    assert(!(x == 0 && t == 0));
    mod_int e = *this, res = mod_int(1);
    for (; t; e *= e, t >>= 1)
      if (t & 1)
        res *= e;
    return res;
  }

  mod_int fact() {
    if (_fact[0].x == 0)
      prepare();
    return _fact[x];
  }

  mod_int inv_fact() {
    if (_fact[0].x == 0)
      prepare();
    return _inv_fact[x];
  }

  mod_int choose(mod_int y) {
    assert(y.x <= x);
    return this->fact() * y.inv_fact() * mod_int(x - y.x).inv_fact();
  }

  static mod_int _inv[TABLE_SIZE + 1];

  static mod_int _fact[TABLE_SIZE + 1];

  static mod_int _inv_fact[TABLE_SIZE + 1];

  static void prepare() {
    _inv[1] = 1;
    for (int i = 2; i <= (int)TABLE_SIZE; ++i) {
      _inv[i] = 1LL * _inv[MODULO % i].x * (MODULO - MODULO / i) % MODULO;
    }
    _fact[0] = 1;
    for (unsigned i = 1; i <= TABLE_SIZE; ++i) {
      _fact[i] = _fact[i - 1] * int(i);
    }
    _inv_fact[TABLE_SIZE] = _fact[TABLE_SIZE].inv();
    for (int i = (int)TABLE_SIZE - 1; i >= 0; --i) {
      _inv_fact[i] = _inv_fact[i + 1] * (i + 1);
    }
  }
};

template <int M, unsigned F>
std::ostream &operator<<(std::ostream &os, const mod_int<M, F> &rhs) {
  return os << rhs.x;
}

template <int M, unsigned F>
std::istream &operator>>(std::istream &is, mod_int<M, F> &rhs) {
  long long s;
  is >> s;
  rhs = mod_int<M, F>(s);
  return is;
}

template <int M, unsigned F> mod_int<M, F> mod_int<M, F>::_inv[TABLE_SIZE + 1];

template <int M, unsigned F> mod_int<M, F> mod_int<M, F>::_fact[TABLE_SIZE + 1];

template <int M, unsigned F>
mod_int<M, F> mod_int<M, F>::_inv_fact[TABLE_SIZE + 1];

template <int M, unsigned F>
bool operator==(const mod_int<M, F> &lhs, const mod_int<M, F> &rhs) {
  return lhs.x == rhs.x;
}

template <int M, unsigned F>
bool operator!=(const mod_int<M, F> &lhs, const mod_int<M, F> &rhs) {
  return !(lhs == rhs);
}

const int MF = 1000010;
const int MOD = 998244353;
;

using mint = mod_int<MOD, MF>;

mint binom(int n, int r) {
  return (r < 0 || r > n || n < 0) ? 0 : mint(n).choose(r);
}

mint fact(int n) { return mint(n).fact(); }

mint inv_fact(int n) { return mint(n).inv_fact(); }
class FKnapsackForAllSubsets {
public:
  void solve(std::istream &cin, std::ostream &cout, std::ostream &cerr) {
    int N, S;
    cin >> N >> S;
    VI a(N);
    cin >> a;
    auto dp = multi_vector<mint>(3050, 3050, 0);
    dp[0][0] = 1;
    ERR(a)
    REP(i, N) FOR(s, 3040, 0) {
      dp[i + 1][s] = dp[i][s] * 2;
      if (s >= a[i])
        dp[i + 1][s] = dp[i + 1][s] + dp[i][s - a[i]];
    }
    mint ans = 0;
    //    REP(i,10)REP(j,10)cout << i << " " << j << " " << dp[i][j]<< endl;
    print(dp[N][S]);
  }
};

#undef int
int main() {

  FKnapsackForAllSubsets solver;
  std::istream &in(std::cin);
  std::ostream &out(std::cout);
  std::ostringstream err;
  in.tie(0);
  ios::sync_with_stdio(0);
  solver.solve(in, out, err);
  return 0;
}


Error: TLE

Fixed submission:

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

#include <bits/stdc++.h>
using namespace std;
using ll = long long;

// #pragma GCC optimize("O3")
// #pragma GCC optimize("unroll-loops")

#define VI vector<int>
#define G(size_1) vector<vector<int>>(size_1, vector<int>())
#define SZ(x) ((int)(x).size())
#define READ                                                                   \\
  ({                                                                           \\
    int t;                                                                     \\
    cin >> t;                                                                  \\
    t;                                                                         \\
  })
#define PII pair<int, int>

#define FOR(i, _begin, _end)                                                   \\
  for (__typeof(_end) end = _end, begin = _begin,                              \\
                      i = (begin) - ((begin) > (end));                         \\
       i != (end) - ((begin) > (end)); i += 1 - 2 * ((begin) > (end)))
#define REP(i, end) for (__typeof(end) i = 0, _len = (end); i < (_len); i += 1)
#define ALL(x) (x).begin(), (x).end()
#define F first
#define S second
#define y0 y3487465
#define y1 y8687969
#define j0 j1347829
#define j1 j234892
#define MOD(x, m) ((((x) % (m)) + (m)) % (m))
#define BIT(n) (1LL << (n))
#define UNIQUE(v) v.erase(unique(v.begin(), v.end()), v.end());
#define EB emplace_back
#define PB push_back
#define fcout cout << fixed << setprecision(12)
#define fcerr cerr << fixed << setprecision(12)
#define print(x) cout << (x) << endl
#define fprint(x) cout << fixed << setprecision(12) << (x) << endl
#define BYE(a)                                                                 \\
  do {                                                                         \\
    cout << (a) << endl;                                                       \\
    return;                                                                    \\
  } while (false)

#ifdef DEBUG
#define ERR(args...)                                                           \\
  {                                                                            \\
    string _s = #args;                                                         \\
    replace(_s.begin(), _s.end(), ',', ' ');                                   \\
    stringstream _ss(_s);                                                      \\
    istream_iterator<string> _it(_ss);                                         \\
    _err(cerr, _it, args);                                                     \\
  }
#define DBG(x) cerr << #x << " is " << x << endl;
#else
#define DBG(x) {};
#define ERR(args...) {};
#endif
void _err(std::ostream &cerr, istream_iterator<string> it) { cerr << endl; }
template <typename T, typename... Args>
void _err(std::ostream &cerr, istream_iterator<string> it, T a, Args... args) {
  cerr << *it << " = " << a << "  ";
  _err(cerr, ++it, args...);
}

const double pi = 2 * acos(.0);
const int inf = 0x3f3f3f3f;
const ll mod = (ll)(1e9) + 7;

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 (b < a) {
    a = b;
    return 1;
  }
  return 0;
}

template <typename T> istream &operator>>(istream &is, vector<T> &V) {
  for (auto &&ele : V)
    is >> ele;
  return is;
}

template <typename T> ostream &operator<<(ostream &os, const vector<T> V) {
  os << "[";
  int cnt = 0;
  T curr;
  if (!V.empty()) {
    for (int i = 0; i < V.size() - 1; ++i) {
      if (V[i] == curr)
        cnt++;
      else
        cnt = 0;
      if (cnt == 4)
        os << "... ";
      if (cnt < 4)
        os << i << ":" << V[i] << " ";
      curr = V[i];
    }
    os << V.size() - 1 << ":" << V.back();
  }
  os << "]\\n";
  return os;
}

template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> P) {
  os << "(";
  os << P.first << "," << P.second;
  os << ")";
  return os;
}

template <typename T, typename U>
ostream &operator<<(ostream &os, const set<T, U> V) {
  os << "{";
  if (!V.empty()) {
    auto it = V.begin();
    for (int i = 0; i < V.size() - 1; ++i) {
      os << *it << " ";
      it++;
    }
    os << *it;
  }
  os << "}\\n";
  return os;
}

template <typename K, typename H, typename P>
ostream &operator<<(ostream &os, const unordered_set<K, H, P> V) {
  os << "{";
  if (!V.empty()) {
    auto it = V.begin();
    for (int i = 0; i < V.size() - 1; ++i) {
      os << *it << " ";
      it++;
    }
    os << *it;
  }
  os << "}\\n";
  return os;
}

template <typename K, typename C>
ostream &operator<<(ostream &os, const multiset<K, C> V) {
  os << "{";
  if (!V.empty()) {
    auto it = V.begin();
    for (int i = 0; i < V.size() - 1; ++i) {
      os << *it << " ";
      it++;
    }
    os << *it;
  }
  os << "}";
  return os;
}

template <typename K, typename T, typename C>
ostream &operator<<(ostream &os, const map<K, T, C> V) {
  os << "{";
  if (!V.empty()) {
    auto it = V.begin();
    for (int i = 0; i < V.size() - 1; ++i) {
      os << "(";
      os << it->first << "," << it->second;
      os << ") ";
      it++;
    }
    os << "(";
    os << it->first << "," << it->second;
    os << ")";
  }
  os << "}\\n";
  return os;
}

template <typename K, typename T, typename C>
ostream &operator<<(ostream &os, const unordered_map<K, T, C> V) {
  os << "{";
  if (!V.empty()) {
    auto it = V.begin();
    for (int i = 0; i < V.size() - 1; ++i) {
      os << "(";
      os << it->first << "," << it->second;
      os << ") ";
      it++;
    }
    os << "(";
    os << it->first << "," << it->second;
    os << ")";
  }
  os << "}\\n";
  return os;
}

template <typename T> ostream &operator<<(ostream &os, const deque<T> V) {
  os << "[";
  if (!V.empty()) {
    for (int i = 0; i < V.size() - 1; ++i) {
      os << V[i] << "->";
    }
    if (!V.empty())
      os << V.back();
  }
  os << "]\\n";
  return os;
};

template <typename T, typename Cont, typename Comp>
ostream &operator<<(ostream &os, const priority_queue<T, Cont, Comp> V) {
  priority_queue<T, Cont, Comp> _V = V;
  os << "[";
  if (!_V.empty()) {
    while (_V.size() > 1) {
      os << _V.top() << "->";
      _V.pop();
    }
    os << _V.top();
  }
  os << "]\\n";
  return os;
};

template <class F> struct y_combinator {
  F f; // the lambda will be stored here

  // a forwarding operator():
  template <class... Args> decltype(auto) operator()(Args &&...args) const {
    // we pass ourselves to f, then the arguments.
    // the lambda should take the first argument as `auto&& recurse` or similar.
    return f(*this, std::forward<Args>(args)...);
  }
};
// helper function that deduces the type of the lambda:
template <class F> y_combinator<std::decay_t<F>> recursive(F &&f) {
  return {std::forward<F>(f)};
}

struct hash_pair {
  template <class T1, class T2> size_t operator()(const pair<T1, T2> &p) const {
    auto hash1 = hash<T1>{}(p.first);
    auto hash2 = hash<T2>{}(p.second);
    return hash1 ^ hash2;
  }
};

template <typename T, typename U> std::vector<T> multi_vector(int n, U v) {
  return std::vector<T>(n, v);
}

template <typename U, typename... Args> auto multi_vector(int n, Args... args) {
  auto val = multi_vector<U>(std::forward<Args>(args)...);
  return std::vector<decltype(val)>(n, std::move(val));
}
template <signed M, unsigned T> struct mod_int {
  constexpr static signed MODULO = M;
  constexpr static unsigned TABLE_SIZE = T;

  signed x;

  mod_int() : x(0) {}

  mod_int(long long y)
      : x(static_cast<signed>(y >= 0 ? y % MODULO : MODULO - (-y) % MODULO)) {}

  mod_int(int y) : x(y >= 0 ? y % MODULO : MODULO - (-y) % MODULO) {}

  explicit operator int() const { return x; }

  explicit operator long long() const { return x; }

  explicit operator double() const { return x; }

  mod_int &operator+=(const mod_int &rhs) {
    if ((x += rhs.x) >= MODULO)
      x -= MODULO;
    return *this;
  }

  mod_int &operator-=(const mod_int &rhs) {
    if ((x += MODULO - rhs.x) >= MODULO)
      x -= MODULO;
    return *this;
  }

  mod_int &operator*=(const mod_int &rhs) {
    x = static_cast<signed>(1LL * x * rhs.x % MODULO);
    return *this;
  }

  mod_int &operator/=(const mod_int &rhs) {
    x = static_cast<signed>((1LL * x * rhs.inv().x) % MODULO);
    return *this;
  }

  mod_int operator-() const { return mod_int(-x); }

  mod_int operator+(const mod_int &rhs) const { return mod_int(*this) += rhs; }

  mod_int operator-(const mod_int &rhs) const { return mod_int(*this) -= rhs; }

  mod_int operator*(const mod_int &rhs) const { return mod_int(*this) *= rhs; }

  mod_int operator/(const mod_int &rhs) const { return mod_int(*this) /= rhs; }

  bool operator<(const mod_int &rhs) const { return x < rhs.x; }

  mod_int inv() const {
    assert(x != 0);
    if (x <= static_cast<signed>(TABLE_SIZE)) {
      if (_inv[1].x == 0)
        prepare();
      return _inv[x];
    } else {
      signed a = x, b = MODULO, u = 1, v = 0, t;
      while (b) {
        t = a / b;
        a -= t * b;
        std::swap(a, b);
        u -= t * v;
        std::swap(u, v);
      }
      return mod_int(u);
    }
  }

  mod_int pow(long long t) const {
    assert(!(x == 0 && t == 0));
    mod_int e = *this, res = mod_int(1);
    for (; t; e *= e, t >>= 1)
      if (t & 1)
        res *= e;
    return res;
  }

  mod_int fact() {
    if (_fact[0].x == 0)
      prepare();
    return _fact[x];
  }

  mod_int inv_fact() {
    if (_fact[0].x == 0)
      prepare();
    return _inv_fact[x];
  }

  mod_int choose(mod_int y) {
    assert(y.x <= x);
    return this->fact() * y.inv_fact() * mod_int(x - y.x).inv_fact();
  }

  static mod_int _inv[TABLE_SIZE + 1];

  static mod_int _fact[TABLE_SIZE + 1];

  static mod_int _inv_fact[TABLE_SIZE + 1];

  static void prepare() {
    _inv[1] = 1;
    for (int i = 2; i <= (int)TABLE_SIZE; ++i) {
      _inv[i] = 1LL * _inv[MODULO % i].x * (MODULO - MODULO / i) % MODULO;
    }
    _fact[0] = 1;
    for (unsigned i = 1; i <= TABLE_SIZE; ++i) {
      _fact[i] = _fact[i - 1] * int(i);
    }
    _inv_fact[TABLE_SIZE] = _fact[TABLE_SIZE].inv();
    for (int i = (int)TABLE_SIZE - 1; i >= 0; --i) {
      _inv_fact[i] = _inv_fact[i + 1] * (i + 1);
    }
  }
};

template <int M, unsigned F>
std::ostream &operator<<(std::ostream &os, const mod_int<M, F> &rhs) {
  return os << rhs.x;
}

template <int M, unsigned F>
std::istream &operator>>(std::istream &is, mod_int<M, F> &rhs) {
  long long s;
  is >> s;
  rhs = mod_int<M, F>(s);
  return is;
}

template <int M, unsigned F> mod_int<M, F> mod_int<M, F>::_inv[TABLE_SIZE + 1];

template <int M, unsigned F> mod_int<M, F> mod_int<M, F>::_fact[TABLE_SIZE + 1];

template <int M, unsigned F>
mod_int<M, F> mod_int<M, F>::_inv_fact[TABLE_SIZE + 1];

template <int M, unsigned F>
bool operator==(const mod_int<M, F> &lhs, const mod_int<M, F> &rhs) {
  return lhs.x == rhs.x;
}

template <int M, unsigned F>
bool operator!=(const mod_int<M, F> &lhs, const mod_int<M, F> &rhs) {
  return !(lhs == rhs);
}

const int MF = 1000010;
const int MOD = 998244353;
;

using mint = mod_int<MOD, MF>;

mint binom(int n, int r) {
  return (r < 0 || r > n || n < 0) ? 0 : mint(n).choose(r);
}

mint fact(int n) { return mint(n).fact(); }

mint inv_fact(int n) { return mint(n).inv_fact(); }
class FKnapsackForAllSubsets {
public:
  void solve(std::istream &cin, std::ostream &cout, std::ostream &cerr) {
    int N, S;
    cin >> N >> S;
    VI a(N);
    cin >> a;
    auto dp = multi_vector<mint>(3050, 3050, 0);
    dp[0][0] = 1;
    ERR(a)
    REP(i, N) FOR(s, 3040, 0) FOR(n, 3030, 0) {
      if (s + a[i] < 3030)
        dp[s + a[i]][n + 1] += dp[s][n];
    }
    mint ans = 0;
    ERR(dp[S])
    //    REP(i,10)REP(j,10)cout << i << " " << j << " " << dp[i][j]<< endl;
    FOR(i, 1, N + 1) ans += dp[S][i] * mint(2).pow(N - i);
    print(ans);
  }
};

#undef int
int main() {

  FKnapsackForAllSubsets solver;
  std::istream &in(std::cin);
  std::ostream &out(std::cout);
  std::ostringstream err;
  in.tie(0);
  ios::sync_with_stdio(0);
  solver.solve(in, out, err);
  return 0;
}