#include #define REP_(i, a_, b_, a, b, ...) for (int i = (a), END_##i = (b); i < END_##i; ++i) #define REP(i, ...) REP_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__) #define ALL(x) std::begin(x), std::end(x) using Int = long long; using Uint = unsigned long long; using Real = long double; template inline bool chmax(T &a, U b) { return a < b and ((a = std::move(b)), true); } template inline bool chmin(T &a, U b) { return a > b and ((a = std::move(b)), true); } template inline int ssize(const T &a) { return (int) a.size(); } struct Void {}; template inline std::ostream &print_one(const T &x, char endc) { if constexpr (std::is_same::value) { return std::cout; // print nothing } else if constexpr (std::is_same::value) { return std::cout << (x ? "Yes" : "No") << endc; } else { return std::cout << x << endc; } } template inline std::ostream &print(const T &x) { return print_one(x, '\n'); } template std::ostream &print(const T &head, Ts... tail) { return print_one(head, ' '), print(tail...); } inline std::ostream &print() { return std::cout << '\n'; } template std::ostream &print_seq(const Container &seq, const char *sep = " ", const char *ends = "\n", std::ostream &os = std::cout) { const auto itl = std::begin(seq), itr = std::end(seq); for (auto it = itl; it != itr; ++it) { if (it != itl) os << sep; os << *it; } return os << ends; } struct CastInput { template operator T() const { T x; std::cin >> x; return x; } struct Sized { std::size_t n; template operator T() const { T x(n); for (auto &e: x) std::cin >> e; return x; } }; Sized operator()(std::size_t n) const { return {n}; } } in; #ifdef MY_DEBUG #include "debug_dump.hpp" #include "backward.hpp" backward::SignalHandling kSignalHandling; #else #define DUMP(...) #define cerr if(false)cerr #endif using namespace std; template constexpr int num_bits = CHAR_BIT * sizeof(T); inline int msb_log(unsigned x) { assert(x != 0); return num_bits - __builtin_clz(x) - 1; } template struct RMQ { static_assert(std::is_integral_v, "mask_t must be integral"); static_assert(std::is_unsigned_v, "mask_t must be unsigned"); static_assert(std::is_invocable_r_v); static constexpr int block_size_ = num_bits; int n_; // sequence size int block_count_; // total number of blocks BetterOp better_than_; // checks if lhs is strictly better than rhs. std::vector indicator_; std::vector> sparse_table_; RMQ(int n, BetterOp better) : n_(n), block_count_((n_ + block_size_ - 1) / block_size_), better_than_(std::move(better)), indicator_(n_), sparse_table_( block_count_ == 0 ? 0 : msb_log(unsigned(block_count_)) + 1, std::vector(block_count_)) { static constexpr int bufsize = block_size_ + 1; static int buf[bufsize]; // ring buffer [lp,rp) int lp = 1, rp = 1, rpm1 = 0; // rpm1 = rp-1 (mod bufsize) // Build the indicator table. for (int r = 0; r < n_; ++r) { while (lp != rp and r - buf[lp] >= block_size_) { ++lp; if (lp == bufsize) lp = 0; } while (lp != rp and not better_than_(buf[rpm1], r)) { rp = rpm1--; if (rp == 0) rpm1 = bufsize - 1; } indicator_[r] = 1; if (lp != rp) { const int p = buf[rpm1]; indicator_[r] |= (indicator_[p] << (r - p)); } buf[rp] = r; rpm1 = rp++; if (rp == bufsize) rp = 0; } // Build the sparse table. for (int i = 0; i < block_count_; ++i) { sparse_table_[0][i] = best_index_small(std::min(block_size_ * (i + 1), n_) - 1); } for (int i = 0, height = int(sparse_table_.size()) - 1; i < height; ++i) { for (int j = 0; j < block_count_; ++j) { sparse_table_[i + 1][j] = better_index( sparse_table_[i][j], sparse_table_[i][std::min(j + (1 << i), block_count_ - 1)]); } } } // Returns the index of the best value in [l, r) (half-open interval). inline int fold(int l, int r) const { assert(l < r); // Internally use closed interval. return best_index(l, r - 1); } private: inline int better_index(int i, int j) const { return better_than_(i, j) ? i : j; } // Returns the index of the best value in [r - width, r] (closed interval). inline int best_index_small(int r, int width = block_size_) const { assert(r < n_); assert(width > 0); assert(width <= block_size_); mask_t ind = indicator_[r]; if (width < block_size_) { ind &= (mask_t(1) << width) - 1; } return r - msb_log(ind); } // Returns the index of the best value in [l, r] (closed interval). inline int best_index(int l, int r) const { l = std::clamp(l, 0, n_ - 1); r = std::clamp(r, 0, n_ - 1); const int width = r - l + 1; if (width <= block_size_) { return best_index_small(r, width); } const int al = best_index_small(std::min(l + block_size_, n_) - 1); const int ar = best_index_small(r); int ans = better_index(al, ar); const int bl = l / block_size_ + 1; const int br = r / block_size_ - 1; if (bl <= br) { const int k = msb_log(unsigned(br - bl + 1)); const int bl2 = br - (1 << k) + 1; const int am = better_index(sparse_table_[k][bl], sparse_table_[k][bl2]); ans = better_index(ans, am); } return ans; } }; const Int kBig = 1e16; auto solve() { int n = in, K = in, M = in; vector a = in(n); vector acc(n + 1); REP(i, n) acc[i + 1] = acc[i] + a[i]; vector acc_minus(n + 1); REP(i, n + 1) acc_minus[i] = -acc[i]; auto dp = vector(n + 1, vector(K + 1, -kBig)); dp[0][0] = 0; REP(k, 1, K + 1) { vector nv1(n + 1, -kBig), nv2(n + 1, -kBig); for (int l = 0; l <= n; ++l) { Int v = dp[l][k - 1]; if (v == -kBig) continue; nv1[l] = v - acc[l]; nv2[l] = v - acc_minus[l]; } RMQ rmq1(n + 1, [&](int i, int j) { return nv1[i] > nv1[j]; }); RMQ rmq2(n + 1, [&](int i, int j) { return nv2[i] > nv2[j]; }); REP(r, 1, n + 1) { if (Int v = rmq1.fold(max(r - M, 0), r); nv1[v] != -kBig) { chmax(dp[r][k], nv1[v] + acc[r]); } if (Int v = rmq2.fold(max(r - M, 0), r); nv2[v] != -kBig) { chmax(dp[r][k], nv2[v] + acc_minus[r]); } } } return dp[n][K]; } int main() { std::ios::sync_with_stdio(false), cin.tie(nullptr); cout << std::fixed << std::setprecision(18); const int T = 1;//in; REP(t, T) { auto ans = solve(); print(ans); } }