:heavy_check_mark: verify/math/LC_sum_of_floor_of_linear.monoid.test.cpp

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Code

#define PROBLEM "https://judge.yosupo.jp/problem/sum_of_floor_of_linear"

#include "template/template.hpp"
#include "math/floor-monoid-product.hpp"

struct T {
  ull x, y, z;
};
T op(T a, T b) { return T{a.x + b.x, a.y + b.y, a.y * b.x + a.z + b.z}; }
T e() { return T{0, 0, 0}; }

int main() {
  int t;
  in(t);
  T x{1, 0, 0}, y{0, 1, 0};
  while (t--) {
    ull n, m, a, b;
    in(n, m, a, b);
    ull sum = FloorMonoidProduct<T, op, e>(n, m, a, b, x, y).z;
    cout << sum << "\n";
  }
}
#line 1 "verify/math/LC_sum_of_floor_of_linear.monoid.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/sum_of_floor_of_linear"

#line 2 "template/template.hpp"
#include <bits/stdc++.h>
using namespace std;

#line 2 "template/macro.hpp"
#define rep(i, a, b) for (int i = (a); i < (int)(b); i++)
#define rrep(i, a, b) for (int i = (int)(b) - 1; i >= (a); i--)
#define ALL(v) (v).begin(), (v).end()
#define UNIQUE(v) sort(ALL(v)), (v).erase(unique(ALL(v)), (v).end())
#define SZ(v) (int)v.size()
#define MIN(v) *min_element(ALL(v))
#define MAX(v) *max_element(ALL(v))
#define LB(v, x) int(lower_bound(ALL(v), (x)) - (v).begin())
#define UB(v, x) int(upper_bound(ALL(v), (x)) - (v).begin())
#define YN(b) cout << ((b) ? "YES" : "NO") << "\n";
#define Yn(b) cout << ((b) ? "Yes" : "No") << "\n";
#define yn(b) cout << ((b) ? "yes" : "no") << "\n";
#line 6 "template/template.hpp"

#line 2 "template/util.hpp"
using uint = unsigned int;
using ll = long long int;
using ull = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;

template <class T, class S = T>
S SUM(const vector<T> &a) {
  return accumulate(ALL(a), S(0));
}
template <class T>
inline bool chmin(T &a, T b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <class T>
inline bool chmax(T &a, T b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}

template <class T>
int popcnt(T x) {
  return __builtin_popcountll(x);
}
template <class T>
int topbit(T x) {
  return (x == 0 ? -1 : 63 - __builtin_clzll(x));
}
template <class T>
int lowbit(T x) {
  return (x == 0 ? -1 : __builtin_ctzll(x));
}
#line 8 "template/template.hpp"

#line 2 "template/inout.hpp"
struct Fast {
  Fast() {
    cin.tie(nullptr);
    ios_base::sync_with_stdio(false);
    cout << fixed << setprecision(15);
  }
} fast;

template <class T1, class T2>
istream &operator>>(istream &is, pair<T1, T2> &p) {
  return is >> p.first >> p.second;
}
template <class T1, class T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
  return os << p.first << " " << p.second;
}
template <class T>
istream &operator>>(istream &is, vector<T> &a) {
  for (auto &v : a) is >> v;
  return is;
}
template <class T>
ostream &operator<<(ostream &os, const vector<T> &a) {
  for (auto it = a.begin(); it != a.end();) {
    os << *it;
    if (++it != a.end()) os << " ";
  }
  return os;
}
template <class T>
ostream &operator<<(ostream &os, const set<T> &st) {
  os << "{";
  for (auto it = st.begin(); it != st.end();) {
    os << *it;
    if (++it != st.end()) os << ",";
  }
  os << "}";
  return os;
}
template <class T1, class T2>
ostream &operator<<(ostream &os, const map<T1, T2> &mp) {
  os << "{";
  for (auto it = mp.begin(); it != mp.end();) {
    os << it->first << ":" << it->second;
    if (++it != mp.end()) os << ",";
  }
  os << "}";
  return os;
}

void in() {}
template <typename T, class... U>
void in(T &t, U &...u) {
  cin >> t;
  in(u...);
}
void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u) {
  cout << t;
  if (sizeof...(u)) cout << sep;
  out(u...);
}
#line 10 "template/template.hpp"

#line 2 "template/debug.hpp"
#ifdef LOCAL
#define debug 1
#define show(...) _show(0, #__VA_ARGS__, __VA_ARGS__)
#else
#define debug 0
#define show(...) true
#endif
template <class T>
void _show(int i, T name) {
  cerr << '\n';
}
template <class T1, class T2, class... T3>
void _show(int i, const T1 &a, const T2 &b, const T3 &...c) {
  for (; a[i] != ',' && a[i] != '\0'; i++) cerr << a[i];
  cerr << ":" << b << " ";
  _show(i + 1, a, c...);
}
#line 2 "math/floor-monoid-product.hpp"

template <class T, T (*op)(T, T), T (*e)(), std::unsigned_integral U = uint64_t>
T FloorMonoidProduct(U n, U m, U a, U b, T x, T y, function<T(T, U)> pow = nullptr) {
  if (!pow) {
    pow = [](T t, U n) {
      T p = e();
      while (n) {
        if (n & 1) p = op(p, t);
        t = op(t, t);
        n >>= 1;
      }
      return p;
    };
  }
  assert(m != 0);
  T pl = e(), pr = e();
  while (true) {
    if (a >= m) {
      U q = a / m;
      x = op(x, pow(y, q));
      a -= m * q;
    }
    if (b >= m) {
      U q = b / m;
      pl = op(pl, pow(y, q));
      b -= m * q;
    }
    U c = a * n + b;
    if (c < m) {
      pl = op(pl, pow(x, n));
      break;
    }
    pr = op(op(y, pow(x, c % m / a)), pr);
    n = c / m - 1;
    b = m + a - b - 1;
    swap(a, m);
    swap(x, y);
  }
  return op(pl, pr);
}

/**
 * @brief モノイド版 Floor Sum
 * @docs docs/math/floor-monoid-product.md
 */
#line 5 "verify/math/LC_sum_of_floor_of_linear.monoid.test.cpp"

struct T {
  ull x, y, z;
};
T op(T a, T b) { return T{a.x + b.x, a.y + b.y, a.y * b.x + a.z + b.z}; }
T e() { return T{0, 0, 0}; }

int main() {
  int t;
  in(t);
  T x{1, 0, 0}, y{0, 1, 0};
  while (t--) {
    ull n, m, a, b;
    in(n, m, a, b);
    ull sum = FloorMonoidProduct<T, op, e>(n, m, a, b, x, y).z;
    cout << sum << "\n";
  }
}
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