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