#include "holiday.h"
#include <bits/stdc++.h>
using namespace std;
const int N = 100'005;
const int LN = 20;
struct PersistentSegTree
{ // Returns the sum of K largest elements in [l, r)
map<int,pii> cp;
// add log2(Q) is storage needed after some update query
int L[LN*N],R[LN*N],S[LN*N]; long long KS[LN*N];
int SZ = 1, roots[N], MX;
PersistentSegTree(int v[], int n) : MX(n) {
int tl = 0, tr = n, idx[n];pii sort_v[n];
rep(i, 0, n) sort_v[i] = {v[i], i};
sort(all(sort_v), greater<pii>());
rep(i,0,n)cp[i]=sort_v[i],idx[sort_v[i].second]=i;
roots[0] = build(tl, tr);
rep(i,0,n)roots[i+1]=update(roots[i],tl,tr,idx[i]);
}
int ver(int s, int ks, int l, int r) {
S[SZ]=s;KS[SZ]=ks;L[SZ]=l;R[SZ]=r;return SZ++;
}
int ver(int l, int r) {
S[SZ]=S[l]+S[r];KS[SZ]=KS[l]+KS[r];
L[SZ]=l;R[SZ]=r;return SZ++;
}
int build(int tl, int tr){
if (tl == tr) return ver(0, 0, -1, -1);
int tm = (tl+tr)/2;
return ver(build(tl, tm),build(tm + 1, tr));
}
int update(int idx, int tl, int tr, int pos){
if (tl == tr)
return ver(S[idx]+1,KS[idx]+cp[pos].first,-1,-1);
int tm = (tl + tr) / 2;
if (pos <= tm)
return ver(update(L[idx],tl,tm,pos),R[idx]);
return ver(L[idx],update(R[idx],tm+1,tr,pos));
}
long long kth(int vl, int vr, int tl, int tr, int k) {
if (tl == tr) return KS[vr]-KS[vl];
int tm = (tl+tr)/2,lc=S[L[vr]]-S[L[vl]];
if (lc >= k)return kth(L[vl], L[vr], tl, tm, k);
return KS[L[vr]]-KS[L[vl]]+kth(R[vl],
R[vr],tm+1,tr,k-lc);
}
long long kth(int l, int r, int k) {
return kth(roots[l], roots[r], 0, MX, 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.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.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];
vector<array<int, 4>> dncg, dncs;
dncg.push_back({start + 1, n - 1, 0, start});
dncs.push_back({0, start - 1, start, n - 1});
while (!dncg.empty())
{
auto [l, r, optl, optr] = dncg.back();
dncg.pop_back();
if (l > r)
continue;
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.push_back({mid + 1, r, opt, optr});
dncg.push_back({l, mid - 1, optl, opt});
}
while (!dncs.empty())
{
auto [l, r, optl, optr] = dncs.back();
dncs.pop_back();
if (l > r)
continue;
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.push_back({mid + 1, r, opt, optr});
dncs.push_back({l, mid - 1, optl, opt});
}
// dncg(start + 1, n - 1, 0, start);
// dncs(0, start - 1, start, n - 1);
return ans;
}
