test/3_yukicoder/2362.test.cpp

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• Last update: 2024-12-26 06:32:57+09:00
• Problem: https://yukicoder.me/problems/no/2362
• Link: View error logs on GitHub Actions

Depends on

• alg/monoid/monoid_for_floor_sum.hpp
• alg/monoid_pow.hpp
• mod/floor_monoid_product.hpp
• mod/floor_sum_of_linear_polynomial.hpp
• my_template.hpp
• other/io.hpp

Code

#define PROBLEM "https://yukicoder.me/problems/no/2362"
#include "my_template.hpp"
#include "other/io.hpp"

#include "mod/floor_sum_of_linear_polynomial.hpp"

void solve() {
  u64 N, M, X, Y;
  read(N, M, X, Y);
  u64 ANS = 0;
  {
    auto a = floor_sum_of_linear_polynomial_nonnegative<u64, 1, 1, u64>(N, X, 0, M);
    ANS -= a[0][1] * N - a[1][1];
  }
  {
    auto a = floor_sum_of_linear_polynomial_nonnegative<u64, 1, 1, u64>(N, X, Y, M);
    ANS -= a[0][1] * (N - 1) - 2 * a[1][1];
  }
  print(ANS);
}

signed main() {
  INT(T);
  FOR(T) solve();
  return 0;
}

#line 1 "test/3_yukicoder/2362.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/2362"
#line 1 "my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else

// https://codeforces.com/blog/entry/96344
#pragma GCC optimize("Ofast,unroll-loops")
// いまの CF だとこれ入れると動かない？
// #pragma GCC target("avx2,popcnt")

#include <bits/stdc++.h>

using namespace std;

using ll = long long;
using u8 = uint8_t;
using u16 = uint16_t;
using u32 = uint32_t;
using u64 = uint64_t;
using i128 = __int128;
using u128 = unsigned __int128;
using f128 = __float128;

template <class T>
constexpr T infty = 0;
template <>
constexpr int infty<int> = 1'010'000'000;
template <>
constexpr ll infty<ll> = 2'020'000'000'000'000'000;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * 2'000'000'000'000'000'000;
template <>
constexpr double infty<double> = infty<ll>;
template <>
constexpr long double infty<long double> = infty<ll>;

using pi = pair<ll, ll>;
using vi = vector<ll>;
template <class T>
using vc = vector<T>;
template <class T>
using vvc = vector<vc<T>>;
template <class T>
using vvvc = vector<vvc<T>>;
template <class T>
using vvvvc = vector<vvvc<T>>;
template <class T>
using vvvvvc = vector<vvvvc<T>>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using pqg = priority_queue<T, vector<T>, greater<T>>;

#define vv(type, name, h, ...) vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...) vector<vector<vector<type>>> name(h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...) \
  vector<vector<vector<vector<type>>>> name(a, vector<vector<vector<type>>>(b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))

// https://trap.jp/post/1224/
#define FOR1(a) for (ll _ = 0; _ < ll(a); ++_)
#define FOR2(i, a) for (ll i = 0; i < ll(a); ++i)
#define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i)
#define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c))
#define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i)
#define overload4(a, b, c, d, e, ...) e
#define overload3(a, b, c, d, ...) d
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)

#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define elif else if

#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second

#define stoi stoll

int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
int popcnt_sgn(int x) { return (__builtin_parity(unsigned(x)) & 1 ? -1 : 1); }
int popcnt_sgn(u32 x) { return (__builtin_parity(x) & 1 ? -1 : 1); }
int popcnt_sgn(ll x) { return (__builtin_parityll(x) & 1 ? -1 : 1); }
int popcnt_sgn(u64 x) { return (__builtin_parityll(x) & 1 ? -1 : 1); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }

template <typename T>
T kth_bit(int k) {
  return T(1) << k;
}
template <typename T>
bool has_kth_bit(T x, int k) {
  return x >> k & 1;
}

template <typename UINT>
struct all_bit {
  struct iter {
    UINT s;
    iter(UINT s) : s(s) {}
    int operator*() const { return lowbit(s); }
    iter &operator++() {
      s &= s - 1;
      return *this;
    }
    bool operator!=(const iter) const { return s != 0; }
  };
  UINT s;
  all_bit(UINT s) : s(s) {}
  iter begin() const { return iter(s); }
  iter end() const { return iter(0); }
};

template <typename UINT>
struct all_subset {
  static_assert(is_unsigned<UINT>::value);
  struct iter {
    UINT s, t;
    bool ed;
    iter(UINT s) : s(s), t(s), ed(0) {}
    int operator*() const { return s ^ t; }
    iter &operator++() {
      (t == 0 ? ed = 1 : t = (t - 1) & s);
      return *this;
    }
    bool operator!=(const iter) const { return !ed; }
  };
  UINT s;
  all_subset(UINT s) : s(s) {}
  iter begin() const { return iter(s); }
  iter end() const { return iter(0); }
};

template <typename T>
T floor(T a, T b) {
  return a / b - (a % b && (a ^ b) < 0);
}
template <typename T>
T ceil(T x, T y) {
  return floor(x + y - 1, y);
}
template <typename T>
T bmod(T x, T y) {
  return x - y * floor(x, y);
}
template <typename T>
pair<T, T> divmod(T x, T y) {
  T q = floor(x, y);
  return {q, x - q * y};
}

template <typename T, typename U>
T SUM(const vector<U> &A) {
  T sm = 0;
  for (auto &&a: A) sm += a;
  return sm;
}

#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define LB(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define UB(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define UNIQUE(x) sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit()

template <typename T>
T POP(deque<T> &que) {
  T a = que.front();
  que.pop_front();
  return a;
}
template <typename T>
T POP(pq<T> &que) {
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(pqg<T> &que) {
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(vc<T> &que) {
  T a = que.back();
  que.pop_back();
  return a;
}

template <typename F>
ll binary_search(F check, ll ok, ll ng, bool check_ok = true) {
  if (check_ok) assert(check(ok));
  while (abs(ok - ng) > 1) {
    auto x = (ng + ok) / 2;
    (check(x) ? ok : ng) = x;
  }
  return ok;
}
template <typename F>
double binary_search_real(F check, double ok, double ng, int iter = 100) {
  FOR(iter) {
    double x = (ok + ng) / 2;
    (check(x) ? ok : ng) = x;
  }
  return (ok + ng) / 2;
}

template <class T, class S>
inline bool chmax(T &a, const S &b) {
  return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
  return (a > b ? a = b, 1 : 0);
}

// ? は -1
vc<int> s_to_vi(const string &S, char first_char) {
  vc<int> A(S.size());
  FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); }
  return A;
}

template <typename T, typename U>
vector<T> cumsum(vector<U> &A, int off = 1) {
  int N = A.size();
  vector<T> B(N + 1);
  FOR(i, N) { B[i + 1] = B[i] + A[i]; }
  if (off == 0) B.erase(B.begin());
  return B;
}

// stable sort
template <typename T>
vector<int> argsort(const vector<T> &A) {
  vector<int> ids(len(A));
  iota(all(ids), 0);
  sort(all(ids), [&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); });
  return ids;
}

// A[I[0]], A[I[1]], ...
template <typename T>
vc<T> rearrange(const vc<T> &A, const vc<int> &I) {
  vc<T> B(len(I));
  FOR(i, len(I)) B[i] = A[I[i]];
  return B;
}

template <typename T, typename... Vectors>
void concat(vc<T> &first, const Vectors &... others) {
  vc<T> &res = first;
  (res.insert(res.end(), others.begin(), others.end()), ...);
}
#endif
#line 1 "other/io.hpp"
#define FASTIO
#include <unistd.h>


// https://judge.yosupo.jp/submission/21623

namespace fastio {
static constexpr uint32_t SZ = 1 << 17;
char ibuf[SZ];
char obuf[SZ];
char out[100];
// pointer of ibuf, obuf

uint32_t pil = 0, pir = 0, por = 0;

struct Pre {
  char num[10000][4];
  constexpr Pre() : num() {
    for (int i = 0; i < 10000; i++) {
      int n = i;
      for (int j = 3; j >= 0; j--) {
        num[i][j] = n % 10 | '0';
        n /= 10;
      }
    }
  }
} constexpr pre;

inline void load() {
  memcpy(ibuf, ibuf + pil, pir - pil);
  pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin);
  pil = 0;
  if (pir < SZ) ibuf[pir++] = '\n';
}

inline void flush() {
  fwrite(obuf, 1, por, stdout);
  por = 0;
}

void rd(char &c) {
  do {
    if (pil + 1 > pir) load();
    c = ibuf[pil++];
  } while (isspace(c));
}

void rd(string &x) {
  x.clear();
  char c;
  do {
    if (pil + 1 > pir) load();
    c = ibuf[pil++];
  } while (isspace(c));
  do {
    x += c;
    if (pil == pir) load();
    c = ibuf[pil++];
  } while (!isspace(c));
}

template <typename T>
void rd_real(T &x) {
  string s;
  rd(s);
  x = stod(s);
}

template <typename T>
void rd_integer(T &x) {
  if (pil + 100 > pir) load();
  char c;
  do
    c = ibuf[pil++];
  while (c < '-');
  bool minus = 0;
  if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
    if (c == '-') { minus = 1, c = ibuf[pil++]; }
  }
  x = 0;
  while ('0' <= c) { x = x * 10 + (c & 15), c = ibuf[pil++]; }
  if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
    if (minus) x = -x;
  }
}

void rd(int &x) { rd_integer(x); }
void rd(ll &x) { rd_integer(x); }
void rd(i128 &x) { rd_integer(x); }
void rd(u32 &x) { rd_integer(x); }
void rd(u64 &x) { rd_integer(x); }
void rd(u128 &x) { rd_integer(x); }
void rd(double &x) { rd_real(x); }
void rd(long double &x) { rd_real(x); }
void rd(f128 &x) { rd_real(x); }

template <class T, class U>
void rd(pair<T, U> &p) {
  return rd(p.first), rd(p.second);
}
template <size_t N = 0, typename T>
void rd_tuple(T &t) {
  if constexpr (N < std::tuple_size<T>::value) {
    auto &x = std::get<N>(t);
    rd(x);
    rd_tuple<N + 1>(t);
  }
}
template <class... T>
void rd(tuple<T...> &tpl) {
  rd_tuple(tpl);
}

template <size_t N = 0, typename T>
void rd(array<T, N> &x) {
  for (auto &d: x) rd(d);
}
template <class T>
void rd(vc<T> &x) {
  for (auto &d: x) rd(d);
}

void read() {}
template <class H, class... T>
void read(H &h, T &... t) {
  rd(h), read(t...);
}

void wt(const char c) {
  if (por == SZ) flush();
  obuf[por++] = c;
}
void wt(const string s) {
  for (char c: s) wt(c);
}
void wt(const char *s) {
  size_t len = strlen(s);
  for (size_t i = 0; i < len; i++) wt(s[i]);
}

template <typename T>
void wt_integer(T x) {
  if (por > SZ - 100) flush();
  if (x < 0) { obuf[por++] = '-', x = -x; }
  int outi;
  for (outi = 96; x >= 10000; outi -= 4) {
    memcpy(out + outi, pre.num[x % 10000], 4);
    x /= 10000;
  }
  if (x >= 1000) {
    memcpy(obuf + por, pre.num[x], 4);
    por += 4;
  } else if (x >= 100) {
    memcpy(obuf + por, pre.num[x] + 1, 3);
    por += 3;
  } else if (x >= 10) {
    int q = (x * 103) >> 10;
    obuf[por] = q | '0';
    obuf[por + 1] = (x - q * 10) | '0';
    por += 2;
  } else
    obuf[por++] = x | '0';
  memcpy(obuf + por, out + outi + 4, 96 - outi);
  por += 96 - outi;
}

template <typename T>
void wt_real(T x) {
  ostringstream oss;
  oss << fixed << setprecision(15) << double(x);
  string s = oss.str();
  wt(s);
}

void wt(int x) { wt_integer(x); }
void wt(ll x) { wt_integer(x); }
void wt(i128 x) { wt_integer(x); }
void wt(u32 x) { wt_integer(x); }
void wt(u64 x) { wt_integer(x); }
void wt(u128 x) { wt_integer(x); }
void wt(double x) { wt_real(x); }
void wt(long double x) { wt_real(x); }
void wt(f128 x) { wt_real(x); }

template <class T, class U>
void wt(const pair<T, U> val) {
  wt(val.first);
  wt(' ');
  wt(val.second);
}
template <size_t N = 0, typename T>
void wt_tuple(const T t) {
  if constexpr (N < std::tuple_size<T>::value) {
    if constexpr (N > 0) { wt(' '); }
    const auto x = std::get<N>(t);
    wt(x);
    wt_tuple<N + 1>(t);
  }
}
template <class... T>
void wt(tuple<T...> tpl) {
  wt_tuple(tpl);
}
template <class T, size_t S>
void wt(const array<T, S> val) {
  auto n = val.size();
  for (size_t i = 0; i < n; i++) {
    if (i) wt(' ');
    wt(val[i]);
  }
}
template <class T>
void wt(const vector<T> val) {
  auto n = val.size();
  for (size_t i = 0; i < n; i++) {
    if (i) wt(' ');
    wt(val[i]);
  }
}

void print() { wt('\n'); }
template <class Head, class... Tail>
void print(Head &&head, Tail &&... tail) {
  wt(head);
  if (sizeof...(Tail)) wt(' ');
  print(forward<Tail>(tail)...);
}

// gcc expansion. called automaticall after main.

void __attribute__((destructor)) _d() { flush(); }
} // namespace fastio

using fastio::read;
using fastio::print;
using fastio::flush;

#if defined(LOCAL)
#define SHOW(...) SHOW_IMPL(__VA_ARGS__, SHOW6, SHOW5, SHOW4, SHOW3, SHOW2, SHOW1)(__VA_ARGS__)
#define SHOW_IMPL(_1, _2, _3, _4, _5, _6, NAME, ...) NAME
#define SHOW1(x) print(#x, "=", (x)), flush()
#define SHOW2(x, y) print(#x, "=", (x), #y, "=", (y)), flush()
#define SHOW3(x, y, z) print(#x, "=", (x), #y, "=", (y), #z, "=", (z)), flush()
#define SHOW4(x, y, z, w) print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w)), flush()
#define SHOW5(x, y, z, w, v) print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w), #v, "=", (v)), flush()
#define SHOW6(x, y, z, w, v, u) print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w), #v, "=", (v), #u, "=", (u)), flush()
#else
#define SHOW(...)
#endif

#define INT(...)   \
  int __VA_ARGS__; \
  read(__VA_ARGS__)
#define LL(...)   \
  ll __VA_ARGS__; \
  read(__VA_ARGS__)
#define U32(...)   \
  u32 __VA_ARGS__; \
  read(__VA_ARGS__)
#define U64(...)   \
  u64 __VA_ARGS__; \
  read(__VA_ARGS__)
#define STR(...)      \
  string __VA_ARGS__; \
  read(__VA_ARGS__)
#define CHAR(...)   \
  char __VA_ARGS__; \
  read(__VA_ARGS__)
#define DBL(...)      \
  double __VA_ARGS__; \
  read(__VA_ARGS__)

#define VEC(type, name, size) \
  vector<type> name(size);    \
  read(name)
#define VV(type, name, h, w)                     \
  vector<vector<type>> name(h, vector<type>(w)); \
  read(name)

void YES(bool t = 1) { print(t ? "YES" : "NO"); }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = 1) { print(t ? "Yes" : "No"); }
void No(bool t = 1) { Yes(!t); }
void yes(bool t = 1) { print(t ? "yes" : "no"); }
void no(bool t = 1) { yes(!t); }
void YA(bool t = 1) { print(t ? "YA" : "TIDAK"); }
void TIDAK(bool t = 1) { YES(!t); }
#line 4 "test/3_yukicoder/2362.test.cpp"

#line 1 "mod/floor_sum_of_linear_polynomial.hpp"

#line 2 "alg/monoid_pow.hpp"

// chat gpt
template <typename U, typename Arg1, typename Arg2>
struct has_power_method {
private:
  // ヘルパー関数の実装
  template <typename V, typename A1, typename A2>
  static auto check(int)
      -> decltype(std::declval<V>().power(std::declval<A1>(),
                                          std::declval<A2>()),
                  std::true_type{});
  template <typename, typename, typename>
  static auto check(...) -> std::false_type;

public:
  // メソッドの有無を表す型
  static constexpr bool value = decltype(check<U, Arg1, Arg2>(0))::value;
};

template <typename Monoid>
typename Monoid::X monoid_pow(typename Monoid::X x, ll exp) {
  using X = typename Monoid::X;
  if constexpr (has_power_method<Monoid, X, ll>::value) {
    return Monoid::power(x, exp);
  } else {
    assert(exp >= 0);
    X res = Monoid::unit();
    while (exp) {
      if (exp & 1) res = Monoid::op(res, x);
      x = Monoid::op(x, x);
      exp >>= 1;
    }
    return res;
  }
}
#line 2 "mod/floor_monoid_product.hpp"

// https://yukicoder.me/submissions/883884
// https://qoj.ac/contest/1411/problem/7620
// U は範囲内で ax+b がオーバーフローしない程度
// yyy x yyyy x ... yyy x yyy (x を N 個)
// k 個目の x までに floor(ak+b,m) 個の y がある
// my<=ax+b における lattice path における辺の列と見なせる
template <typename Monoid, typename X, typename U>
X floor_monoid_product(X x, X y, U N, U a, U b, U m) {
  U c = (a * N + b) / m;
  X pre = Monoid::unit(), suf = Monoid::unit();
  while (1) {
    const U p = a / m, q = b / m;
    a %= m, b %= m;
    x = Monoid::op(x, monoid_pow<Monoid>(y, p));
    pre = Monoid::op(pre, monoid_pow<Monoid>(y, q));
    c -= (p * N + q);
    if (c == 0) break;
    const U d = (m * c - b - 1) / a + 1;
    suf = Monoid::op(y, Monoid::op(monoid_pow<Monoid>(x, N - d), suf));
    b = m - b - 1 + a, N = c - 1, c = d;
    swap(m, a), swap(x, y);
  }
  x = monoid_pow<Monoid>(x, N);
  return Monoid::op(Monoid::op(pre, x), suf);
}
#line 1 "alg/monoid/monoid_for_floor_sum.hpp"
// sum i^k1floor^k2: floor path で (x,y) から x 方向に進むときに x^k1y^k2 を足す
template <typename T, int K1, int K2>
struct Monoid_for_floor_sum {
  using ARR = array<array<T, K2 + 1>, K1 + 1>;
  struct Data {
    ARR dp;
    T dx, dy;
  };

  using value_type = Data;
  using X = value_type;
  static X op(X a, X b) {
    static constexpr int n = max(K1, K2);
    static T comb[n + 1][n + 1];
    if (comb[0][0] != T(1)) {
      comb[0][0] = T(1);
      FOR(i, n) FOR(j, i + 1) { comb[i + 1][j] += comb[i][j], comb[i + 1][j + 1] += comb[i][j]; }
    }

    array<T, K1 + 1> pow_x;
    array<T, K2 + 1> pow_y;
    pow_x[0] = 1, pow_y[0] = 1;
    FOR(i, K1) pow_x[i + 1] = pow_x[i] * a.dx;
    FOR(i, K2) pow_y[i + 1] = pow_y[i] * a.dy;

    // +dy
    FOR(i, K1 + 1) {
      FOR_R(j, K2 + 1) {
        T x = b.dp[i][j];
        FOR(k, j + 1, K2 + 1) b.dp[i][k] += comb[k][j] * pow_y[k - j] * x;
      }
    }
    // +dx
    FOR(j, K2 + 1) {
      FOR_R(i, K1 + 1) { FOR(k, i, K1 + 1) a.dp[k][j] += comb[k][i] * pow_x[k - i] * b.dp[i][j]; }
    }

    a.dx += b.dx, a.dy += b.dy;
    return a;
  }

  static X to_x() {
    X x = unit();
    x.dp[0][0] = 1, x.dx = 1;
    return x;
  }
  static X to_y() {
    X x = unit();
    x.dy = 1;
    return x;
  }
  static constexpr X unit() { return {ARR{}, T(0), T(0)}; }
  static constexpr bool commute = 0;
};
#line 4 "mod/floor_sum_of_linear_polynomial.hpp"

// 全部非負, T は答, U は ax+b がオーバーフローしない
template <typename T, int K1, int K2, typename U>
array<array<T, K2 + 1>, K1 + 1> floor_sum_of_linear_polynomial_nonnegative(U N, U a, U b, U mod) {
  static_assert(is_same_v<U, u64> || is_same_v<U, u128>);
  assert(a == 0 || N < (U(-1) - b) / a);
  using Mono = Monoid_for_floor_sum<T, K1, K2>;
  auto x = floor_monoid_product<Mono>(Mono::to_x(), Mono::to_y(), N, a, b, mod);
  return x.dp;
};

// sum_{L<=x<R} x^i floor(ax+b,mod)^j
// a+bx が I, U でオーバーフローしない
template <typename T, int K1, int K2, typename I>
array<array<T, K2 + 1>, K1 + 1> floor_sum_of_linear_polynomial(I L, I R, I a, I b, I mod) {
  static_assert(is_same_v<I, ll> || is_same_v<I, i128>);
  assert(L <= R && mod > 0);
  if (a < 0) {
    auto ANS = floor_sum_of_linear_polynomial<T, K1, K2, I>(-R + 1, -L + 1, -a, b, mod);
    FOR(i, K1 + 1) {
      if (i % 2 == 1) { FOR(j, K2 + 1) ANS[i][j] = -ANS[i][j]; }
    }
    return ANS;
  }
  assert(a >= 0);
  I ADD_X = L;
  I N = R - L;
  b += a * L;
  I ADD_Y = floor<I>(b, mod);
  b -= ADD_Y * mod;
  assert(a >= 0 && b >= 0);

  using Mono = Monoid_for_floor_sum<T, K1, K2>;
  using Data = typename Mono::Data;
  using U = std::conditional_t<is_same_v<I, ll>, i128, u128>;
  Data A = floor_monoid_product<Mono, Data, U>(Mono::to_x(), Mono::to_y(), N, a, b, mod);
  Data offset = Mono::unit();
  offset.dx = T(ADD_X), offset.dy = T(ADD_Y);
  A = Mono::op(offset, A);
  return A.dp;
};
#line 6 "test/3_yukicoder/2362.test.cpp"

void solve() {
  u64 N, M, X, Y;
  read(N, M, X, Y);
  u64 ANS = 0;
  {
    auto a = floor_sum_of_linear_polynomial_nonnegative<u64, 1, 1, u64>(N, X, 0, M);
    ANS -= a[0][1] * N - a[1][1];
  }
  {
    auto a = floor_sum_of_linear_polynomial_nonnegative<u64, 1, 1, u64>(N, X, Y, M);
    ANS -= a[0][1] * (N - 1) - 2 * a[1][1];
  }
  print(ANS);
}

signed main() {
  INT(T);
  FOR(T) solve();
  return 0;
}

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