Problem p02653 (C++)

Buggy submission (status: Runtime Error):
#include <bits/stdc++.h>
// #include <boost/multiprecision/cpp_int.hpp>
// using i128 = boost::multiprecision::int128_t;
#define _GLIBCXX_DEBUG
using namespace std;
using ll = long long;
using ld = long double;
using V = vector<int>;
using Vll = vector<ll>;
using Vld = vector<ld>;
using Vbo = vector<bool>;
using VV = vector<V>;
using VVll = vector<Vll>;
using VVld = vector<Vld>;
using VVbo = vector<Vbo>;
using VVV = vector<VV>;
using VVVll = vector<VVll>;
using P = pair<int, int>;
using Pll = pair<ll, ll>;
using Pld = pair<ld, ld>;
#define rep2(i, m, n) for (ll i = int(m); i < int(n); ++i)
#define drep2(i, m, n) for (ll i = int(m) - 1; i >= int(n); --i)
#define rep(i, n) rep2(i, 0, n)
#define drep(i, n) drep2(i, n, 0)
#define all(a) a.begin(), a.end()
struct fast_ios {
  fast_ios() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(20);
  };
} fast_ios_;
template <typename T> inline bool chmin(T &a, T b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <typename T> inline bool chmax(T &a, T b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <typename T1, typename T2>
istream &operator>>(istream &is, pair<T1, T2> &p) {
  is >> p.first >> p.second;
  return is;
}
template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
  os << "(" << p.first << ", " << p.second << ")";
  return os;
}
template <typename T> istream &operator>>(istream &is, vector<T> &v) {
  for (auto &e : v)
    is >> e;
  return is;
}
template <typename T> ostream &operator<<(ostream &os, const vector<T> &v) {
  for (auto &e : v)
    os << e << " ";
  return os;
}
template <typename T> inline int count_between(vector<T> &a, T l, T r) {
  return lower_bound(all(a), r) - lower_bound(all(a), l);
} // [l, r)
inline int Log2(ll x) {
  int k;
  for (k = 0; x > 0; ++k)
    x >>= 1;
  return k;
} // number of binary digits
const int INF = 1 << 30;
const ll INFll = 1ll << 62;
const ld EPS = 1e-10;
const ld PI = acos(-1.0);
const int MOD = int(1e9) + 7;

struct mint {
  ll x;
  mint(ll x = 0) : x((x % MOD + MOD) % MOD) {}
  mint operator-() const { return mint(-x); }
  mint &operator+=(const mint a) {
    if ((x += a.x) >= MOD)
      x -= MOD;
    return *this;
  }
  mint &operator-=(const mint a) {
    if ((x -= a.x) < 0)
      x += MOD;
    return *this;
  }
  mint &operator*=(const mint a) {
    (x *= a.x) %= MOD;
    return *this;
  }
  mint operator+(const mint a) const { return mint(*this) += a; }
  mint operator-(const mint a) const { return mint(*this) -= a; }
  mint operator*(const mint a) const { return mint(*this) *= a; }
  mint pow(ll t) const {
    if (!t)
      return 1;
    mint a = pow(t >> 1);
    a *= a;
    if (t & 1)
      a *= *this;
    return a;
  }
  mint &operator/=(const mint r) {
    ll a = r.x, b = MOD, u = 1, v = 0;
    while (b) {
      ll t = a / b;
      a -= t * b;
      swap(a, b);
      u -= t * v;
      swap(u, v);
    }
    x = x * u % MOD;
    if (x < 0)
      x += MOD;
    return *this;
  }
  mint operator/(const mint a) const { return mint(*this) /= a; }
};
// istream& operator>>(istream& is, mint& a) { return is >> a.x;}
ostream &operator<<(ostream &os, const mint &a) { return os << a.x; }
using Vm = vector<mint>;
using VVm = vector<Vm>;
using VVVm = vector<VVm>;

template <typename T> struct Polynomial : vector<T> {
  using vector<T>::vector;
  using P = Polynomial;
  P operator-() const {
    P res((*this).size());
    rep(i, (*this).size()) res[i] = -(*this)[i];
    return res;
  }
  P &operator+=(const P q) {
    rep(i, (*this).size()) if (i < q.size())(*this)[i] += q[i];
    return *this;
  }
  P &operator-=(const P q) {
    rep(i, (*this).size()) if (i < q.size())(*this)[i] -= q[i];
    return *this;
  }
  P &operator*=(const P q) {
    drep(i, (*this).size()) {
      (*this)[i] *= q[0];
      rep2(j, 1, q.size()) if (j <= i)(*this)[i] += q[j] * (*this)[i - j];
    }
    return *this;
  }
  P &operator/=(const P q) {
    rep(i, (*this).size()) {
      rep2(j, 1, q.size()) if (j <= i)(*this)[i] -= q[j] * (*this)[i - j];
      (*this)[i] /= q[0];
    }
    return *this;
  }
  P operator+(const P q) const { return P(*this) += q; }
  P operator-(const P q) const { return P(*this) -= q; }
  P operator*(const P q) const { return P(*this) *= q; }
  P operator/(const P q) const { return P(*this) /= q; }
  P &mul(map<int, T> q) {
    drep(i, (*this).size()) {
      (*this)[i] *= q[0];
      for (auto &[j, b] : q)
        if (j != 0 && j <= i)
          (*this)[i] += b * (*this)[i - j];
    }
    return *this;
  }
  P &div(map<int, T> q) {
    rep(i, (*this).size()) {
      for (auto &[j, b] : q)
        if (j != 0 && j <= i)
          (*this)[i] -= b * (*this)[i - j];
      (*this)[i] /= q[0];
    }
    return *this;
  }
  // P &div(map<int, T> q) {
  //   rep(i, (*this).size()) {
  //     for (auto &b : q) if (b.first != 0 && b.first <= i) (*this)[i] -=
  //     b.second * (*this)[i-b.first];
  //     (*this)[i] /= q[0];
  //   }
  //   return *this;
  // }
};

int main() {
  ll n, a, b;
  cin >> n >> a >> b;
  if (a > b)
    swap(a, b);

  Polynomial<mint> p(n + 1), q(n + 1), f(n + 1);
  p[a] = 1;
  p.div({{0, 1}, {1, -1}});
  q[1] = 1;
  q.div({{0, 1}, {1, -1}});
  f[1] = 1;
  f[a] -= 1;
  f.div({{0, 1}, {1, -1}});

  auto r = -p * q;
  r[0] += 1;

  auto g2 = q / r;
  auto g1 = q;
  g1[0] += 1;
  g1 /= r;
  auto g0 = p + q;
  g0[0] += 2;
  g0 /= r;

  rep2(i, b, n + 2) g0[i] = 0;
  rep2(i, b, n + 2) g1[i] = 0;
  rep2(i, b, n + 2) g2[i] = 0;

  auto h = f;
  h *= g1 * g1;
  auto h0 = -f * g2;
  h0[0] += 1;
  h /= h0;
  h += g0;

  mint ans = mint(2).pow(n) - h[n];
  cout << ans << "\n";
  return 0;
}


Fixed submission:
#include <bits/stdc++.h>
// #include <boost/multiprecision/cpp_int.hpp>
// using i128 = boost::multiprecision::int128_t;
#define _GLIBCXX_DEBUG
using namespace std;
using ll = long long;
using ld = long double;
using V = vector<int>;
using Vll = vector<ll>;
using Vld = vector<ld>;
using Vbo = vector<bool>;
using VV = vector<V>;
using VVll = vector<Vll>;
using VVld = vector<Vld>;
using VVbo = vector<Vbo>;
using VVV = vector<VV>;
using VVVll = vector<VVll>;
using P = pair<int, int>;
using Pll = pair<ll, ll>;
using Pld = pair<ld, ld>;
#define rep2(i, m, n) for (ll i = int(m); i < int(n); ++i)
#define drep2(i, m, n) for (ll i = int(m) - 1; i >= int(n); --i)
#define rep(i, n) rep2(i, 0, n)
#define drep(i, n) drep2(i, n, 0)
#define all(a) a.begin(), a.end()
struct fast_ios {
  fast_ios() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(20);
  };
} fast_ios_;
template <typename T> inline bool chmin(T &a, T b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <typename T> inline bool chmax(T &a, T b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <typename T1, typename T2>
istream &operator>>(istream &is, pair<T1, T2> &p) {
  is >> p.first >> p.second;
  return is;
}
template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
  os << "(" << p.first << ", " << p.second << ")";
  return os;
}
template <typename T> istream &operator>>(istream &is, vector<T> &v) {
  for (auto &e : v)
    is >> e;
  return is;
}
template <typename T> ostream &operator<<(ostream &os, const vector<T> &v) {
  for (auto &e : v)
    os << e << " ";
  return os;
}
template <typename T> inline int count_between(vector<T> &a, T l, T r) {
  return lower_bound(all(a), r) - lower_bound(all(a), l);
} // [l, r)
inline int Log2(ll x) {
  int k;
  for (k = 0; x > 0; ++k)
    x >>= 1;
  return k;
} // number of binary digits
const int INF = 1 << 30;
const ll INFll = 1ll << 62;
const ld EPS = 1e-10;
const ld PI = acos(-1.0);
const int MOD = int(1e9) + 7;

struct mint {
  ll x;
  mint(ll x = 0) : x((x % MOD + MOD) % MOD) {}
  mint operator-() const { return mint(-x); }
  mint &operator+=(const mint a) {
    if ((x += a.x) >= MOD)
      x -= MOD;
    return *this;
  }
  mint &operator-=(const mint a) {
    if ((x -= a.x) < 0)
      x += MOD;
    return *this;
  }
  mint &operator*=(const mint a) {
    (x *= a.x) %= MOD;
    return *this;
  }
  mint operator+(const mint a) const { return mint(*this) += a; }
  mint operator-(const mint a) const { return mint(*this) -= a; }
  mint operator*(const mint a) const { return mint(*this) *= a; }
  mint pow(ll t) const {
    if (!t)
      return 1;
    mint a = pow(t >> 1);
    a *= a;
    if (t & 1)
      a *= *this;
    return a;
  }
  mint &operator/=(const mint r) {
    ll a = r.x, b = MOD, u = 1, v = 0;
    while (b) {
      ll t = a / b;
      a -= t * b;
      swap(a, b);
      u -= t * v;
      swap(u, v);
    }
    x = x * u % MOD;
    if (x < 0)
      x += MOD;
    return *this;
  }
  mint operator/(const mint a) const { return mint(*this) /= a; }
};
// istream& operator>>(istream& is, mint& a) { return is >> a.x;}
ostream &operator<<(ostream &os, const mint &a) { return os << a.x; }
using Vm = vector<mint>;
using VVm = vector<Vm>;
using VVVm = vector<VVm>;

template <typename T> struct Polynomial : vector<T> {
  using vector<T>::vector;
  using P = Polynomial;
  P operator-() const {
    P res((*this).size());
    rep(i, (*this).size()) res[i] = -(*this)[i];
    return res;
  }
  P &operator+=(const P q) {
    rep(i, (*this).size()) if (i < q.size())(*this)[i] += q[i];
    return *this;
  }
  P &operator-=(const P q) {
    rep(i, (*this).size()) if (i < q.size())(*this)[i] -= q[i];
    return *this;
  }
  P &operator*=(const P q) {
    drep(i, (*this).size()) {
      (*this)[i] *= q[0];
      rep2(j, 1, q.size()) if (j <= i)(*this)[i] += q[j] * (*this)[i - j];
    }
    return *this;
  }
  P &operator/=(const P q) {
    rep(i, (*this).size()) {
      rep2(j, 1, q.size()) if (j <= i)(*this)[i] -= q[j] * (*this)[i - j];
      (*this)[i] /= q[0];
    }
    return *this;
  }
  P operator+(const P q) const { return P(*this) += q; }
  P operator-(const P q) const { return P(*this) -= q; }
  P operator*(const P q) const { return P(*this) *= q; }
  P operator/(const P q) const { return P(*this) /= q; }
  P &mul(map<int, T> q) {
    drep(i, (*this).size()) {
      (*this)[i] *= q[0];
      for (auto &[j, b] : q)
        if (j != 0 && j <= i)
          (*this)[i] += b * (*this)[i - j];
    }
    return *this;
  }
  P &div(map<int, T> q) {
    rep(i, (*this).size()) {
      for (auto &[j, b] : q)
        if (j != 0 && j <= i)
          (*this)[i] -= b * (*this)[i - j];
      (*this)[i] /= q[0];
    }
    return *this;
  }
  // P &div(map<int, T> q) {
  //   rep(i, (*this).size()) {
  //     for (auto &b : q) if (b.first != 0 && b.first <= i) (*this)[i] -=
  //     b.second * (*this)[i-b.first];
  //     (*this)[i] /= q[0];
  //   }
  //   return *this;
  // }
};

int main() {
  ll n, a, b;
  cin >> n >> a >> b;
  if (a > b)
    swap(a, b);

  Polynomial<mint> p(n + 1), q(n + 1), f(n + 1);
  p[a] = 1;
  p.div({{0, 1}, {1, -1}});
  q[1] = 1;
  q.div({{0, 1}, {1, -1}});
  f[1] = 1;
  f[a] -= 1;
  f.div({{0, 1}, {1, -1}});

  auto r = -p * q;
  r[0] += 1;

  auto g2 = q / r;
  auto g1 = q;
  g1[0] += 1;
  g1 /= r;
  auto g0 = p + q;
  g0[0] += 2;
  g0 /= r;

  rep2(i, b, n + 1) g0[i] = 0;
  rep2(i, b, n + 1) g1[i] = 0;
  rep2(i, b, n + 1) g2[i] = 0;

  auto h = f;
  h *= g1 * g1;
  auto h0 = -f * g2;
  h0[0] += 1;
  h /= h0;
  h += g0;

  mint ans = mint(2).pow(n) - h[n];
  cout << ans << "\n";
  return 0;
}