結果

問題 No.3397 Max Weighted Floor of Linear
コンテスト
ユーザー KumaTachiRen
提出日時 2025-12-04 01:03:38
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 631 ms / 2,000 ms
コード長 8,238 bytes
記録
コンパイル時間 3,441 ms
コンパイル使用メモリ 285,216 KB
実行使用メモリ 7,716 KB
最終ジャッジ日時 2025-12-04 01:03:53
合計ジャッジ時間 15,330 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge1
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 23
権限があれば一括ダウンロードができます

ソースコード

diff #
raw source code 

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

#line 2 "library/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 "library/template/template.hpp"

#line 2 "library/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 "library/template/template.hpp"

#line 2 "library/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 "library/template/template.hpp"

#line 2 "library/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 "main.cpp"

#line 2 "library/math/util.hpp"

namespace Math {
template <class T>
T safe_mod(T a, T b) {
  assert(b != 0);
  if (b < 0) a = -a, b = -b;
  a %= b;
  return a >= 0 ? a : a + b;
}
template <class T>
T floor(T a, T b) {
  assert(b != 0);
  if (b < 0) a = -a, b = -b;
  return a >= 0 ? a / b : (a + 1) / b - 1;
}
template <class T>
T ceil(T a, T b) {
  assert(b != 0);
  if (b < 0) a = -a, b = -b;
  return a > 0 ? (a - 1) / b + 1 : a / b;
}
long long isqrt(long long n) {
  if (n <= 0) return 0;
  long long x = sqrt(n);
  while ((x + 1) * (x + 1) <= n) x++;
  while (x * x > n) x--;
  return x;
}
// return g=gcd(a,b)
// a*x+b*y=g
// - b!=0 -> 0<=x<|b|/g
// - b=0  -> ax=g
template <class T>
T ext_gcd(T a, T b, T& x, T& y) {
  T a0 = a, b0 = b;
  bool sgn_a = a < 0, sgn_b = b < 0;
  if (sgn_a) a = -a;
  if (sgn_b) b = -b;
  if (b == 0) {
    x = sgn_a ? -1 : 1;
    y = 0;
    return a;
  }
  T x00 = 1, x01 = 0, x10 = 0, x11 = 1;
  while (b != 0) {
    T q = a / b, r = a - b * q;
    x00 -= q * x01;
    x10 -= q * x11;
    swap(x00, x01);
    swap(x10, x11);
    a = b, b = r;
  }
  x = x00, y = x10;
  if (sgn_a) x = -x;
  if (sgn_b) y = -y;
  if (b0 != 0) {
    a0 /= a, b0 /= a;
    if (b0 < 0) a0 = -a0, b0 = -b0;
    T q = x >= 0 ? x / b0 : (x + 1) / b0 - 1;
    x -= b0 * q;
    y += a0 * q;
  }
  return a;
}
constexpr long long inv_mod(long long x, long long m) {
  x %= m;
  if (x < 0) x += m;
  long long a = m, b = x;
  long long y0 = 0, y1 = 1;
  while (b > 0) {
    long long q = a / b;
    swap(a -= q * b, b);
    swap(y0 -= q * y1, y1);
  }
  if (y0 < 0) y0 += m / a;
  return y0;
}
long long pow_mod(long long x, long long n, long long m) {
  x = (x % m + m) % m;
  long long y = 1;
  while (n) {
    if (n & 1) y = y * x % m;
    x = x * x % m;
    n >>= 1;
  }
  return y;
}
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
  if (m == 1) return 0;
  unsigned int _m = (unsigned int)(m);
  unsigned long long r = 1;
  unsigned long long y = x % m;
  if (y >= m) y += m;
  while (n) {
    if (n & 1) r = (r * y) % _m;
    y = (y * y) % _m;
    n >>= 1;
  }
  return r;
}
constexpr bool is_prime_constexpr(int n) {
  if (n <= 1) return false;
  if (n == 2 || n == 7 || n == 61) return true;
  if (n % 2 == 0) return false;
  long long d = n - 1;
  while (d % 2 == 0) d /= 2;
  constexpr long long bases[3] = {2, 7, 61};
  for (long long a : bases) {
    long long t = d;
    long long y = pow_mod_constexpr(a, t, n);
    while (t != n - 1 && y != 1 && y != n - 1) {
      y = y * y % n;
      t <<= 1;
    }
    if (y != n - 1 && t % 2 == 0) {
      return false;
    }
  }
  return true;
}
template <int n>
constexpr bool is_prime = is_prime_constexpr(n);
};  // namespace Math
#line 4 "main.cpp"

template <class T>
pair<vector<T>, vector<T>> MinOfModOfLinear(T a, T b, T mod) {
  assert(0 <= a && a < mod);
  assert(0 <= b && b < mod);

  vector<T> xs{0}, dxs;
  T g = gcd(a, mod);
  a /= g, b /= g, mod /= g;
  T la = 0, lb = 1, ra = 1, rb = 1;
  T l = mod - a, r = a;
  T x = 0, y = b;
  while (y != 0) {
    T k = r / l;
    r %= l;
    if (r == 0) {
      --k;
      r = l;
    }
    ra += k * la, rb += k * lb;
    while (true) {
      T k = max(T(0), Math::ceil(l - y, r));
      if (l - k * r <= 0) break;
      l -= k * r;
      la += k * ra, lb += k * rb;
      k = y / l;
      y -= k * l;
      x += lb * k;
      xs.push_back(x);
      dxs.push_back(lb);
    }
    k = l / r;
    l -= k * r;
    la += k * ra, lb += k * rb;
    assert(la >= 0 && lb >= 0 && ra >= 0 && rb >= 0);
  }
  return {xs, dxs};
}

ll sub(ll n, ll m, ll a, ll b, ll c, ll d) {
  ll k = Math::floor(d, m);
  d -= m * k;
  // show(n, m, a, b, c, d, k);
  auto f = [&](ll x) -> ll {
    ll v = a * x + b * (Math::floor(c * x + d, m) + k);
    // show(x, v);
    return v;
  };

  ll ans = f(0);
  auto [xs, dxs] = b >= 0 ? MinOfModOfLinear(c, d, m) : MinOfModOfLinear(Math::safe_mod(-c, m), m - 1 - d, m);
  xs.push_back(xs.back() + m * (Math::ceil(n - xs.back(), m) - 1));
  dxs.push_back(m);
  // show(xs);
  // show(dxs);

  rep(i, 0, xs.size() - 1) {
    ll l = xs[i], r = xs[i + 1];
    ll dx = dxs[i];
    if (l >= n) break;
    ll x = l;
    ll t = Math::ceil(n - x, dx) - 1;
    chmin(t, (r - l) / dx);
    x += t * dx;
    chmax(ans, f(x));
  }

  rep(i, 0, xs.size()) {
    ll x = xs[i];
    if (x >= n) break;
    ll t = Math::ceil(n - x, m) - 1;
    chmax(ans, f(x + t * m));
  }

  return ans;
}

void solve() {
  ll n, m, a, b, c, d;
  in(n, m, a, b, c, d);

  ll ans = max(sub(n, m, a, b, c, d), sub(n, m, -a, -b, c, -d - c * (n - 1) + m - 1) + a * (n - 1));
  out(ans);
}

int main() {
  int t = 1;
  in(t);
  while (t--) solve();
}
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