#pragma region preprocessor #ifdef LOCAL //* #define _GLIBCXX_DEBUG // gcc /*/ #define _LIBCPP_DEBUG 0 // clang //*/ // #define __buffer_check__ #else #pragma GCC optimize("Ofast") // #define NDEBUG #endif #define __precision__ 15 #define __iostream_untie__ true #include #include #ifdef LOCAL #include "dump.hpp" #define mesg(str) std::cerr << "[ " << __LINE__ << " : " << __FUNCTION__ << " ] " << str << "\n" #else #define dump(...) ((void)0) #define mesg(str) ((void)0) #endif #pragma endregion #pragma region std-overload namespace std { // hash template size_t hash_combine(size_t seed, T const &key) { return seed ^ (hash()(key) + 0x9e3779b9 + (seed << 6) + (seed >> 2)); } template struct hash> { size_t operator()(pair const &pr) const { return hash_combine(hash_combine(0, pr.first), pr.second); } }; template ::value - 1> struct tuple_hash_calc { static size_t apply(size_t seed, tuple_t const &t) { return hash_combine(tuple_hash_calc::apply(seed, t), get(t)); } }; template struct tuple_hash_calc { static size_t apply(size_t seed, tuple_t const &t) { return hash_combine(seed, get<0>(t)); } }; template struct hash> { size_t operator()(tuple const &t) const { return tuple_hash_calc>::apply(0, t); } }; // iostream template istream &operator>>(istream &is, pair &p) { return is >> p.first >> p.second; } template ostream &operator<<(ostream &os, const pair &p) { return os << p.first << ' ' << p.second; } template struct tupleis { static istream &apply(istream &is, tuple_t &t) { tupleis::apply(is, t); return is >> get(t); } }; template struct tupleis { static istream &apply(istream &is, tuple_t &t) { return is; } }; template istream &operator>>(istream &is, tuple &t) { return tupleis, tuple_size>::value - 1>::apply(is, t); } template <> istream &operator>>(istream &is, tuple<> &t) { return is; } template struct tupleos { static ostream &apply(ostream &os, const tuple_t &t) { tupleos::apply(os, t); return os << ' ' << get(t); } }; template struct tupleos { static ostream &apply(ostream &os, const tuple_t &t) { return os << get<0>(t); } }; template ostream &operator<<(ostream &os, const tuple &t) { return tupleos, tuple_size>::value - 1>::apply(os, t); } template <> ostream &operator<<(ostream &os, const tuple<> &t) { return os; } template , string>::value, nullptr_t> = nullptr> istream& operator>>(istream& is, Container &cont) { for(auto&& e : cont) is >> e; return is; } template , string>::value, nullptr_t> = nullptr> ostream& operator<<(ostream& os, const Container &cont) { bool flag = 1; for(auto&& e : cont) flag ? flag = 0 : (os << ' ', 0), os << e; return os; } } // namespace std #pragma endregion #pragma region config namespace config { const auto start_time{std::chrono::system_clock::now()}; int64_t elapsed() { using namespace std::chrono; const auto end_time{std::chrono::system_clock::now()}; return duration_cast(end_time - start_time).count(); } __attribute__((constructor)) void setup() { using namespace std; if(__iostream_untie__) ios::sync_with_stdio(false), cin.tie(nullptr); cout << fixed << setprecision(__precision__); #ifdef DEBUG freopen("debug.out","w",stdout); freopen("debug.err","w",stderr); if(!freopen("debug.in","r",stdin)) { cerr << "error: \"./debug.in\" not found.\n"; exit(EXIT_FAILURE); } #endif #ifdef stderr_path freopen(stderr_path, "a", stderr); #endif #ifdef LOCAL cerr << fixed << setprecision(__precision__) << boolalpha << "\n----- stderr at LOCAL -----\n\n"; atexit([]{ cerr << "\n----- Exec time : " << elapsed() << " ms -----\n\n"; }); #endif #ifdef __buffer_check__ atexit([]{ ofstream cnsl("CON"); char bufc; if(cin >> bufc) cnsl << "\n\033[1;35mwarning\033[0m: buffer not empty.\n\n"; }); #endif } } // namespace config #pragma endregion #pragma region utility // lambda wrapper for recursive method. template class fixed_point { lambda_type func; public: fixed_point(lambda_type &&f) : func(std::move(f)) {} template auto operator()(Args &&... args) const { return func(*this, std::forward(args)...); } }; // read with std::cin. template struct read { typename std::remove_const::type value; template read(types... args) : value(args...) { std::cin >> value; } operator T() const { return value; } }; template <> struct read { template operator T() const { T value; std::cin >> value; return value; } }; // substitute y for x if x > y. template inline bool chmin(T &x, const T &y) { return x > y ? x = y, true : false; } // substitute y for x if x < y. template inline bool chmax(T &x, const T &y) { return x < y ? x = y, true : false; } // binary search on discrete range. template iter_type binary(iter_type __ok, iter_type __ng, pred_type pred) { assert(__ok != __ng); std::ptrdiff_t dist(__ng - __ok); while(std::abs(dist) > 1) { iter_type mid(__ok + dist / 2); if(pred(mid)) __ok = mid, dist -= dist / 2; else __ng = mid, dist /= 2; } return __ok; } // binary search on real numbers. template long double binary(long double __ok, long double __ng, const long double eps, pred_type pred) { assert(__ok != __ng); while(std::abs(__ok - __ng) > eps) { long double mid{(__ok + __ng) / 2}; (pred(mid) ? __ok : __ng) = mid; } return __ok; } // trinary search on discrete range. template iter_type trinary(iter_type __first, iter_type __last, comp_type comp) { assert(__first < __last); std::ptrdiff_t dist(__last - __first); while(dist > 2) { iter_type __left(__first + dist / 3), __right(__first + dist * 2 / 3); if(comp(__left, __right)) __last = __right, dist = dist * 2 / 3; else __first = __left, dist -= dist / 3; } if(dist > 1 && comp(next(__first), __first)) ++__first; return __first; } // trinary search on real numbers. template long double trinary(long double __first, long double __last, const long double eps, comp_type comp) { assert(__first < __last); while(__last - __first > eps) { long double __left{(__first * 2 + __last) / 3}, __right{(__first + __last * 2) / 3}; if(comp(__left, __right)) __last = __right; else __first = __left; } return __first; } // size of array. template size_t size(A (&array)[N]) { return N; } // be careful that val is type-sensitive. template void init(A (&array)[N], const T &val) { std::fill((T*)array, (T*)(array + N), val); } #pragma endregion #pragma region alias using namespace std; using i32 = int_least32_t; using i64 = int_least64_t; using u32 = uint_least32_t; using u64 = uint_least64_t; using p32 = pair; using p64 = pair; template > using heap = priority_queue, Comp>; template using hashset = unordered_set; template using hashmap = unordered_map; using namespace __gnu_cxx; #pragma endregion #pragma region library #include #include template class deque_aggregation { template class stack_aggregation { friend deque_aggregation; struct data { monoid value, acc; }; size_t capacity; data *stack, *end, *itr; bool top_referred; void recalc() { if(top_referred) { assert(itr != stack); top_referred = false; monoid top_val{top().value}; pop(); push(top_val); } } public: stack_aggregation() : capacity(1), stack(new data[1]), end(std::next(stack)), itr(stack), top_referred() {} ~stack_aggregation() { delete[] stack; } bool empty() const { return stack == itr; } size_t size() const { return itr - stack; } // copy of the element at the index. data operator[](size_t index) const { assert(index < size()); recalc(); return stack[index]; } // reference to the last element data &top() { assert(itr != stack); top_referred = true; return *std::prev(itr); } void pop() { assert(itr != stack); --itr; top_referred = false; } void push(const monoid &mono) { recalc(); if(itr == end) { data *tmp = new data[capacity << 1]; std::swap(stack, tmp); end = (itr = std::copy(tmp, tmp + capacity, stack)) + capacity; capacity <<= 1; delete[] tmp; } if(left_operand_added) *itr = data{mono, mono + fold()}; else *itr = data{mono, fold() + mono}; ++itr; } monoid fold() { if(itr == stack) return monoid(); recalc(); return std::prev(itr)->acc; } }; // class stack_aggregation stack_aggregation left; stack_aggregation right; void balance_to_left() { if(!left.empty() || right.empty()) return; left.recalc(); right.recalc(); size_t mid = (right.size() + 1) >> 1; auto *itr = right.stack + mid; do { left.push((--itr)->value); } while(itr != right.stack); monoid acc; for(auto *p = right.stack + mid; p != right.itr; ++p, ++itr) { *itr = {p->value, acc = acc + p->value}; } right.itr = itr; } void balance_to_right() { if(!right.empty() || left.empty()) return; left.recalc(); right.recalc(); size_t mid = (left.size() + 1) >> 1; auto *itr = left.stack + mid; do { right.push((--itr)->value); } while(itr != left.stack); monoid acc; for(auto *p = left.stack + mid; p != left.itr; ++p, ++itr) { *itr = {p->value, acc = p->value + acc}; } left.itr = itr; } public: bool empty() const { return left.empty() && right.empty(); } size_t size() const { return left.size() + right.size(); } // reference to the first element. monoid &front() { assert(!empty()); return balance_to_left(), left.top().value; } // reference to the last element. monoid &back() { assert(!empty()); return balance_to_right(), right.top().value; } // copy of the element at the index. monoid operator[](size_t index) const { assert(index < left.size() + right.size()); return index < left.size() ? left[index].value : right[index - left.size()].value; } void push_front(const monoid &mono) { left.push(mono); } void push_back(const monoid &mono) { right.push(mono); } void pop_front() { assert(!empty()); balance_to_left(); left.pop(); } void pop_back() { assert(!empty()); balance_to_right(); right.pop(); } monoid fold() { return left.fold() + right.fold(); } }; // class deque_aggregation #pragma endregion struct solver; template void main_(); int main() { main_(); } template void main_() { unsigned t = 1; #ifdef LOCAL t = 1; #endif // t = -1; // infinite loop // cin >> t; // case number given while(t--) solver(); } struct solver { solver() { int n,k,m; cin>>n>>k>>m; vector>> q1(k+1),q2(k+1); q1[0].emplace_back(0,0); q2[0].emplace_back(0,0); for(i64 s=0,i=0;i(); for(int j=k-1; j>=0; j--) { if(!q1[j].empty() and q1[j].front().first==i-m) q1[j].pop_front(); if(!q2[j].empty() and q2[j].front().first==i-m) q2[j].pop_front(); i64 opt=INT64_MIN/2; if(!q1[j].empty()) chmax(opt,q1[j].front().second+s); if(!q2[j].empty()) chmax(opt,q2[j].front().second-s); if(j==k-1 and i==n-1) cout << opt << "\n"; { auto &q=q1[j+1]; auto pu=opt-s; while(!q.empty() and q.back().second<=pu) q.pop_back(); q.emplace_back(i+1,pu); } { auto &q=q2[j+1]; auto pu=opt+s; while(!q.empty() and q.back().second<=pu) q.pop_back(); q.emplace_back(i+1,pu); } } } } };