Problem p03134 (C++)

Buggy submission (status: Runtime Error):
#include <bits/stdc++.h>
using namespace std;

#define int long long
#define double long double
#define rep(i, n) for (int i = 0; i < (n); i++)
#define reps(i, n) for (int i = 1; i <= (n); i++)
#define all(x) (x).begin(), (x).end()
#define uniq(x) (x).erase(unique(all(x)), (x).end())
#define bit(n) (1LL << (n))
#define dump(x) cerr << #x " = " << (x) << endl
#define next asdnext
#define prev asdprev
using vint = vector<int>;
using vvint = vector<vint>;
using pint = pair<int, int>;
using vpint = vector<pint>;
template <typename T>
using priority_queue_rev = priority_queue<T, vector<T>, greater<T>>;
constexpr double pi = 3.1415926535897932384626433832795028;
constexpr int dy[8] = {0, 1, 0, -1, 1, 1, -1, -1};
constexpr int dx[8] = {1, 0, -1, 0, 1, -1, -1, 1};
int gcd(int a, int b) {
  while (b) {
    swap(a %= b, b);
  }
  return a;
}
int lcm(int a, int b) { return a / gcd(a, b) * b; }
template <typename T1, typename T2> bool chmax(T1 &a, const T2 &b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <typename T1, typename T2> bool chmin(T1 &a, const T2 &b) {
  if (b < a) {
    a = b;
    return true;
  }
  return false;
}
template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &rhs) {
  os << "(" << rhs.first << ", " << rhs.second << ")";
  return os;
}
template <typename T> ostream &operator<<(ostream &os, const vector<T> &rhs) {
  os << "{";
  for (auto itr = rhs.begin(); itr != rhs.end(); itr++) {
    os << *itr << (next(itr) != rhs.end() ? ", " : "");
  }
  os << "}";
  return os;
}
struct setup {
  static constexpr int PREC = 20;
  setup() {
    cout << fixed << setprecision(PREC);
    cerr << fixed << setprecision(PREC);
  };
} setup;

template <int MOD = 1000000007> struct mod_int {
  int val;
  mod_int(long long val_ = 0)
      : val(val_ >= 0 ? val_ % MOD : (MOD - (-val_) % MOD) % MOD) {}
  bool operator==(const mod_int &rhs) const { return val == rhs.val; }
  bool operator!=(const mod_int &rhs) const {
    return std::rel_ops::operator!=(*this, rhs);
  }
  mod_int &operator+=(const mod_int &rhs) {
    if ((val += rhs.val) >= MOD) {
      val -= MOD;
    }
    return *this;
  }
  mod_int &operator-=(const mod_int &rhs) {
    if ((val += MOD - rhs.val) >= MOD) {
      val -= MOD;
    }
    return *this;
  }
  mod_int &operator*=(const mod_int &rhs) {
    val = (int)((long long)val * rhs.val % MOD);
    return *this;
  }
  mod_int &operator/=(const mod_int &rhs) { return *this *= rhs.inv(); }
  mod_int operator+() const { return *this; }
  mod_int operator-() const { return mod_int(-val); }
  mod_int operator++() { return *this += 1; }
  mod_int operator--() { return *this -= 1; }
  mod_int operator++(signed) {
    const mod_int ret(*this);
    ++*this;
    return ret;
  }
  mod_int operator--(signed) {
    const mod_int ret(*this);
    --*this;
    return ret;
  }
  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; }
  mod_int inv() const {
    int a = MOD, b = val, u = 0, v = 1;
    while (b > 0) {
      int t = a / b;
      std::swap(a -= t * b, b);
      std::swap(u -= t * v, v);
    }
    return mod_int(u);
  }
  mod_int pow(long long n) const {
    if (n < 0) {
      return pow(-n).inv();
    }
    mod_int ret = 1, mul = *this;
    while (n > 0) {
      if (n & 1) {
        ret *= mul;
      }
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }
  friend std::istream &operator>>(std::istream &is, mod_int &rhs) {
    long long v;
    is >> v;
    rhs = v;
    return is;
  }
  friend std::ostream &operator<<(std::ostream &os, const mod_int &rhs) {
    return os << rhs.val;
  }
  struct combination {
    std::vector<mod_int> fact{1, 1}, f_inv{1, 1}, inv{0, 1};
    void calc(int n) {
      while (fact.size() <= n) {
        int i = fact.size();
        fact.push_back(fact[i - 1] * i);
        inv.push_back(-inv[MOD % i] * (MOD / i));
        f_inv.push_back(f_inv[i - 1] * inv[i]);
      }
    }
    mod_int P(int n, int r) {
      return r < 0 || n < r ? 0 : (calc(n), fact[n] * f_inv[n - r]);
    }
    mod_int C(int n, int r) {
      return r < 0 || n < r ? 0 : (calc(n), fact[n] * f_inv[r] * f_inv[n - r]);
    }
    mod_int H(int n, int r) { return C(n + r - 1, r); }
  };
};

string S;
int N;
using mint = mod_int<998244353>;
mint dp[2200][2200];
signed main() {
  cin >> S;
  N = S.length();
  vint rlim(2 * N), blim(2 * N);
  rep(i, N) {
    if (S[i] == '0') {
      rlim[i + 1] = rlim[i] + 2, blim[i + 1] = blim[i];
    }
    if (S[i] == '1') {
      rlim[i + 1] = rlim[i] + 1, blim[i + 1] = blim[i] + 1;
    }
    if (S[i] == '2') {
      rlim[i + 1] = rlim[i], blim[i + 1] = blim[i] + 2;
    }
  }
  rep(i, N) { rlim[i + N + 1] = rlim[i + N], blim[i + N + 1] = blim[i + N]; }
  dp[0][0] = 1;
  reps(i, 2 * N) {
    for (int j = 0; j <= 2 * N; j++) {
      if (j > rlim[i] || i - j > blim[i]) {
        continue;
      }
      dp[i][j] = dp[i - 1][j];
      if (j != 0) {
        dp[i][j] += dp[i - 1][j - 1];
      }
    }
  }
  cout << dp[2 * N][rlim[2 * N]] << endl;
}

Fixed submission:
#include <bits/stdc++.h>
using namespace std;

#define int long long
#define double long double
#define rep(i, n) for (int i = 0; i < (n); i++)
#define reps(i, n) for (int i = 1; i <= (n); i++)
#define all(x) (x).begin(), (x).end()
#define uniq(x) (x).erase(unique(all(x)), (x).end())
#define bit(n) (1LL << (n))
#define dump(x) cerr << #x " = " << (x) << endl
#define next asdnext
#define prev asdprev
using vint = vector<int>;
using vvint = vector<vint>;
using pint = pair<int, int>;
using vpint = vector<pint>;
template <typename T>
using priority_queue_rev = priority_queue<T, vector<T>, greater<T>>;
constexpr double pi = 3.1415926535897932384626433832795028;
constexpr int dy[8] = {0, 1, 0, -1, 1, 1, -1, -1};
constexpr int dx[8] = {1, 0, -1, 0, 1, -1, -1, 1};
int gcd(int a, int b) {
  while (b) {
    swap(a %= b, b);
  }
  return a;
}
int lcm(int a, int b) { return a / gcd(a, b) * b; }
template <typename T1, typename T2> bool chmax(T1 &a, const T2 &b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <typename T1, typename T2> bool chmin(T1 &a, const T2 &b) {
  if (b < a) {
    a = b;
    return true;
  }
  return false;
}
template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &rhs) {
  os << "(" << rhs.first << ", " << rhs.second << ")";
  return os;
}
template <typename T> ostream &operator<<(ostream &os, const vector<T> &rhs) {
  os << "{";
  for (auto itr = rhs.begin(); itr != rhs.end(); itr++) {
    os << *itr << (next(itr) != rhs.end() ? ", " : "");
  }
  os << "}";
  return os;
}
struct setup {
  static constexpr int PREC = 20;
  setup() {
    cout << fixed << setprecision(PREC);
    cerr << fixed << setprecision(PREC);
  };
} setup;

template <int MOD = 1000000007> struct mod_int {
  int val;
  mod_int(long long val_ = 0)
      : val(val_ >= 0 ? val_ % MOD : (MOD - (-val_) % MOD) % MOD) {}
  bool operator==(const mod_int &rhs) const { return val == rhs.val; }
  bool operator!=(const mod_int &rhs) const {
    return std::rel_ops::operator!=(*this, rhs);
  }
  mod_int &operator+=(const mod_int &rhs) {
    if ((val += rhs.val) >= MOD) {
      val -= MOD;
    }
    return *this;
  }
  mod_int &operator-=(const mod_int &rhs) {
    if ((val += MOD - rhs.val) >= MOD) {
      val -= MOD;
    }
    return *this;
  }
  mod_int &operator*=(const mod_int &rhs) {
    val = (int)((long long)val * rhs.val % MOD);
    return *this;
  }
  mod_int &operator/=(const mod_int &rhs) { return *this *= rhs.inv(); }
  mod_int operator+() const { return *this; }
  mod_int operator-() const { return mod_int(-val); }
  mod_int operator++() { return *this += 1; }
  mod_int operator--() { return *this -= 1; }
  mod_int operator++(signed) {
    const mod_int ret(*this);
    ++*this;
    return ret;
  }
  mod_int operator--(signed) {
    const mod_int ret(*this);
    --*this;
    return ret;
  }
  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; }
  mod_int inv() const {
    int a = MOD, b = val, u = 0, v = 1;
    while (b > 0) {
      int t = a / b;
      std::swap(a -= t * b, b);
      std::swap(u -= t * v, v);
    }
    return mod_int(u);
  }
  mod_int pow(long long n) const {
    if (n < 0) {
      return pow(-n).inv();
    }
    mod_int ret = 1, mul = *this;
    while (n > 0) {
      if (n & 1) {
        ret *= mul;
      }
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }
  friend std::istream &operator>>(std::istream &is, mod_int &rhs) {
    long long v;
    is >> v;
    rhs = v;
    return is;
  }
  friend std::ostream &operator<<(std::ostream &os, const mod_int &rhs) {
    return os << rhs.val;
  }
  struct combination {
    std::vector<mod_int> fact{1, 1}, f_inv{1, 1}, inv{0, 1};
    void calc(int n) {
      while (fact.size() <= n) {
        int i = fact.size();
        fact.push_back(fact[i - 1] * i);
        inv.push_back(-inv[MOD % i] * (MOD / i));
        f_inv.push_back(f_inv[i - 1] * inv[i]);
      }
    }
    mod_int P(int n, int r) {
      return r < 0 || n < r ? 0 : (calc(n), fact[n] * f_inv[n - r]);
    }
    mod_int C(int n, int r) {
      return r < 0 || n < r ? 0 : (calc(n), fact[n] * f_inv[r] * f_inv[n - r]);
    }
    mod_int H(int n, int r) { return C(n + r - 1, r); }
  };
};

string S;
int N;
using mint = mod_int<998244353>;
mint dp[4400][4400];
signed main() {
  cin >> S;
  N = S.length();
  vint rlim(2 * N), blim(2 * N);
  rep(i, N) {
    if (S[i] == '0') {
      rlim[i + 1] = rlim[i] + 2, blim[i + 1] = blim[i];
    }
    if (S[i] == '1') {
      rlim[i + 1] = rlim[i] + 1, blim[i + 1] = blim[i] + 1;
    }
    if (S[i] == '2') {
      rlim[i + 1] = rlim[i], blim[i + 1] = blim[i] + 2;
    }
  }
  rep(i, N) { rlim[i + N + 1] = rlim[i + N], blim[i + N + 1] = blim[i + N]; }
  dp[0][0] = 1;
  reps(i, 2 * N) {
    for (int j = 0; j <= 2 * N; j++) {
      if (j > rlim[i] || i - j > blim[i]) {
        continue;
      }
      dp[i][j] = dp[i - 1][j];
      if (j != 0) {
        dp[i][j] += dp[i - 1][j - 1];
      }
    }
  }
  cout << dp[2 * N][rlim[2 * N]] << endl;
}