#include"holiday.h"
#include <bits/stdc++.h>
#define F first
#define S second
#define V vector
#define PB push_back
#define EB emplace_back
#define MP make_pair
#define SZ(v) int((v).size())
#define ALL(v) (v).begin(), (v).end()
using namespace std;
typedef long long ll;
typedef pair<int, int> pi;
typedef V<int> vi;
const int INF = 1e9 + 7, N = 1e5 + 7;
ll go(int n, int s, int d, int a[]) {
priority_queue<int, vi, greater<int>> pq;
ll ans = 0, sum = 0;
int cost = 0;
for(int i = s; i < n; i++) {
pq.push(a[i]);
sum += a[i];
while(SZ(pq) + cost > d) {
if(pq.empty()) return ans;
sum -= pq.top();
pq.pop();
}
ans = max(ans, sum);
cost++;
}
return ans;
}
struct DS {
vi a;
V<pi> stk;
int c, n;
V<vi> cnt;
V<V<ll>> sum;
void add(int pos, int val) {
for(; pos <= n; pos += pos & -pos)
cnt[pos].PB(val);
}
int qry_cnt(int pos, int val) { // <= val
int res = 0;
for(; pos; pos -= pos & -pos) {
res += upper_bound(ALL(cnt[pos]), val) - cnt[pos].begin();
}
return res;
}
ll qry_sum(int pos, int val) { // <= val
ll res = 0;
for(; pos; pos -= pos & -pos) {
int tt = upper_bound(ALL(cnt[pos]), val) - cnt[pos].begin();
if(tt)
res += sum[pos][tt - 1];
}
return res;
}
ll qry(int pos, int need) {
int lb = -INF, rb = 0;
while(lb <= rb) {
int mb = (lb + rb) / 2;
if(qry_cnt(pos, mb) >= need)
rb = mb - 1;
else
lb = mb + 1;
}
return qry_sum(pos, lb) - 1LL * (qry_cnt(pos, lb) - need) * lb;
}
ll test(int d, int i) {
if(i * c > d) return -1;
d -= i * c;
d = min(d, i + 1);
return -qry(i + 1, d);
}
DS(vi _a, int _c) {
a = _a;
c = _c;
n = SZ(a);
cnt.resize(n + 1);
sum.resize(n + 1);
for(int i = 1; i <= n; i++)
add(i, -a[i - 1]);
for(int i = 1; i <= n; i++) {
sort(ALL(cnt[i]));
sum[i] = V<ll>(ALL(cnt[i]));
for(int j = 1; j < SZ(sum[i]); j++)
sum[i][j] += sum[i][j - 1];
}
for(int i = 0; i < n; i++) {
while(SZ(stk) && test(stk.back().F, stk.back().S) <= test(stk.back().F, i))
stk.pop_back();
if(stk.empty())
stk.EB(i * c, i);
else {
int lb = stk.back().F + 1, rb = INF;
// find first x s.t. test(x, stk.back().S) <= test(x, i)
while(lb <= rb) {
int mb = (lb + rb) / 2;
if(test(mb, stk.back().S) <= test(mb, i))
rb = mb - 1;
else
lb = mb + 1;
}
stk.EB(lb, i);
}
}
}
ll qry(int d) {
int it = upper_bound(ALL(stk), pi(d, INF)) - stk.begin() - 1;
return test(d, stk[it].S);
}
};
ll solve(int n, int s, int d, int a[]) { // go left in the first step
if(s == 0) return 0;
vi pl, pr;
for(int i = s - 1; i >= 0; i--) pl.PB(a[i]);
for(int i = s; i < n; i++) pr.PB(a[i]);
DS dsl = DS(pl, 2);
DS dsr = DS(pr, 1);
ll ans = 0;
for(int i = 0; i + 2 <= d; i++) {
ans = max(ans, dsl.qry(i) + dsr.qry(d - i - 2));
}
return ans;
}
ll findMaxAttraction(int n, int s, int d, int a[]) {
ll ans = go(n, s, d, a);
ans = max(ans, solve(n, s, d, a));
reverse(a, a + n);
s = n - s - 1;
ans = max(ans, go(n, s, d, a));
ans = max(ans, solve(n, s, d, a));
return ans;
}
