Problem p03134 (C++)

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

typedef unsigned long long ull;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef pair<double, double> pdd;
// const ull mod = 1e9 + 7;
const ll mod = 998244353;
#define REP(i, n) for (int i = 0; i < (int)n; ++i)

// debug
#define dump(x) cerr << #x << " = " << (x) << endl;
#define debug(x)                                                               \
  cerr << #x << " = " << (x) << " (L" << __LINE__ << ")"                       \
       << " " << __FILE__ << endl;

template <class S, class T>
ostream &operator<<(ostream &os, const pair<S, T> v) {
  os << "(" << v.first << ", " << v.second << ")";
  return os;
}
template <class T> ostream &operator<<(ostream &os, const vector<T> v) {
  for (int i = 0; i < (int)v.size(); i++) {
    if (i > 0) {
      os << " ";
    }
    os << v[i];
  }
  return os;
}
template <class T> ostream &operator<<(ostream &os, const vector<vector<T>> v) {
  for (int i = 0; i < (int)v.size(); i++) {
    if (i > 0) {
      os << endl;
    }
    os << v[i];
  }
  return os;
}
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;
}

// conversion number to bit
string num2bit(ll num, ll len) {
  string bit = "";
  REP(i, len) { bit += char('0' + (num >> i & 1)); }
  return bit;
}

ll dp[2020][2020];

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);

  string S;
  cin >> S;
  ll N = S.size();

  dp[0][0] = 1;

  ll R = 0, B = 0;
  REP(i, 2 * N) {
    if (i < N) {
      if (S[i] == '0')
        R += 2;
      else if (S[i] == '2')
        B += 2;
      else
        R++, B++;
    }

    REP(j, i + 1) {
      ll idx = j;
      ll jdx = i - j;
      if (idx < R)
        dp[idx + 1][jdx] += dp[idx][jdx];
      dp[idx + 1][jdx] %= mod;
      if (jdx < B)
        dp[idx][jdx + 1] += dp[idx][jdx];
      dp[idx][jdx + 1] %= mod;
    }
  }

  ll res = 0;
  REP(i, 2 * N + 1) {
    res += dp[i][2 * N - i];
    res %= mod;
  }
  cout << res << endl;
  return 0;
}

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

typedef unsigned long long ull;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef pair<double, double> pdd;
// const ull mod = 1e9 + 7;
const ll mod = 998244353;
#define REP(i, n) for (int i = 0; i < (int)n; ++i)

// debug
#define dump(x) cerr << #x << " = " << (x) << endl;
#define debug(x)                                                               \
  cerr << #x << " = " << (x) << " (L" << __LINE__ << ")"                       \
       << " " << __FILE__ << endl;

template <class S, class T>
ostream &operator<<(ostream &os, const pair<S, T> v) {
  os << "(" << v.first << ", " << v.second << ")";
  return os;
}
template <class T> ostream &operator<<(ostream &os, const vector<T> v) {
  for (int i = 0; i < (int)v.size(); i++) {
    if (i > 0) {
      os << " ";
    }
    os << v[i];
  }
  return os;
}
template <class T> ostream &operator<<(ostream &os, const vector<vector<T>> v) {
  for (int i = 0; i < (int)v.size(); i++) {
    if (i > 0) {
      os << endl;
    }
    os << v[i];
  }
  return os;
}
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;
}

// conversion number to bit
string num2bit(ll num, ll len) {
  string bit = "";
  REP(i, len) { bit += char('0' + (num >> i & 1)); }
  return bit;
}

ll dp[4020][4020];

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);

  string S;
  cin >> S;
  ll N = S.size();

  dp[0][0] = 1;

  ll R = 0, B = 0;
  REP(i, 2 * N) {
    if (i < N) {
      if (S[i] == '0')
        R += 2;
      else if (S[i] == '2')
        B += 2;
      else
        R++, B++;
    }

    REP(j, i + 1) {
      ll idx = j;
      ll jdx = i - j;
      if (idx < R)
        dp[idx + 1][jdx] += dp[idx][jdx];
      dp[idx + 1][jdx] %= mod;
      if (jdx < B)
        dp[idx][jdx + 1] += dp[idx][jdx];
      dp[idx][jdx + 1] %= mod;
    }
  }

  ll res = 0;
  REP(i, 2 * N + 1) {
    res += dp[i][2 * N - i];
    res %= mod;
  }
  cout << res << endl;
  return 0;
}