// ===== template.hpp =====
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cmath>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
#define OVERRIDE(a, b, c, d, ...) d
#define REP2(i, n) for (i32 i = 0; i < (i32) (n); ++i)
#define REP3(i, m, n) for (i32 i = (i32) (m); i < (i32) (n); ++i)
#define REP(...) OVERRIDE(__VA_ARGS__, REP3, REP2)(__VA_ARGS__)
#define PER(i, n) for (i32 i = (i32) (n) - 1; i >= 0; --i)
#define ALL(x) begin(x), end(x)
using namespace std;
using u32 = unsigned int;
using u64 = unsigned long long;
using u128 = __uint128_t;
using i32 = signed int;
using i64 = signed long long;
using i128 = __int128_t;
using f64 = double;
using f80 = long double;
template <typename T>
using Vec = vector<T>;
template <typename T>
bool chmin(T &x, const T &y) {
if (x > y) {
x = y;
return true;
}
return false;
}
template <typename T>
bool chmax(T &x, const T &y) {
if (x < y) {
x = y;
return true;
}
return false;
}
istream &operator>>(istream &is, i128 &x) {
i64 v;
is >> v;
x = v;
return is;
}
ostream &operator<<(ostream &os, i128 x) {
os << (i64) x;
return os;
}
istream &operator>>(istream &is, u128 &x) {
u64 v;
is >> v;
x = v;
return is;
}
ostream &operator<<(ostream &os, u128 x) {
os << (u64) x;
return os;
}
template <typename F, typename Comp = less<>>
Vec<i32> sort_index(i32 n, F f, Comp comp = Comp()) {
Vec<i32> idx(n);
iota(ALL(idx), 0);
sort(ALL(idx), [&](i32 i, i32 j) -> bool {
return comp(f(i), f(j));
});
return idx;
}
[[maybe_unused]] constexpr i32 INF = 1000000100;
[[maybe_unused]] constexpr i64 INF64 = 3000000000000000100;
struct FastIO {
FastIO() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
cout << fixed << setprecision(10);
}
} fast_io;
// ===== template.hpp =====
#ifdef DEBUGF
#include "cpl/template/debug.hpp"
#else
#define DBG(x) (void) 0
#endif
// ===== utils.hpp =====
constexpr bool is_prime(unsigned n) {
if (n == 0 || n == 1) {
return false;
}
for (unsigned i = 2; i * i <= n; ++i) {
if (n % i == 0) {
return false;
}
}
return true;
}
constexpr unsigned mod_pow(unsigned x, unsigned y, unsigned mod) {
unsigned ret = 1, self = x;
while (y != 0) {
if (y & 1) {
ret = static_cast<unsigned>(static_cast<unsigned long long>(ret) * self % mod);
}
self = static_cast<unsigned>(static_cast<unsigned long long>(self) * self % mod);
y /= 2;
}
return ret;
}
template <unsigned mod>
constexpr unsigned primitive_root() {
static_assert(is_prime(mod), "`mod` must be a prime number.");
if (mod == 2) {
return 1;
}
unsigned primes[32] = {};
int it = 0;
{
unsigned m = mod - 1;
for (unsigned i = 2; i * i <= m; ++i) {
if (m % i == 0) {
primes[it++] = i;
while (m % i == 0) {
m /= i;
}
}
}
if (m != 1) {
primes[it++] = m;
}
}
for (unsigned i = 2; i < mod; ++i) {
bool ok = true;
for (int j = 0; j < it; ++j) {
if (mod_pow(i, (mod - 1) / primes[j], mod) == 1) {
ok = false;
break;
}
}
if (ok)
return i;
}
return 0;
}
// y >= 1
template <typename T>
constexpr T safe_mod(T x, T y) {
x %= y;
if (x < 0) {
x += y;
}
return x;
}
// y != 0
template <typename T>
constexpr T floor_div(T x, T y) {
if (y < 0) {
x *= -1;
y *= -1;
}
if (x >= 0) {
return x / y;
} else {
return -((-x + y - 1) / y);
}
}
// y != 0
template <typename T>
constexpr T ceil_div(T x, T y) {
if (y < 0) {
x *= -1;
y *= -1;
}
if (x >= 0) {
return (x + y - 1) / y;
} else {
return -(-x / y);
}
}
// ===== utils.hpp =====
// monotone
class CHT {
deque<tuple<i64, i64, i32>> que;
bool need(const tuple<i64, i64, i32> &a, const tuple<i64, i64, i32> &b, const tuple<i64, i64, i32> &c) const {
i64 ab = floor_div(get<1>(b) - get<1>(a), get<0>(a) - get<0>(b));
i64 bc = floor_div(get<1>(c) - get<1>(b), get<0>(b) - get<0>(c));
return ab < bc;
}
public:
CHT() : que() {}
void add(i64 a, i64 b, i32 idx) {
if (!que.empty() && get<0>(que.back()) == a) {
if (get<1>(que.back()) > b) {
que.pop_back();
} else {
return;
}
}
que.emplace_back(a, b, idx);
while (que.size() >= 3) {
if (!need(que[que.size() - 3], que[que.size() - 2], que[que.size() - 1])) {
swap(que[que.size() - 2], que[que.size() - 1]);
que.pop_back();
} else {
break;
}
}
}
i32 argmin(i64 x) {
assert(!que.empty());
while (que.size() >= 2) {
i64 fi = get<0>(que[0]) * x + get<1>(que[0]);
i64 se = get<0>(que[1]) * x + get<1>(que[1]);
if (fi >= se) {
que.pop_front();
} else {
break;
}
}
return get<2>(que[0]);
}
};
int main() {
i32 n, k;
cin >> n >> k;
++k;
Vec<i64> a(n);
REP(i, n) {
cin >> a[i];
}
Vec<i64> sum(n + 1, 0), sqsum(n + 1, 0);
REP(i, n) {
sum[i + 1] = sum[i] + a[i];
sqsum[i + 1] = sqsum[i] + a[i] * a[i];
}
const auto product_sum = [&](i32 l, i32 r) -> i64 {
i64 s = sum[r] - sum[l], sq = sqsum[r] - sqsum[l];
return (s * s - sq) / 2;
};
Vec<i64> dp(n + 1, INF64);
dp[0] = 0;
Vec<Vec<i64>> hist;
const i32 interval = 10;
REP(i, k) {
if (i % interval == 0) {
hist.push_back(dp);
}
Vec<i64> ndp(n + 1, INF64);
CHT cht;
REP(j, i + 1, n + 1) {
cht.add(-sum[j - 1], dp[j - 1] + (sum[j - 1] * sum[j - 1] + sqsum[j - 1]) / 2, j - 1);
i32 arg = cht.argmin(sum[j]);
ndp[j] = dp[arg] + product_sum(arg, j);
}
dp = move(ndp);
}
hist.push_back(dp);
i64 ans = product_sum(0, n) - dp[n];
Vec<i64> prevs;
prevs.reserve(k);
i32 now = n;
PER(i, hist.size() - 1) {
i32 l = interval * i;
i32 r = min(k, interval * (i + 1));
Vec<i64> dp_ = hist[i];
Vec<Vec<i64>> args(r - l, Vec<i64>(n + 1, -1));
REP(j, r - l) {
Vec<i64> ndp(n + 1, INF64);
CHT cht;
REP(m, l + j + 1, n + 1) {
cht.add(-sum[m - 1], dp_[m - 1] + (sum[m - 1] * sum[m - 1] + sqsum[m - 1]) / 2, m - 1);
i32 arg = cht.argmin(sum[m]);
ndp[m] = dp_[arg] + product_sum(arg, m);
args[j][m] = arg;
}
DBG(ndp);
dp_ = move(ndp);
}
DBG(dp_);
DBG(hist[i + 1]);
PER(j, r - l) {
now = args[j][now];
prevs.push_back(now);
}
}
reverse(ALL(prevs));
cout << ans << '\n';
REP(i, 1, k) {
cout << prevs[i] << " \n"[i + 1 == k];
}
}
