/* #region Head */ // #define _GLIBCXX_DEBUG #include using namespace std; using ll = long long; using ull = unsigned long long; using ld = long double; using pll = pair; template using vc = vector; template using vvc = vc>; using vll = vc; using vvll = vvc; using vld = vc; using vvld = vvc; using vs = vc; using vvs = vvc; template using um = unordered_map; template using pq = priority_queue; template using pqa = priority_queue, greater>; template using us = unordered_set; #define REP(i, m, n) for (ll i = (m), i##_len = (ll)(n); i < i##_len; ++(i)) #define REPM(i, m, n) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; ++(i)) #define REPR(i, m, n) for (ll i = (m), i##_min = (ll)(n); i >= i##_min; --(i)) #define REPD(i, m, n, d) for (ll i = (m), i##_len = (ll)(n); i < i##_len; i += (d)) #define REPMD(i, m, n, d) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; i += (d)) #define REPI(itr, ds) for (auto itr = ds.begin(); itr != ds.end(); itr++) #define ALL(x) begin(x), end(x) #define SIZE(x) ((ll)(x).size()) #define PERM(c) \ sort(ALL(c)); \ for (bool c##p = 1; c##p; c##p = next_permutation(ALL(c))) #define UNIQ(v) v.erase(unique(ALL(v)), v.end()); #define endl '\n' #define sqrt sqrtl #define floor floorl #define log2 log2l constexpr ll INF = 1'010'000'000'000'000'017LL; constexpr ll MOD = 1'000'000'007LL; // 1e9 + 7 constexpr ld EPS = 1e-12; constexpr ld PI = 3.14159265358979323846; template istream &operator>>(istream &is, vc &vec) { // vector 入力 for (T &x : vec) is >> x; return is; } template ostream &operator<<(ostream &os, vc &vec) { // vector 出力 (for dump) os << "{"; REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "" : ", "); os << "}"; return os; } template ostream &operator>>(ostream &os, vc &vec) { // vector 出力 (inline) REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "\n" : " "); return os; } template istream &operator>>(istream &is, pair &pair_var) { // pair 入力 is >> pair_var.first >> pair_var.second; return is; } template ostream &operator<<(ostream &os, pair &pair_var) { // pair 出力 os << "(" << pair_var.first << ", " << pair_var.second << ")"; return os; } // map, um, set, us 出力 template ostream &out_iter(ostream &os, T &map_var) { os << "{"; REPI(itr, map_var) { os << *itr; auto itrcp = itr; if (++itrcp != map_var.end()) os << ", "; } return os << "}"; } template ostream &operator<<(ostream &os, map &map_var) { return out_iter(os, map_var); } template ostream &operator<<(ostream &os, um &map_var) { os << "{"; REPI(itr, map_var) { auto [key, value] = *itr; os << "(" << key << ", " << value << ")"; auto itrcp = itr; if (++itrcp != map_var.end()) os << ", "; } os << "}"; return os; } template ostream &operator<<(ostream &os, set &set_var) { return out_iter(os, set_var); } template ostream &operator<<(ostream &os, us &set_var) { return out_iter(os, set_var); } template ostream &operator<<(ostream &os, pq &pq_var) { pq pq_cp(pq_var); os << "{"; if (!pq_cp.empty()) { os << pq_cp.top(), pq_cp.pop(); while (!pq_cp.empty()) os << ", " << pq_cp.top(), pq_cp.pop(); } return os << "}"; } // dump #define DUMPOUT cerr void dump_func() { DUMPOUT << endl; } template void dump_func(Head &&head, Tail &&... tail) { DUMPOUT << head; if (sizeof...(Tail) > 0) DUMPOUT << ", "; dump_func(move(tail)...); } // chmax (更新「される」かもしれない値が前) template > bool chmax(T &xmax, const U &x, Comp comp = {}) { if (comp(xmax, x)) { xmax = x; return true; } return false; } // chmin (更新「される」かもしれない値が前) template > bool chmin(T &xmin, const U &x, Comp comp = {}) { if (comp(x, xmin)) { xmin = x; return true; } return false; } // ローカル用 #define DEBUG_ #ifdef DEBUG_ #define DEB #define dump(...) \ DUMPOUT << " " << string(#__VA_ARGS__) << ": " \ << "[" << to_string(__LINE__) << ":" << __FUNCTION__ << "]" << endl \ << " ", \ dump_func(__VA_ARGS__) #else #define DEB if (false) #define dump(...) #endif struct AtCoderInitialize { static constexpr int IOS_PREC = 15; static constexpr bool AUTOFLUSH = false; AtCoderInitialize() { ios_base::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr); cout << fixed << setprecision(IOS_PREC); if (AUTOFLUSH) cout << unitbuf; } } ATCODER_INITIALIZE; void Yn(bool p) { cout << (p ? "Yes" : "No") << endl; } void YN(bool p) { cout << (p ? "YES" : "NO") << endl; } /* #endregion */ /* #region Num */ // テスト用 template struct Num { T x; Num(T x) : x(x) {} // member function Num &operator+=(const Num &another) { return *this = *this + another; } Num &operator-=(const Num &another) { return *this = *this - another; } Num &operator*=(const Num &another) { return *this = *this * another; } Num &operator/=(const Num &another) { return *this = *this / another; } Num &operator++() { return *this = *this + 1; } Num operator++(int) { Num before = *this; *this = *this + 1; return before; } Num &operator--() { return *this = *this - 1; } Num operator--(int) { Num before = *this; *this = *this - 1; return before; } Num operator+() const { return *this; } Num operator-() const { return Num{-x}; } // friend functions friend Num operator+(const Num &left, const Num &right) { if (abs(left.x) == INF) return Num{left.x}; if (abs(right.x) == INF) return Num{right.x}; return Num{left.x + right.x}; } friend Num operator-(const Num &left, const Num &right) { return left + (-right); } friend Num operator*(const Num &left, const Num &right) { if (abs(left.x) == INF || abs(right.x) == INF) return (left.x == INF ^ right.x == INF) ? Num{-INF} : Num{INF}; return Num{left.x * right.x}; } friend Num operator/(const Num &left, const Num &right) { if (abs(left.x) == INF) return (right.x > 0) ? Num{left.x} : Num{-left.x}; if (abs(right.x) == INF) return Num{0}; return Num{left.x / right.x}; } friend bool operator==(const Num &left, const Num &right) { return left.x == right.x; } friend bool operator!=(const Num &left, const Num &right) { return left.x != right.x; } friend bool operator<(const Num &left, const Num &right) { return left.x < right.x; } friend bool operator>(const Num &left, const Num &right) { return left.x > right.x; } friend bool operator<=(const Num &left, const Num &right) { return left.x <= right.x; } friend bool operator>=(const Num &left, const Num &right) { return left.x >= right.x; } friend ostream &operator<<(ostream &os, const Num &obj) { if (obj.x == INF) os << "INF"; else if (obj.x == -INF) os << "-INF"; else os << obj.x; return os; } friend istream &operator>>(istream &is, Num &obj) { is >> obj.x; return is; } }; /* #endregion */ /* #region SlideMinMax */ // seq: シーケンス // w: ウィンドウ幅 // f: 要素同士の比較(キュー末尾,追加要素)-> 末尾を捨てるかどうか template vc slideMinMax(vc &seq, int w, function f) { ll n = SIZE(seq); // ret[i]: 区間 [i-w+1,i] (閉区間) における seq の最大値・最小値を与えるインデックス. // 末尾が i 番目になる長さ w の部分列の最大値・最小値を与えるインデックス. // (長さ w 未満の左側領域・右側領域もついでに計算) vc ret(n + w - 1); deque q; REP(i, 0, n) { if (!q.empty() && q.front() == i - w) q.pop_front(); // 期限切れ while (!q.empty() && f(seq[q.back()], seq[i])) q.pop_back(); q.push_back(i); ret[i] = q.front(); } REP(i, n, n + w - 1) { if (!q.empty() && q.front() == i - w) q.pop_front(); // 期限切れ ret[i] = q.front(); } return ret; } /* #endregion */ // Problem void solve() { ll n, k, m; cin >> n >> k >> m; vll a(n); cin >> a; vll acc(n + 1); REP(i, 0, n) acc[i + 1] += acc[i] + a[i]; using N = Num; // dp[i+1][j] := i 番目の要素まで見て j 個グループを作ったときの最大スコア vc> dp(n + 1, vc(k + 1, -INF)); dp[0][0] = 0; // REP(i, 0, n) REPM(j, 1, k) REPM(l, 0, i) { // // dump(i, j, l, dp[i + 1][j], dp[l][j - 1] + abs(acc[i + 1] - acc[l])); // // 愚直 // // chmax(dp[i + 1][j], dp[l][j - 1] + abs(acc[i + 1] - acc[l])); // // abs を分けて整理 // // chmax(dp[i + 1][j], dp[l][j - 1] - acc[l] + acc[i + 1]); // // chmax(dp[i + 1][j], dp[l][j - 1] + acc[l] - acc[i + 1]); // } auto f = [](N a, N latest) -> bool { return a < latest; }; REPM(j, 1, k) { // dp[l][j-1]-acc[l], および dp[l][j-1]+acc[l] の幅 m のスライド最大値 vc data1(n, 0), data2(n, 0); REP(l, 0, n) { data1[l] = dp[l][j - 1] - acc[l]; data2[l] = dp[l][j - 1] + acc[l]; } vc indices1 = slideMinMax(data1, m, f); vc indices2 = slideMinMax(data2, m, f); REP(i, 0, n) { chmax(dp[i + 1][j], data1[indices1[i]] + acc[i + 1]); chmax(dp[i + 1][j], data2[indices2[i]] - acc[i + 1]); } } // dump(dp); cout << dp[n][k] << endl; } // entry point int main() { solve(); return 0; }