#include<bits/stdc++.h>
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/tree_policy.hpp>
#include<ext/rope>
using namespace std;
using namespace __gnu_pbds;
using namespace __gnu_cxx;
template<class L, class R> istream &operator>>(istream &in, pair<L, R> &p){ return in >> p.first >> p.second; }
template<class Tuple, size_t ...Is> void read_tuple(istream &in, Tuple &t, index_sequence<Is...>){ ((in >> get<Is>(t)), ...); }
template<class ...Args> istream &operator>>(istream &in, tuple<Args...> &t){ read_tuple(in, t, index_sequence_for<Args...>{}); return in; }
template<class ...Args, template<class...> class T> istream &operator>>(enable_if_t<!is_same_v<T<Args...>, string>, istream> &in, T<Args...> &arr){ for(auto &x: arr) in >> x; return in; }
template<class L, class R> ostream &operator<<(ostream &out, const pair<L, R> &p){ return out << "(" << p.first << ", " << p.second << ")"; }
//template<class L, class R> ostream &operator<<(ostream &out, const pair<L, R> &p){ return out << p.first << " " << p.second << "\n"; }
template<class Tuple, size_t ...Is> void print_tuple(ostream &out, const Tuple &t, index_sequence<Is...>){ ((out << (Is ? " " : "") << get<Is>(t)), ...); }
template<class ...Args> ostream &operator<<(ostream &out, const tuple<Args...> &t){ print_tuple(out, t, index_sequence_for<Args...>{}); return out << "\n"; }
template<class ...Args, template<class...> class T> ostream &operator<<(enable_if_t<!is_same_v<T<Args...>, string>, ostream> &out, const T<Args...> &arr){ for(auto &x: arr) out << x << " "; return out << "\n"; }
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
mt19937_64 rngll(chrono::steady_clock::now().time_since_epoch().count());
#define all(a) a.begin(), a.end()
#define sz(a) (int)a.size()
typedef long long ll;
typedef vector<int> vi; typedef vector<ll> vl; typedef vector<double> vd; typedef vector<string> vs;
typedef pair<int, int> pii; typedef pair<ll, ll> pll; typedef pair<int, ll> pil; typedef pair<ll, int> pli;
typedef vector<pii> vpii; typedef vector<pil> vpil; typedef vector<pli> vpli; typedef vector<pll> vpll;
template<class T> T ctmax(T &x, const T &y){ return x = max(x, y); }
template<class T> T ctmin(T &x, const T &y){ return x = min(x, y); }
template<class T> using Tree = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
typedef tuple<int, int, int> tpl; typedef vector<tpl> vtpl;
struct line{
ll d, k, p;
int ind;
ll eval(ll x){ return d * x + k; }
};
template<bool GET_MAX = true>
struct sorted_line_container: deque<line>{
// (for doubles, use inf = 1/.0, div(a,b) = a/b)
const ll inf = LLONG_MAX;
ll div(ll a, ll b){ return a / b - ((a ^ b) < 0 && a % b); }
bool isect_front(iterator x, iterator y){
if(y == this->end()){ x->p = inf; return false; }
else{ x->p = div(y->k - x->k, x->d - y->d); return x->p >= y->p; }
}
bool isect_back(reverse_iterator x, reverse_iterator y){
if(x == this->rend()) return false;
else{ x->p = div(y->k - x->k, x->d - y->d); return x->p >= y->p; }
}
void push(line L){
if(!GET_MAX) L.d = -L.d, L.k = -L.k;
if(empty() || L.d < front().d){
L.p = 0, push_front(L), isect_front(begin(), ++ begin());
while(size() >= 2 && isect_front(begin(), ++ begin())) erase(++ begin());
}
else if(L.d > back().d){
L.p = inf, push_back(L); isect_back(++ rbegin(), rbegin());
while(size() >= 2 && isect_back(++ ++ rbegin(), ++ rbegin())) erase(-- -- end()), isect_back(++ rbegin(), rbegin());
}
else assert(false);
}
ll dec_query(ll x){
while(size() >= 2 && rbegin()->eval(x) <= (++ rbegin())->eval(x)) pop_back(); rbegin()->p = inf;
return rbegin()->eval(x) * (GET_MAX ? 1 : -1);
}
ll inc_query(ll x){
while(size() >= 2 && begin()->eval(x) <= (++ begin())->eval(x)) pop_front();
return begin()->eval(x) * (GET_MAX ? 1 : -1);
}
ll query(ll x){
if(size() == 1) return begin()->eval(x) * (GET_MAX ? 1 : -1);
int low = 0, high = int(size()) - 1;
if(begin()->eval(x) >= (++ begin())->eval(x)) return begin()->eval(x) * (GET_MAX ? 1 : -1);
while(high - low > 1){
int mid = low + high >> 1;
(*this)[mid].eval(x) < (*this)[mid + 1].eval(x) ? low = mid : high = mid;
}
return (*this)[low + 1].eval(x) * (GET_MAX ? 1 : -1);
}
};
template<class Pred>
ll custom_binary_search(ll low, ll high, const ll &step, Pred p, bool is_left = true){
assert(low < high && (high - low) % step == 0);
const ll rem = low % step;
if(is_left){
while(high - low > step){
ll mid = low + (high - low >> 1);
mid = mid / step * step + rem;
p(mid) ? low = mid : high = mid;
}
return low;
}
else{
while(high - low > step){
ll mid = low + (high - low >> 1);
mid = mid / step * step + rem;
p(mid) ? high = mid : low = mid;
}
return high;
}
}
template<class DP, bool GET_MAX = true>
pair<ll, vi> LagrangeDP(int n, DP f, ll k, ll low, ll high){
ll resp, resq;
vi prevp(n + 1), cntp(n + 1), prevq(n + 1), cntq(n + 1);
auto pred = [&](ll lambda){
swap(resp, resq), swap(prevp, prevq), swap(cntp, cntq);
resp = f(lambda, prevp, cntp);
return GET_MAX ? cntp.back() <= k : cntp.back() >= k;
};
ll lambda = custom_binary_search(2 * low - 1, 2 * high + 1, 2, pred);
pred(lambda + 2), pred(lambda);
if(cntp.back() == k){
vi path{n};
for(int u = n; u; ) path.push_back(u = prevp[u]);
return {resp - lambda * k >> 1, path};
}
else{
resp = resp - lambda * cntp.back() >> 1, resq = resq - (lambda + 2) * cntq.back() >> 1;
ll res = resp + (resq - resp) / (cntq.back() - cntp.back()) * (k - cntp.back());
int i = n, j = n, d = k - cntp.back();
while(1){
if(prevp[i] <= prevq[j]){
while(prevp[i] <= prevq[j] && cntq[j] - cntp[i] > d) j = prevq[j];
if(prevp[i] <= prevq[j] && cntq[j] - cntp[i] == d) break;
}
else i = prevp[i], j = prevq[j];
}
vi path{n};
for(int u = n; u != i; ) path.push_back(u = prevp[u]);
path.push_back(prevq[j]);
for(int u = prevq[j]; u; ) path.push_back(u = prevq[u]);
return {res, path};
}
}
int main(){
cin.tie(0)->sync_with_stdio(0);
int n, k;
cin >> n >> k, ++ k;
vpli a(n);
for(auto &p: a){
static int cnt = 1;
cin >> p.first, p.second = cnt ++;
}
int pcnt = 0;
for(int i = 0; i < n; ++ i){
if(a[i].first){
++ pcnt;
}
}
if(pcnt <= k){
ll sum = 0, sqsum = 0;
for(auto &[l, r]: a){
sum += l, sqsum += l * l;
}
sum = sum * sum - sqsum >> 1;
vi flag(n - 1);
int cur = 1;
for(int i = 0; i < n - 1 && cur < k; ++ i){
if(a[i].first){
flag[i] = true;
++ cur;
}
}
for(int i = 0; i < n - 1 && cur < k; ++ i){
if(!flag[i]){
flag[i] = true;
++ cur;
}
}
cout << sum << "\n";
for(int i = 0; i < n - 1; ++ i){
if(flag[i]){
cout << i + 1 << " ";
}
}
return 0;
}
a.resize(stable_partition(all(a), [](pli x){ return x.first; }) - a.begin());
n = sz(a);
vl SUM(n + 1);
for(int i = 0; i < n; ++ i){
SUM[i + 1] = SUM[i] + a[i].first;
}
auto solve = [&](const ll &lambda, vi &prev, vi &cnt){
ll res;
sorted_line_container lc;
lc.push({0, lambda, 0, 0});
for(int i = 1; i <= n; ++ i){
lc.push({2 * SUM[i], (res = lc.inc_query(SUM[i])) - 2 * SUM[i] * SUM[i] + lambda, 0, i});
prev[i] = lc.front().ind;
cnt[i] = cnt[prev[i]] + 1;
}
return res;
};
auto [res, seq] = LagrangeDP(n, solve, k, -1e18, 0);
cout << res << "\n";
for(int i = 1; i < sz(seq) - 1; ++ i){
cout << a[seq[i] - 1].second << " ";
}
return 0;
}
/*
7 3
4 1 3 4 0 2 3
14 7
3 2 1 4 1 3 3 3 2 1 1 1 4 2
p: 14->12->9 ->7->6->4->(2->0)
q: 14->13->12->9->7->6->4->3->(1->0)
dp[i][j]: partition i times, max cost for first j
dp[i][j] = max{k < j}( dp[i-1][k] + cost[k][j] )
cost[k][j] = sum(0, k) * sum(k, j) = K * (J - K) = K * J - K^2
a<=b<=c<=d
cost[a][c] + cost[b][d] = A(C-A) + B(D-B)
cost[a][d] + cost[b][c] = A(D-A) + B(C-B)
dp'[i] = max{j < i}( dp[j] - SUM^2[j] + SUM[j] * SUM[i] + lambda )
*/
////////////////////////////////////////////////////////////////////////////////////////
// //
// Coded by Aeren //
// //
////////////////////////////////////////////////////////////////////////////////////////
Compilation message
sequence.cpp: In member function 'll sorted_line_container<GET_MAX>::dec_query(ll)':
sequence.cpp:61:3: warning: this 'while' clause does not guard... [-Wmisleading-indentation]
while(size() >= 2 && rbegin()->eval(x) <= (++ rbegin())->eval(x)) pop_back(); rbegin()->p = inf;
^~~~~
sequence.cpp:61:81: note: ...this statement, but the latter is misleadingly indented as if it were guarded by the 'while'
while(size() >= 2 && rbegin()->eval(x) <= (++ rbegin())->eval(x)) pop_back(); rbegin()->p = inf;
^~~~~~
sequence.cpp: In function 'int main()':
sequence.cpp:154:18: warning: unused variable 'r' [-Wunused-variable]
for(auto &[l, r]: a){
^
sequence.cpp:157:19: warning: suggest parentheses around '-' inside '>>' [-Wparentheses]
sum = sum * sum - sqsum >> 1;
~~~~~~~~~~^~~~~~~
sequence.cpp: In instantiation of 'std::pair<long long int, std::vector<int> > LagrangeDP(int, DP, ll, ll, ll) [with DP = main()::<lambda(const ll&, vi&, vi&)>; bool GET_MAX = true; ll = long long int]':
sequence.cpp:197:52: required from here
sequence.cpp:116:16: warning: suggest parentheses around '-' inside '>>' [-Wparentheses]
return {resp - lambda * k >> 1, path};
~~~~~^~~~~~~~~~~~
sequence.cpp:119:15: warning: suggest parentheses around '-' inside '>>' [-Wparentheses]
resp = resp - lambda * cntp.back() >> 1, resq = resq - (lambda + 2) * cntq.back() >> 1;
~~~~~^~~~~~~~~~~~~~~~~~~~~~
sequence.cpp:119:56: warning: suggest parentheses around '-' inside '>>' [-Wparentheses]
resp = resp - lambda * cntp.back() >> 1, resq = resq - (lambda + 2) * cntq.back() >> 1;
~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~
sequence.cpp: In instantiation of 'll custom_binary_search(ll, ll, const ll&, Pred, bool) [with Pred = LagrangeDP(int, DP, ll, ll, ll) [with DP = main()::<lambda(const ll&, vi&, vi&)>; bool GET_MAX = true; ll = long long int]::<lambda(ll)>; ll = long long int]':
sequence.cpp:111:34: required from 'std::pair<long long int, std::vector<int> > LagrangeDP(int, DP, ll, ll, ll) [with DP = main()::<lambda(const ll&, vi&, vi&)>; bool GET_MAX = true; ll = long long int]'
sequence.cpp:197:52: required from here
sequence.cpp:86:25: warning: suggest parentheses around '-' inside '>>' [-Wparentheses]
ll mid = low + (high - low >> 1);
~~~~~^~~~~
sequence.cpp:94:25: warning: suggest parentheses around '-' inside '>>' [-Wparentheses]
ll mid = low + (high - low >> 1);
~~~~~^~~~~
sequence.cpp: In lambda function:
sequence.cpp:108:3: warning: 'res' may be used uninitialized in this function [-Wmaybe-uninitialized]
resp = f(lambda, prevp, cntp);
^~~~
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
5 ms |
376 KB |
contestant found the optimal answer: 108 == 108 |
| 2 |
Correct |
5 ms |
376 KB |
contestant found the optimal answer: 999 == 999 |
| 3 |
Correct |
5 ms |
376 KB |
contestant found the optimal answer: 0 == 0 |
| 4 |
Correct |
5 ms |
376 KB |
contestant found the optimal answer: 1542524 == 1542524 |
| 5 |
Correct |
5 ms |
376 KB |
contestant found the optimal answer: 4500000000 == 4500000000 |
| 6 |
Correct |
5 ms |
376 KB |
contestant found the optimal answer: 1 == 1 |
| 7 |
Correct |
5 ms |
376 KB |
contestant found the optimal answer: 1 == 1 |
| 8 |
Correct |
5 ms |
376 KB |
contestant found the optimal answer: 1 == 1 |
| 9 |
Correct |
6 ms |
376 KB |
contestant found the optimal answer: 100400096 == 100400096 |
| 10 |
Correct |
5 ms |
376 KB |
contestant found the optimal answer: 900320000 == 900320000 |
| 11 |
Correct |
5 ms |
376 KB |
contestant found the optimal answer: 3698080248 == 3698080248 |
| 12 |
Correct |
5 ms |
376 KB |
contestant found the optimal answer: 3200320000 == 3200320000 |
| 13 |
Correct |
5 ms |
376 KB |
contestant found the optimal answer: 140072 == 140072 |
| 14 |
Correct |
5 ms |
376 KB |
contestant found the optimal answer: 376041456 == 376041456 |
| 15 |
Correct |
5 ms |
376 KB |
contestant found the optimal answer: 805 == 805 |
| 16 |
Correct |
5 ms |
376 KB |
contestant found the optimal answer: 900189994 == 900189994 |
| 17 |
Correct |
5 ms |
376 KB |
contestant found the optimal answer: 999919994 == 999919994 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
5 ms |
376 KB |
contestant found the optimal answer: 1093956 == 1093956 |
| 2 |
Correct |
5 ms |
376 KB |
contestant found the optimal answer: 302460000 == 302460000 |
| 3 |
Correct |
5 ms |
376 KB |
contestant found the optimal answer: 122453454361 == 122453454361 |
| 4 |
Correct |
5 ms |
376 KB |
contestant found the optimal answer: 93663683509 == 93663683509 |
| 5 |
Correct |
5 ms |
376 KB |
contestant found the optimal answer: 1005304678 == 1005304678 |
| 6 |
Correct |
5 ms |
376 KB |
contestant found the optimal answer: 933702 == 933702 |
| 7 |
Correct |
6 ms |
504 KB |
contestant found the optimal answer: 25082842857 == 25082842857 |
| 8 |
Correct |
5 ms |
376 KB |
contestant found the optimal answer: 687136 == 687136 |
| 9 |
Correct |
5 ms |
376 KB |
contestant found the optimal answer: 27295930079 == 27295930079 |
| 10 |
Correct |
5 ms |
376 KB |
contestant found the optimal answer: 29000419931 == 29000419931 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
6 ms |
380 KB |
contestant found the optimal answer: 610590000 == 610590000 |
| 2 |
Correct |
6 ms |
376 KB |
contestant found the optimal answer: 311760000 == 311760000 |
| 3 |
Correct |
5 ms |
376 KB |
contestant found the optimal answer: 1989216017013 == 1989216017013 |
| 4 |
Correct |
6 ms |
376 KB |
contestant found the optimal answer: 1499437552673 == 1499437552673 |
| 5 |
Correct |
6 ms |
376 KB |
contestant found the optimal answer: 1019625819 == 1019625819 |
| 6 |
Correct |
5 ms |
376 KB |
contestant found the optimal answer: 107630884 == 107630884 |
| 7 |
Correct |
5 ms |
376 KB |
contestant found the optimal answer: 475357671774 == 475357671774 |
| 8 |
Correct |
6 ms |
380 KB |
contestant found the optimal answer: 193556962 == 193556962 |
| 9 |
Correct |
6 ms |
376 KB |
contestant found the optimal answer: 482389919803 == 482389919803 |
| 10 |
Correct |
6 ms |
376 KB |
contestant found the optimal answer: 490686959791 == 490686959791 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
8 ms |
376 KB |
contestant found the optimal answer: 21503404 == 21503404 |
| 2 |
Correct |
8 ms |
504 KB |
contestant found the optimal answer: 140412195 == 140412195 |
| 3 |
Correct |
9 ms |
376 KB |
contestant found the optimal answer: 49729674225461 == 49729674225461 |
| 4 |
Correct |
10 ms |
376 KB |
contestant found the optimal answer: 37485571387523 == 37485571387523 |
| 5 |
Correct |
8 ms |
376 KB |
contestant found the optimal answer: 679388326 == 679388326 |
| 6 |
Correct |
8 ms |
504 KB |
contestant found the optimal answer: 4699030287 == 4699030287 |
| 7 |
Correct |
8 ms |
376 KB |
contestant found the optimal answer: 12418819758185 == 12418819758185 |
| 8 |
Correct |
8 ms |
380 KB |
contestant found the optimal answer: 31093317350 == 31093317350 |
| 9 |
Correct |
10 ms |
376 KB |
contestant found the optimal answer: 12194625429236 == 12194625429236 |
| 10 |
Correct |
9 ms |
376 KB |
contestant found the optimal answer: 12345131038664 == 12345131038664 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
37 ms |
856 KB |
contestant found the optimal answer: 1818678304 == 1818678304 |
| 2 |
Correct |
37 ms |
1012 KB |
contestant found the optimal answer: 1326260195 == 1326260195 |
| 3 |
Correct |
37 ms |
888 KB |
contestant found the optimal answer: 4973126687469639 == 4973126687469639 |
| 4 |
Correct |
44 ms |
888 KB |
contestant found the optimal answer: 3748491676694116 == 3748491676694116 |
| 5 |
Correct |
36 ms |
984 KB |
contestant found the optimal answer: 1085432199 == 1085432199 |
| 6 |
Correct |
40 ms |
856 KB |
contestant found the optimal answer: 514790755404 == 514790755404 |
| 7 |
Correct |
43 ms |
996 KB |
contestant found the optimal answer: 1256105310476641 == 1256105310476641 |
| 8 |
Correct |
44 ms |
856 KB |
contestant found the optimal answer: 3099592898816 == 3099592898816 |
| 9 |
Correct |
36 ms |
856 KB |
contestant found the optimal answer: 1241131419367412 == 1241131419367412 |
| 10 |
Correct |
36 ms |
856 KB |
contestant found the optimal answer: 1243084101967798 == 1243084101967798 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
359 ms |
4952 KB |
contestant found the optimal answer: 19795776960 == 19795776960 |
| 2 |
Correct |
327 ms |
5212 KB |
contestant found the optimal answer: 19874432173 == 19874432173 |
| 3 |
Correct |
306 ms |
5932 KB |
contestant found the optimal answer: 497313449256899208 == 497313449256899208 |
| 4 |
Correct |
379 ms |
5932 KB |
contestant found the optimal answer: 374850090734572421 == 374850090734572421 |
| 5 |
Correct |
320 ms |
5592 KB |
contestant found the optimal answer: 36183271951 == 36183271951 |
| 6 |
Correct |
304 ms |
4952 KB |
contestant found the optimal answer: 51629847150471 == 51629847150471 |
| 7 |
Correct |
362 ms |
5948 KB |
contestant found the optimal answer: 124074747024496432 == 124074747024496432 |
| 8 |
Correct |
374 ms |
5724 KB |
contestant found the optimal answer: 309959349080800 == 309959349080800 |
| 9 |
Correct |
297 ms |
5468 KB |
contestant found the optimal answer: 124113525649823701 == 124113525649823701 |
| 10 |
Correct |
307 ms |
5696 KB |
contestant found the optimal answer: 124309619349406845 == 124309619349406845 |
