Problem p02591 (C++) — buggy submission, verdict: Time Limit Exceeded

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

#define int long long
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define reps(i, n) for (int i = 1; i <= (int)(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 cdiv(a, b) (((a)-1) / (b) + 1)
#define dump(x) cerr << #x " = " << (x) << endl
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[9] = {0, 1, 0, -1, 1, 1, -1, -1, 0};
constexpr int DX[9] = {1, 0, -1, 0, 1, -1, -1, 1, 0};
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; }
int sign(int x) { return (x > 0) - (x < 0); }
template <typename T> void fin(T mes) {
  cout << mes << endl;
  exit(0);
}
template <typename T, typename U> bool chmax(T &a, const U &b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <typename T, typename U> bool chmin(T &a, const U &b) {
  if (b < a) {
    a = b;
    return true;
  }
  return false;
}
template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &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;
}
template <typename T> ostream &operator<<(ostream &os, const deque<T> &rhs) {
  os << "{";
  for (auto itr = rhs.begin(); itr != rhs.end(); itr++) {
    os << *itr << (next(itr) != rhs.end() ? ", " : "");
  }
  os << "}";
  return os;
}
template <typename T> ostream &operator<<(ostream &os, const set<T> &rhs) {
  os << "{";
  for (auto itr = rhs.begin(); itr != rhs.end(); itr++) {
    os << *itr << (next(itr) != rhs.end() ? ", " : "");
  }
  os << "}";
  return os;
}
template <typename T, typename U>
ostream &operator<<(ostream &os, const map<T, U> &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_ % MOD) {
    if (val < 0) {
      val += 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 -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 {
    assert(val != 0);
    int a = val, b = MOD, x = 1, u = 0;
    while (b) {
      int t = a / b;
      std::swap(a -= t * b, b);
      std::swap(x -= t * u, u);
    }
    return x;
  }
  mod_int pow(long long n) const {
    if (n < 0) {
      return pow(-n).inv();
    }
    mod_int ret = 1, mul = *this;
    while (n) {
      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); }
  };
};

int H;
int P[440000];
using mint = mod_int<>;
mint co[440000];
mint inv[440000];
signed main() {
  cin >> H;
  int L = bit(H - 1);
  reps(i, L * 2) { inv[i] = mint(i).inv(); }
  rep(i, L) { cin >> P[i], P[i]--; }
  mint ans = 0;
  auto f = [&](int a, int b) -> mint {
    if (a < b) {
      return 0;
    }
    mint ret = 1;
    while (a != b) {
      ret *= b;
      a >>= 1;
      b >>= 1;
    }
    b >>= 1;
    while (b > 0) {
      ret *= inv[b];
      b >>= 1;
    }
    return ret;
  };
  rep(i, L) {
    int x = i + L, y = P[i] + L;
    int t = __builtin_ctzll(x);
    rep(j, bit(t) + 1) {
      int x_ = x - bit(t) + j;
      if (x_ < L) {
        continue;
      }
      mint add = f(x, x_) - f(x - 1, x_);
      int yc = P[x_ - L] + L;
      int ycc = yc;
      while (ycc > 0) {
        add *= inv[ycc], ycc >>= 1;
      }
      while (yc > 0) {
        add *= yc * yc;
        co[yc] += add * (inv[yc] - mint(yc >> 1));
        yc >>= 1;
      }
    }
    ans -= x * y;
    mint u = 1;
    while (x > 0) {
      u *= x, x >>= 1;
    }
    int yc = y;
    while (yc > 0) {
      u *= yc, yc >>= 1;
    }
    while (y > 0) {
      ans += co[y] * u, y >>= 1;
    }
  }
  cout << ans << endl;
}


Error: TLE

Fixed submission:

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

#define int long long
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define reps(i, n) for (int i = 1; i <= (int)(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 cdiv(a, b) (((a)-1) / (b) + 1)
#define dump(x) cerr << #x " = " << (x) << endl
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[9] = {0, 1, 0, -1, 1, 1, -1, -1, 0};
constexpr int DX[9] = {1, 0, -1, 0, 1, -1, -1, 1, 0};
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; }
int sign(int x) { return (x > 0) - (x < 0); }
template <typename T> void fin(T mes) {
  cout << mes << endl;
  exit(0);
}
template <typename T, typename U> bool chmax(T &a, const U &b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <typename T, typename U> bool chmin(T &a, const U &b) {
  if (b < a) {
    a = b;
    return true;
  }
  return false;
}
template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &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;
}
template <typename T> ostream &operator<<(ostream &os, const deque<T> &rhs) {
  os << "{";
  for (auto itr = rhs.begin(); itr != rhs.end(); itr++) {
    os << *itr << (next(itr) != rhs.end() ? ", " : "");
  }
  os << "}";
  return os;
}
template <typename T> ostream &operator<<(ostream &os, const set<T> &rhs) {
  os << "{";
  for (auto itr = rhs.begin(); itr != rhs.end(); itr++) {
    os << *itr << (next(itr) != rhs.end() ? ", " : "");
  }
  os << "}";
  return os;
}
template <typename T, typename U>
ostream &operator<<(ostream &os, const map<T, U> &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_ % MOD) {
    if (val < 0) {
      val += 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 -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 {
    assert(val != 0);
    int a = val, b = MOD, x = 1, u = 0;
    while (b) {
      int t = a / b;
      std::swap(a -= t * b, b);
      std::swap(x -= t * u, u);
    }
    return x;
  }
  mod_int pow(long long n) const {
    if (n < 0) {
      return pow(-n).inv();
    }
    mod_int ret = 1, mul = *this;
    while (n) {
      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); }
  };
};

int H;
int P[440000];
using mint = mod_int<>;
mint co[440000];
signed main() {
  cin >> H;
  int L = bit(H - 1);
  rep(i, L) { cin >> P[i], P[i]--; }
  mint ans = 0;
  auto f = [&](int a, int b) -> mint {
    if (a < b) {
      return 0;
    }
    mint ret = 1;
    while (a != b) {
      ret *= b;
      a /= 2;
      b /= 2;
    }
    b /= 2;
    while (b > 0) {
      ret /= b;
      b /= 2;
    }
    return ret;
  };
  rep(i, L) {
    int x = i + L, y = P[i] + L;
    int t = __builtin_ctzll(x);
    rep(j, bit(t) + 1) {
      int x_ = x - bit(t) + j;
      if (x_ < L) {
        continue;
      }
      mint add = f(x, x_) - f(x - 1, x_);
      int yc = P[x_ - L] + L;
      int ycc = yc;
      while (ycc > 0) {
        add /= ycc, ycc /= 2;
      }
      while (yc > 0) {
        add *= yc * yc;
        co[yc] += add * (mint(1) / yc - mint(yc / 2));
        yc /= 2;
      }
    }
    ans -= x * y;
    mint u = 1;
    while (x > 0) {
      u *= x, x /= 2;
    }
    int yc = y;
    while (yc > 0) {
      u *= yc, yc /= 2;
    }
    while (y > 0) {
      ans += co[y] * u, y /= 2;
    }
  }
  cout << ans << endl;
}