Problem p03118 (C++)

Buggy submission (status: Runtime Error):
#pragma GCC optimize("O3")
#include <bits/stdc++.h>
// #include <ext/pb_ds/assoc_container.hpp>
// using namespace __gnu_pbds;
// gp_hash_table<int, int> mapka;

using namespace std;
#define PB push_back
#define MP make_pair
#define LL long long
#define int LL
#define FOR(i, a, b) for (int i = (a); i <= (b); i++)
#define RE(i, n) FOR(i, 1, n)
#define REP(i, n) FOR(i, 0, (int)(n)-1)
#define R(i, n) REP(i, n)
#define VI vector<int>
#define PII pair<int, int>
#define LD long double
#define FI first
#define SE second
#define st FI
#define nd SE
#define ALL(x) (x).begin(), (x).end()
#define SZ(x) ((int)(x).size())

template <class C> void mini(C &a4, C b4) { a4 = min(a4, b4); }
template <class C> void maxi(C &a4, C b4) { a4 = max(a4, b4); }

template <class TH> void _dbg(const char *sdbg, TH h) {
  cerr << sdbg << '=' << h << endl;
}
template <class TH, class... TA> void _dbg(const char *sdbg, TH h, TA... a) {
  while (*sdbg != ',')
    cerr << *sdbg++;
  cerr << '=' << h << ',';
  _dbg(sdbg + 1, a...);
}

template <class T> ostream &operator<<(ostream &os, vector<T> V) {
  os << "[";
  for (auto vv : V)
    os << vv << ",";
  return os << "]";
}
template <class L, class R> ostream &operator<<(ostream &os, pair<L, R> P) {
  return os << "(" << P.st << "," << P.nd << ")";
}

#ifdef LOCAL
#define debug(...) _dbg(#__VA_ARGS__, __VA_ARGS__)
#else
#define debug(...) (__VA_ARGS__)
#define cerr                                                                   \
  if (0)                                                                       \
  cout
#endif

const int P = 1e9 + 7;
void add(int &a, int b) {
  a += b;
  if (a >= P)
    a -= P;
}
void sub(int &a, int b) {
  a -= b;
  if (a < 0)
    a += P;
}

int mul(int a, int b) { return a * b % P; }
struct war {
  int a, b, c;
  void operator+=(war x) {
    add(a, x.a);
    add(b, x.b);
    add(c, x.c);
  }
  void operator-=(war x) {
    sub(a, x.a);
    sub(b, x.b);
    sub(c, x.c);
  }

  void operator*=(war x) {
    c = mul(c, x.a);
    add(c, mul(a, x.c));
    add(c, mul(b, x.b));

    b = mul(b, x.a);
    add(b, mul(a, x.b));

    a = mul(a, x.a);
  }
};

const int MAX = 1001;
int dp[MAX][3];

war licz1(int x) {
  war res = {0, 1, 0};
  R(i, x - 1) { res -= {0, dp[i + 1][2], 0}; }
  debug(x, res.b * 3 % P);
  return res;
}

war licz2(int x) {
  debug(x);
  if (x == 1) {
    return {(P + 1) / 2, 0, (P - 1) / 2};
  }
  war res = {1, 0, 0};
  res -= licz2(x - 1);
  R(i, 2 * x - 2) {
    war pom = licz1((i + 1) / 2);
    pom *= {0, 1, 0};
    res -= pom;
  }
  return res;
}

int pot(int a, int w) {
  int r = 1;
  while (w) {
    if (w & 1) {
      r = r * a % P;
    }
    w /= 2;
    a = a * a % P;
  }
  return r;
}

int32_t main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout << fixed << setprecision(11);
  cerr << fixed << setprecision(6);

  dp[0][1] = dp[0][0] = 1;
  dp[0][2] = 0;
  R(i, MAX) if (i) R(j, 3) {
    R(k, i) {
      add(dp[i][j], mul(pot(2 * i - 1 + j, P - 2),
                        mul(dp[k][j / 2], dp[i - k - 1][(j + 1) / 2])));
    }
  }
  debug(dp[0][2]);
  debug(dp[1][2] * 3 % P);
  debug(dp[2][2] * 5 % P);
  debug(dp[3][2] * 7 % P);

  int n;
  string z;
  cin >> n >> z;
  R(i, n - 1) if (z[i] == 'X' && z[i + 1] == 'X') {
    cout << "0 0 0\n";
    return 0;
  }
  int ile = 0;
  war res = {1, 0, 0};
  vector<int> x;
  R(i, n) {
    if (z[i] == '-') {
      if (i && z[i - 1] == '-') {
        x.PB(ile);
        ile = 0;
      }
    } else {
      ile++;
    }
  }
  debug(ile, x);
  if (x.empty()) {
    res = licz2(ile);
  } else {
    res *= licz1(ile);
    res *= licz1(x[0]);
    R(i, SZ(x)) if (i) { res *= {dp[x[i]][2], 0, 0}; }
  }
  cout << res.a << " " << res.b << " " << res.c << "\n";
}


Fixed submission:
#pragma GCC optimize("O3")
#include <bits/stdc++.h>
// #include <ext/pb_ds/assoc_container.hpp>
// using namespace __gnu_pbds;
// gp_hash_table<int, int> mapka;

using namespace std;
#define PB push_back
#define MP make_pair
#define LL long long
#define int LL
#define FOR(i, a, b) for (int i = (a); i <= (b); i++)
#define RE(i, n) FOR(i, 1, n)
#define REP(i, n) FOR(i, 0, (int)(n)-1)
#define R(i, n) REP(i, n)
#define VI vector<int>
#define PII pair<int, int>
#define LD long double
#define FI first
#define SE second
#define st FI
#define nd SE
#define ALL(x) (x).begin(), (x).end()
#define SZ(x) ((int)(x).size())

template <class C> void mini(C &a4, C b4) { a4 = min(a4, b4); }
template <class C> void maxi(C &a4, C b4) { a4 = max(a4, b4); }

template <class TH> void _dbg(const char *sdbg, TH h) {
  cerr << sdbg << '=' << h << endl;
}
template <class TH, class... TA> void _dbg(const char *sdbg, TH h, TA... a) {
  while (*sdbg != ',')
    cerr << *sdbg++;
  cerr << '=' << h << ',';
  _dbg(sdbg + 1, a...);
}

template <class T> ostream &operator<<(ostream &os, vector<T> V) {
  os << "[";
  for (auto vv : V)
    os << vv << ",";
  return os << "]";
}
template <class L, class R> ostream &operator<<(ostream &os, pair<L, R> P) {
  return os << "(" << P.st << "," << P.nd << ")";
}

#ifdef LOCAL
#define debug(...) _dbg(#__VA_ARGS__, __VA_ARGS__)
#else
#define debug(...) (__VA_ARGS__)
#define cerr                                                                   \
  if (0)                                                                       \
  cout
#endif

const int P = 1e9 + 7;
void add(int &a, int b) {
  a += b;
  if (a >= P)
    a -= P;
}
void sub(int &a, int b) {
  a -= b;
  if (a < 0)
    a += P;
}

int mul(int a, int b) { return a * b % P; }
struct war {
  int a, b, c;
  void operator+=(war x) {
    add(a, x.a);
    add(b, x.b);
    add(c, x.c);
  }
  void operator-=(war x) {
    sub(a, x.a);
    sub(b, x.b);
    sub(c, x.c);
  }

  void operator*=(war x) {
    c = mul(c, x.a);
    add(c, mul(a, x.c));
    add(c, mul(b, x.b));

    b = mul(b, x.a);
    add(b, mul(a, x.b));

    a = mul(a, x.a);
  }
};

const int MAX = 1001;
int dp[MAX][3];

war licz1(int x) {
  war res = {0, 1, 0};
  R(i, x - 1) { res -= {0, dp[i + 1][2], 0}; }
  debug(x, res.b * 3 % P);
  return res;
}

war licz2(int x) {
  debug(x);
  if (x == 1) {
    return {(P + 1) / 2, 0, (P - 1) / 2};
  }
  war res = {1, 0, 0};
  res -= licz2(x - 1);
  R(i, 2 * x - 2) {
    war pom = licz1((i + 1) / 2);
    pom *= {0, 1, 0};
    res -= pom;
  }
  return res;
}

int pot(int a, int w) {
  int r = 1;
  while (w) {
    if (w & 1) {
      r = r * a % P;
    }
    w /= 2;
    a = a * a % P;
  }
  return r;
}

int32_t main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout << fixed << setprecision(11);
  cerr << fixed << setprecision(6);

  dp[0][1] = dp[0][0] = 1;
  dp[0][2] = 0;
  R(i, MAX) if (i) R(j, 3) {
    R(k, i) {
      add(dp[i][j], mul(pot(2 * i - 1 + j, P - 2),
                        mul(dp[k][j / 2], dp[i - k - 1][(j + 1) / 2])));
    }
  }
  debug(dp[0][2]);
  debug(dp[1][2] * 3 % P);
  debug(dp[2][2] * 5 % P);
  debug(dp[3][2] * 7 % P);

  int n;
  string z;
  cin >> n >> z;
  if (n == 1 && z[0] == '-') {
    cout << (P + 1) / 2 << " 0 " << (P + 1) / 2 << "\n";
    return 0;
  }
  R(i, n - 1) if (z[i] == 'X' && z[i + 1] == 'X') {
    cout << "0 0 0\n";
    return 0;
  }
  int ile = 0;
  war res = {1, 0, 0};
  vector<int> x;
  R(i, n) {
    if (z[i] == '-') {
      if (i && z[i - 1] == '-') {
        x.PB(ile);
        ile = 0;
      }
    } else {
      ile++;
    }
  }
  debug(ile, x);
  if (x.empty()) {
    res = licz2(ile);
  } else {
    res *= licz1(ile);
    res *= licz1(x[0]);
    R(i, SZ(x)) if (i) { res *= {dp[x[i]][2], 0, 0}; }
  }
  cout << res.a << " " << res.b << " " << res.c << "\n";
}