#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using lint = long long; using pint = pair; using plint = pair; struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_; #define ALL(x) (x).begin(), (x).end() #define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i=i##_begin_;i--) #define REP(i, n) FOR(i,0,n) #define IREP(i, n) IFOR(i,0,n) template bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; } template bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; } const std::vector> grid_dxs{{1, 0}, {-1, 0}, {0, 1}, {0, -1}}; int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); } template T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); } template std::pair operator+(const std::pair &l, const std::pair &r) { return std::make_pair(l.first + r.first, l.second + r.second); } template std::pair operator-(const std::pair &l, const std::pair &r) { return std::make_pair(l.first - r.first, l.second - r.second); } template std::vector sort_unique(std::vector vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; } template int arglb(const std::vector &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); } template int argub(const std::vector &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); } template IStream &operator>>(IStream &is, std::vector &vec) { for (auto &v : vec) is >> v; return is; } template OStream &operator<<(OStream &os, const std::vector &vec); template OStream &operator<<(OStream &os, const std::array &arr); template OStream &operator<<(OStream &os, const std::unordered_set &vec); template OStream &operator<<(OStream &os, const pair &pa); template OStream &operator<<(OStream &os, const std::deque &vec); template OStream &operator<<(OStream &os, const std::set &vec); template OStream &operator<<(OStream &os, const std::multiset &vec); template OStream &operator<<(OStream &os, const std::unordered_multiset &vec); template OStream &operator<<(OStream &os, const std::pair &pa); template OStream &operator<<(OStream &os, const std::map &mp); template OStream &operator<<(OStream &os, const std::unordered_map &mp); template OStream &operator<<(OStream &os, const std::tuple &tpl); template OStream &operator<<(OStream &os, const std::vector &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; } template OStream &operator<<(OStream &os, const std::array &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; } template std::istream &operator>>(std::istream &is, std::tuple &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; } template OStream &operator<<(OStream &os, const std::tuple &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; } template OStream &operator<<(OStream &os, const std::unordered_set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::deque &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; } template OStream &operator<<(OStream &os, const std::set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::unordered_multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::pair &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; } template OStream &operator<<(OStream &os, const std::map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::unordered_map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } #ifdef HITONANODE_LOCAL const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m"; #define dbg(x) std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl #define dbgif(cond, x) ((cond) ? std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl : std::cerr) #else #define dbg(x) ((void)0) #define dbgif(cond, x) ((void)0) #endif // Convex Hull Trick // Implementation Idea: // https://github.com/satanic0258/Cpp_snippet/blob/master/src/technique/ConvexHullTrick.cpp // #include // using mpint = boost::multiprecision::cpp_int; namespace CHT { using T_CHT = long long; static const T_CHT T_MIN = std::numeric_limits::lowest() + 1; struct Line { T_CHT a, b; // y = ax + b mutable std::pair rp; // (numerator, denominator) `x` coordinate of the crossing point with next line Line(T_CHT a, T_CHT b) : a(a), b(b), rp(T_MIN, T_MIN) {} static std::pair cross(const Line &ll, const Line &lr) { return std::make_pair(ll.b - lr.b, lr.a - ll.a); // `ll.a < lr.a` is assumed implicitly } bool operator<(const Line &r) const { if (b == T_MIN) { return r.rp.first == T_MIN ? true : a * r.rp.second < r.rp.first; } else if (r.b == T_MIN) { return rp.first == T_MIN ? false : !(r.a * rp.second < rp.first); } else { return a < r.a; } } }; template struct Lines : std::multiset { bool flg_min; // true iff for minimization inline bool isNeedless(iterator itr) { if (size() == 1) return false; auto nxt = std::next(itr); if (itr == begin()) return itr->a == nxt->a and itr->b <= nxt->b; else { auto prv = std::prev(itr); if (nxt == end()) return itr->a == prv->a and itr->b <= prv->b; else return T_MP(prv->b - itr->b) * (nxt->a - itr->a) >= T_MP(itr->b - nxt->b) * (itr->a - prv->a); } } void add_line(T_CHT a, T_CHT b) { if (flg_min) a = -a, b = -b; auto itr = insert({a, b}); if (isNeedless(itr)) erase(itr); else { while (std::next(itr) != end() and isNeedless(std::next(itr))) { erase(std::next(itr)); } while (itr != begin() and isNeedless(std::prev(itr))) { erase(std::prev(itr)); } if (std::next(itr) != end()) { itr->rp = CHT::Line::cross(*itr, *std::next(itr)); } if (itr != begin()) { std::prev(itr)->rp = CHT::Line::cross(*std::prev(itr), *itr); } } } Lines(bool is_minimizer) : flg_min(is_minimizer) {} std::pair get(T_CHT x) { auto itr = lower_bound({x, CHT::T_MIN}); T_CHT retval = CHT::T_MIN, reta = CHT::T_MIN; if (itr != end()) { retval = itr->a * x + itr->b, reta = itr->a; } if (itr != begin()) { T_CHT tmp = std::prev(itr)->a * x + std::prev(itr)->b; if (tmp >= retval) { retval = tmp, reta = std::max(reta, std::prev(itr)->a); } } return std::make_pair(flg_min ? -retval : retval, flg_min ? -reta : reta); } }; } // namespace CHT template struct ConvexHullTrick { using T_CHT = CHT::T_CHT; CHT::Lines lines; ConvexHullTrick(bool is_minimizer) : lines(is_minimizer) {} void add_line(T_CHT a, T_CHT b) { lines.add_line(a, b); } // Add y = ax + b std::pair get(T_CHT x) { return lines.get(x); } void add_convex_parabola(T_CHT c, T_CHT a, T_CHT b) { add_line(c * a * (-2), c * a * a + b); } // Add y = c(x - a)^2 + b T_CHT parabola_lower_bound(T_CHT c, T_CHT x) { return lines.get(x).first + c * x * x; } }; lint f(lint a, lint d, lint x) { // a + a + d + a + 2d + ... + a + (x-1)d // = x * a + d * (x-1) * x / 2 return (a + a + d * (x - 1)) * x / 2; } int main() { int N, M; cin >> N >> M; vector A(N), D(N); REP(i, N) cin >> A.at(i) >> D.at(i); vector X(N); lint ret = -(1LL << 61); REP(i, N) { lint tmp = f(A.at(i), D.at(i), M); dbg(make_tuple(i, tmp)); chmax(ret, tmp); } priority_queue pq; lint tmp = 0; REP(i, N) { if (D.at(i) <= 0) { tmp += f(A.at(i), D.at(i), 0); pq.emplace(f(A.at(i), D.at(i), 1) - f(A.at(i), D.at(i), 0), i); } } vector diffs; REP(_, M) { if (pq.empty()) { diffs.push_back(-1e12); continue; } auto [diff, i] = pq.top(); dbgif(M <= 10, make_tuple(diff, i)); pq.pop(); tmp += diff; diffs.push_back(diff); X.at(i)++; pq.emplace(f(A.at(i), D.at(i), X.at(i) + 1) - f(A.at(i), D.at(i), X.at(i)), i); } // reverse(ALL(diffs)); dbgif(M <= 10, diffs); vector diffs_sum(M + 1); FOR(i, 1, diffs_sum.size()) diffs_sum.at(i) = diffs_sum.at(i - 1) + diffs.at(i - 1); dbgif(M <= 10, diffs_sum); chmax(ret, diffs_sum.back()); ConvexHullTrick<__int128> cht(false); bool flg = false; REP(i, N) { if (D.at(i) > 0) { cht.add_line(D.at(i), A.at(i) * 2 - D.at(i)); flg = true; // int lo = 0, hi = M; // auto e = [&](int j) -> lint { return f(A.at(i), D.at(i), j) + diffs_sum.at(M - j); }; // while (hi - lo > 2) { // int mid1 = (lo * 2 + hi) / 3; // int mid2 = (lo + hi * 2) / 3; // if (e(mid1) < e(mid2)) { // lo = mid1; // } else { // hi = mid2; // } // } // FOR(j, lo, hi + 1) chmax(ret, e(j)); } } REP(m, M + 1) { if (!flg) continue; lint v = cht.get(m).first / 2 * m; dbgif(M <= 100, make_tuple(m, v)); chmax(ret, v + diffs_sum.at(M - m)); } cout << ret << '\n'; }