#include "holiday.h"
#include <bits/stdc++.h>
using namespace std;
const int N = 100'002;
struct Vertex
{
Vertex *l, *r;
int sum;
long long k_sum;
Vertex(int val) : l(nullptr), r(nullptr), sum(val), k_sum(0) {}
Vertex(int val, long long k_sum) : l(nullptr), r(nullptr), sum(val), k_sum(k_sum) {}
Vertex(Vertex *l, Vertex *r) : l(l), r(r), sum(0), k_sum(0)
{
if (l)
sum += l->sum, k_sum += l->k_sum;
if (r)
sum += r->sum, k_sum += r->k_sum;
}
};
Vertex *roots[N];
struct PersistentSegTree
{ // find_kth returns the kth smallest element in the array in [l, r)
map<int, pair<int, int>> compress;
int n;
PersistentSegTree(int v[], int n) : n(n)
{
int tl = 0, tr = n;
pair<int, int> sort_v[n];
for (int i = 0; i < n; i++)
sort_v[i] = {v[i], i};
sort(sort_v, sort_v + n, greater<pair<int, int>>());
int idx[n];
for (int i = 0; i < n; i++)
compress[i] = sort_v[i], idx[sort_v[i].second] = i;
roots[0] = build(tl, tr);
for (int i = 0; i < n; i++)
roots[i + 1] = update(roots[i], tl, tr, idx[i]);
}
Vertex *build(int tl, int tr)
{
if (tl == tr)
return new Vertex(0, 0);
int tm = (tl + tr) / 2;
return new Vertex(build(tl, tm), build(tm + 1, tr));
}
Vertex *update(Vertex *v, int tl, int tr, int pos)
{
if (tl == tr)
return new Vertex(v->sum + 1, v->k_sum + compress[pos].first);
int tm = (tl + tr) / 2;
if (pos <= tm)
return new Vertex(update(v->l, tl, tm, pos), v->r);
else
return new Vertex(v->l, update(v->r, tm + 1, tr, pos));
}
long long find_kth(Vertex *vl, Vertex *vr, int tl, int tr, int k)
{
if (tl == tr)
return vr->k_sum - vl->k_sum;
int tm = (tl + tr) / 2;
int left_count = vr->l->sum - vl->l->sum;
if (left_count >= k)
return find_kth(vl->l, vr->l, tl, tm, k);
return vr->l->k_sum - vl->l->k_sum + find_kth(vl->r, vr->r, tm + 1, tr, k - left_count);
}
long long find_kth(int l, int r, int k)
{
return find_kth(roots[l], roots[r], 0, n, k);
}
};
long long int findMaxAttraction(int n, int start, int d, int attraction[])
{
long long int ans = 0;
PersistentSegTree pst(attraction, n);
function<long long(int, int)> C1 = [&](int k, int mid) -> long long
{
int days_rem = d - (mid - k + start - k);
if (days_rem <= 0)
return 0;
return pst.find_kth(k, mid + 1, days_rem);
// return mid - k;
};
function<long long(int, int)> C2 = [&](int mid, int k) -> long long
{
int days_rem = d - (k - mid + k - start);
if (days_rem <= 0)
return 0;
return pst.find_kth(mid, k + 1, days_rem);
// return k - mid;
};
function<void(int, int, int, int)> dncg = [&](int l, int r, int optl, int optr)
{
if (l > r)
return;
int mid = (l + r) >> 1;
pair<long long, int> best = {-1, -1};
for (int k = optl; k <= min(mid, optr); k++)
best = max(best, {C1(k, mid), k});
// debug(dp, best, ndp);
// debug(ans, best, mid);
ans = max(best.first, ans);
int opt = best.second;
dncg(l, mid - 1, optl, opt);
dncg(mid + 1, r, opt, optr);
};
function<void(int, int, int, int)> dncs = [&](int l, int r, int optl, int optr)
{
if (l > r)
return;
int mid = (l + r) >> 1;
pair<long long, int> best = {-1, -1};
for (int k = optr; k >= max(mid, optl); k--)
best = max(best, {C2(mid, k), k});
// debug(dp, best, ndp);
// debug(ans, best, mid);
ans = max(best.first, ans);
int opt = best.second;
dncs(l, mid - 1, optl, opt);
dncs(mid + 1, r, opt, optr);
};
if (d == 0)
return 0;
ans = attraction[start];
dncg(start + 1, n - 1, 0, start);
dncs(0, start - 1, start, n - 1);
return ans;
}
