#line 2 "library/other/template.hpp"
#include<bits/stdc++.h>
#ifndef __COUNTER__
#define __COUNTER__ __LINE__
#endif
#define REP_SELECTER(a, b, c, d, e, ...) e
#define REP1_0(b, c) REP1_1(b, c)
#define REP1_1(b, c) for (ll REP_COUNTER_ ## c = 0; REP_COUNTER_ ## c < (ll)(b); ++ REP_COUNTER_ ## c)
#define REP1(b) REP1_0(b, __COUNTER__)
#define REP2(i, b) for (ll i = 0; i < (ll)(b); ++i)
#define REP3(i, a, b) for (ll i = (ll)(a); i < (ll)(b); ++i)
#define REP4(i, a, b, c) for (ll i = (ll)(a); i < (ll)(b); i += (ll)(c))
#define rep(...) REP_SELECTER(__VA_ARGS__, REP4, REP3, REP2, REP1) (__VA_ARGS__)
#define RREP2(i, a) for (ll i = (ll)(a) - 1; i >= 0; --i)
#define RREP3(i, a, b) for (ll i = (ll)(a) - 1; i >= (ll)(b); --i)
#define RREP4(i, a, b, c) for (ll i = (ll)(a) - 1; i >= (ll)(b); i -= (ll)(c))
#define rrep(...) REP_SELECTER(__VA_ARGS__, RREP4, RREP3, RREP2) (__VA_ARGS__)
#define REPS2(i, b) for (ll i = 1; i <= (ll)(b); ++i)
#define REPS3(i, a, b) for (ll i = (ll)(a) + 1; i <= (ll)(b); ++i)
#define REPS4(i, a, b, c) for (ll i = (ll)(a) + 1; i <= (ll)(b); i += (ll)(c))
#define reps(...) REP_SELECTER(__VA_ARGS__, REPS4, REPS3, REPS2) (__VA_ARGS__)
#define RREPS2(i, a) for (ll i = (ll)(a); i > 0; --i)
#define RREPS3(i, a, b) for (ll i = (ll)(a); i > (ll)(b); --i)
#define RREPS4(i, a, b, c) for (ll i = (ll)(a); i > (ll)(b); i -= (ll)(c))
#define rreps(...) REP_SELECTER(__VA_ARGS__, RREPS4, RREPS3, RREPS2) (__VA_ARGS__)
#define each_for(...) for (auto&& __VA_ARGS__)
#define each_const(...) for (const auto& __VA_ARGS__)
#define all(v) std::begin(v), std::end(v)
#define rall(v) std::rbegin(v), std::rend(v)
#if __cplusplus >= 201402L
#define CONSTEXPR constexpr
#else
#define CONSTEXPR
#endif
#ifdef __cpp_if_constexpr
#define IF_CONSTEXPR constexpr
#else
#define IF_CONSTEXPR
#endif
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using PLL = std::pair<ll, ll>;
template<class T> using prique = std::priority_queue<T, std::vector<T>, std::greater<T>>;
template<class T> class infinity {
public:
static constexpr T value = std::numeric_limits<T>::max() / 2;
static constexpr T mvalue = std::numeric_limits<T>::min() / 2;
static constexpr T max = std::numeric_limits<T>::max();
static constexpr T min = std::numeric_limits<T>::min();
};
#if __cplusplus <= 201402L
template<class T> constexpr T infinity<T>::value;
template<class T> constexpr T infinity<T>::mvalue;
template<class T> constexpr T infinity<T>::max;
template<class T> constexpr T infinity<T>::min;
#endif
#if __cplusplus >= 201402L
template<class T> constexpr T INF = infinity<T>::value;
#endif
constexpr ll inf = infinity<ll>::value;
constexpr ld EPS = 1e-8;
constexpr ld PI = 3.1415926535897932384626;
template<class T, class U> std::ostream& operator<<(std::ostream& ost, const std::pair<T, U>& p) {
return ost << p.first << ' ' << p.second;
}
template<class T, class U> std::istream& operator>>(std::istream& ist, std::pair<T, U>& p) {
return ist >> p.first >> p.second;
}
template<class Container,
typename std::enable_if<!std::is_same<Container, std::string>::value>::type* = nullptr>
auto operator<<(std::ostream& ost, const Container& cont)
-> decltype(cont.begin(), cont.end(), ost)
{
for (auto itr = cont.begin(); itr != cont.end(); ++itr) {
if (itr != cont.begin()) ost << ' ';
ost << *itr;
}
return ost;
}
template<class Container,
typename std::enable_if<!std::is_same<Container, std::string>::value>::type* = nullptr>
auto operator>>(std::istream& ist, Container& cont)
-> decltype(cont.begin(), cont.end(), ist)
{
for (auto itr = cont.begin(); itr != cont.end(); ++itr) ist >> *itr;
return ist;
}
template<class T, class U> inline constexpr bool chmin(T &a, const U &b) noexcept {
return a > b ? a = b, true : false;
}
template<class T, class U> inline constexpr bool chmax(T &a, const U &b) noexcept {
return a < b ? a = b, true : false;
}
inline CONSTEXPR ll gcd(ll a, ll b) noexcept {
while (b) {
const ll c = a;
a = b;
b = c % b;
}
return a;
}
inline CONSTEXPR ll lcm(ll a, ll b) noexcept {
return a / gcd(a, b) * b;
}
inline CONSTEXPR bool is_prime(ll N) noexcept {
if (N <= 1) return false;
for (ll i = 2; i * i <= N; ++i) {
if (N % i == 0) return false;
}
return true;
}
inline std::vector<ll> prime_factor(ll N) noexcept {
std::vector<ll> res;
for (ll i = 2; i * i <= N; ++i) {
while (N % i == 0) {
res.push_back(i);
N /= i;
}
}
if (N != 1) res.push_back(N);
return res;
}
inline CONSTEXPR ll my_pow(ll a, ll b) noexcept {
ll res = 1;
while (b) {
if (b & 1) res *= a;
b >>= 1;
a *= a;
}
return res;
}
inline CONSTEXPR ll mod_pow(ll a, ll b, ll mod) noexcept {
a %= mod;
ll res = 1;
while (b) {
if (b & 1) (res *= a) %= mod;
b >>= 1;
(a *= a) %= mod;
}
return res;
}
inline PLL extGCD(ll a, ll b) noexcept {
const ll n = a, m = b;
ll x = 1, y = 0, u = 0, v = 1;
ll t;
while (b) {
t = a / b;
std::swap(a -= t * b, b);
std::swap(x -= t * u, u);
std::swap(y -= t * v, v);
}
if (x < 0) {
x += m;
y -= n;
}
return {x, y};
}
inline ll mod_inv(ll a, ll mod) noexcept {
ll b = mod;
ll x = 1, u = 0;
ll t;
while (b) {
t = a / b;
std::swap(a -= t * b, b);
std::swap(x -= t * u, u);
}
if (x < 0) x += mod;
assert(a == 1);
return x;
}
inline PLL ChineseRemainder(ll b1, ll m1, ll b2, ll m2) noexcept {
const PLL p = extGCD(m1, m2);
const ll g = p.first * m1 + p.second * m2;
const ll l = m1 / g * m2;
if ((b2 - b1) % g != 0) return PLL{-1, -1};
const ll x = (b2 - b1) / g * p.first % (m2 / g);
return {(x * m1 + b1 + l) % l, l};
}
PLL ChineseRemainders(const std::vector<ll>& b, const std::vector<ll>& m) noexcept {
PLL res{0, 1};
rep (i, b.size()) {
res = ChineseRemainder(res.first, res.second, b[i], m[i]);
if (res.first == -1) return res;
}
return res;
}
template<class F> class RecLambda {
private:
F f;
public:
explicit constexpr RecLambda(F&& f_) : f(std::forward<F>(f_)) {}
template<class... Args> constexpr auto operator()(Args&&... args) const
-> decltype(f(*this, std::forward<Args>(args)...)) {
return f(*this, std::forward<Args>(args)...);
}
};
template<class F> inline constexpr RecLambda<F> rec_lambda(F&& f) {
return RecLambda<F>(std::forward<F>(f));
}
template<class Head, class... Tail> struct multi_dim_vector {
using type = std::vector<typename multi_dim_vector<Tail...>::type>;
};
template<class T> struct multi_dim_vector<T> {
using type = T;
};
template<class T, class Arg> constexpr std::vector<T> make_vec(int n, Arg&& arg) {
return std::vector<T>(n, std::forward<Arg>(arg));
}
template<class T, class... Args>
constexpr typename multi_dim_vector<Args..., T>::type make_vec(int n, Args&&... args) {
return typename multi_dim_vector<Args..., T>::type (n, make_vec<T>(std::forward<Args>(args)...));
}
inline CONSTEXPR int popcnt(ull x) {
#if __cplusplus >= 202002L
return std::popcount(x);
#endif
x = (x & 0x5555555555555555) + ((x >> 1 ) & 0x5555555555555555);
x = (x & 0x3333333333333333) + ((x >> 2 ) & 0x3333333333333333);
x = (x & 0x0f0f0f0f0f0f0f0f) + ((x >> 4 ) & 0x0f0f0f0f0f0f0f0f);
x = (x & 0x00ff00ff00ff00ff) + ((x >> 8 ) & 0x00ff00ff00ff00ff);
x = (x & 0x0000ffff0000ffff) + ((x >> 16) & 0x0000ffff0000ffff);
return (x & 0x00000000ffffffff) + ((x >> 32) & 0x00000000ffffffff);
}
template<class T, class Comp = std::less<T>> class presser {
protected:
std::vector<T> dat;
Comp cmp;
bool sorted = false;
public:
presser() : presser(Comp()) {}
presser(const Comp& cmp) : cmp(cmp) {}
presser(const std::vector<T>& vec, const Comp& cmp = Comp()) : dat(vec), cmp(cmp) {}
presser(std::vector<T>&& vec, const Comp& cmp = Comp()) : dat(std::move(vec)), cmp(cmp) {}
presser(std::initializer_list<T> il, const Comp& cmp = Comp()) : dat(il.begin(), il.end()), cmp(cmp) {}
void reserve(int n) {
assert(!sorted);
dat.reserve(n);
}
void push_back(const T& v) {
assert(!sorted);
dat.push_back(v);
}
void push_back(T&& v) {
assert(!sorted);
dat.push_back(std::move(v));
}
void push(const std::vector<T>& vec) {
assert(!sorted);
const int n = dat.size();
dat.resize(n + vec.size());
rep (i, vec.size()) dat[n + i] = vec[i];
}
int build() {
assert(!sorted); sorted = true;
std::sort(all(dat), cmp);
dat.erase(std::unique(all(dat), [&](const T& a, const T& b) -> bool {
return !cmp(a, b) && !cmp(b, a);
}), dat.end());
return dat.size();
}
const T& operator[](int k) const& {
assert(sorted);
assert(0 <= k && k < (int)dat.size());
return dat[k];
}
T operator[](int k) && {
assert(sorted);
assert(0 <= k && k < (int)dat.size());
return std::move(dat[k]);
}
int get_index(const T& val) const {
assert(sorted);
return static_cast<int>(std::lower_bound(all(dat), val, cmp) - dat.begin());
}
std::vector<int> pressed(const std::vector<T>& vec) const {
assert(sorted);
std::vector<int> res(vec.size());
rep (i, vec.size()) res[i] = get_index(vec[i]);
return res;
}
void press(std::vector<T>& vec) const {
static_assert(std::is_integral<T>::value, "template argument must be convertible from int type");
assert(sorted);
each_for (i : vec) i = get_index(i);
}
int size() const {
assert(sorted);
return dat.size();
}
const std::vector<T>& data() const& { return dat; }
std::vector<T> data() && { return std::move(dat); }
};
#line 2 "library/data-struct/cht/ConvexHullTrickAddMonotone.hpp"
#line 4 "library/data-struct/cht/ConvexHullTrickAddMonotone.hpp"
template<class T = ll, bool is_max = false, class LargeT = __int128_t> class ConvexHullTrickAddMonotone {
protected:
struct Line {
T a, b;
bool is_query;
int idx;
mutable ll nxt_a, nxt_b;
mutable bool has_nxt;
T get(T x) const { return a * x + b; }
T get_nxt(T x) const { return nxt_a * x + nxt_b; }
Line() = default;
Line(T a, T b, int id, bool i = false) : a(a), b(b), idx(id), is_query(i), has_nxt(false) {}
friend bool operator<(const Line& lhs, const Line& rhs) {
assert(!lhs.is_query || !rhs.is_query);
if (lhs.is_query) {
if (!rhs.has_nxt) return true;
return rhs.get(lhs.a) < rhs.get_nxt(lhs.a);
}
if (rhs.is_query) {
if (!lhs.has_nxt) return false;
return lhs.get(rhs.a) > lhs.get_nxt(rhs.a);
}
return lhs.a == rhs.a ? lhs.b < rhs.b : lhs.a < rhs.a;
}
};
int line_count = 0;
std::deque<Line> que;
bool is_necessary(const typename std::deque<Line>::iterator& itr) {
if (itr != que.begin() && itr->a == prev(itr)->a) return itr->b < prev(itr)->b;
if (itr != prev(que.end()) && itr->a == next(itr)->a) return itr->b < next(itr)->b;
if (itr == que.begin() || itr == prev(que.end())) return true;
return (LargeT)(itr->b - prev(itr)->b) * (next(itr)->a - itr->a)
< (LargeT)(itr->b - next(itr)->b) * (prev(itr)->a - itr->a);
}
public:
ConvexHullTrickAddMonotone() = default;
int add_line(T a, T b) {
if IF_CONSTEXPR (is_max) a = - a, b = - b;
typename std::deque<Line>::iterator itr;
if (que.empty() || que.back().a <= a) {
que.emplace_back(a, b, line_count);
itr = prev(que.end());
}
else {
assert(a <= que.front().a);
que.emplace_front(a, b, line_count);
itr = que.begin();
}
if (!is_necessary(itr)) {
que.erase(itr);
return line_count++;
}
while (itr != que.begin() && !is_necessary(prev(itr))) {
que.pop_back(); que.pop_back();
que.emplace_back(a, b, line_count);
itr = prev(que.end());
}
while (itr != prev(que.end()) && !is_necessary(next(itr))) {
que.pop_front(); que.pop_front();
que.emplace_front(a, b, line_count);
itr = que.begin();
}
if (itr != que.begin()) {
prev(itr)->nxt_a = itr->a;
prev(itr)->nxt_b = itr->b;
prev(itr)->has_nxt = true;
}
if (itr != prev(que.end())) {
itr->nxt_a = next(itr)->a;
itr->nxt_b = next(itr)->b;
itr->has_nxt = true;
}
else itr->has_nxt = false;
return line_count++;
}
Line get_min_line(T x) const {
auto itr = lower_bound(all(que), Line{x, 0, -1, true});
Line res{*itr};
if IF_CONSTEXPR (is_max) res.a = - res.a, res.b = - res.b;
return res;
}
T get_min(T x) const { return get_min_line(x).get(x); }
Line dec_get_min_line(T x) {
while (que.size() > 1 && que.begin()->get(x) > next(que.begin())->get(x)) que.pop_front();
Line res{que.front()};
if IF_CONSTEXPR (is_max) res.a = - res.a, res.b = - res.b;
return res;
}
T dec_get_min(T x) { return dec_get_min_line(x).get(x); }
Line inc_get_min_line(T x) {
while (que.size() > 1 && prev(que.end())->get(x) > prev(que.end(), 2)->get(x)) que.pop_back();
Line res{que.back()};
if IF_CONSTEXPR (is_max) res.a = - res.a, res.b = - res.b;
return res;
}
T inc_get_min(T x) { return inc_get_min_line(x).get(x); }
bool empty() const { return que.empty(); }
};
/**
* @brief ConvexHullTrickAddMonotone
* @docs docs/ConvexHullTrickAddMonotone.md
*/
#line 3 "main.cpp"
using namespace std;
int main() {
ll n, k; cin >> n >> k;
vector<ll> a(n); cin >> a;
vector<ll> r(n + 1);
rep (i, n) r[i + 1] = r[i] + a[i];
vector<ll> b(n + 1, -inf);
vector<vector<int>> c(k + 2, vector<int>(n + 1, -1));
b[0] = 0;
rep (j, k + 1) {
vector<ll> d(n + 1, -inf);
ConvexHullTrickAddMonotone<ll, true> cht;
cht.add_line(0, b[0]);
reps (i, n) {
auto l = cht.inc_get_min_line(r[i]);
d[i] = l.get(r[i]);
c[j + 1][i] = l.idx;
cht.add_line(r[i], b[i] - r[i] * r[i]);
}
b = d;
}
cout << b[n] << endl;
vector<ll> ans(k);
{
int x = n;
rrep (i, k + 2, 2) {
ans[i - 2] = c[i][x];
x = c[i][x];
}
}
cout << ans << endl;
}
